From ff5665227725e872bb293b03fb07b2e0018392e0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Fri, 9 Oct 2020 18:10:40 +0200 Subject: [PATCH 01/28] Added makefile for loading data --- README.md | 11 +++++++++++ qlpdb/Makefile | 25 +++++++++++++++++++++++++ 2 files changed, 36 insertions(+) create mode 100644 qlpdb/Makefile diff --git a/README.md b/README.md index 2f7758b..b850084 100644 --- a/README.md +++ b/README.md @@ -12,6 +12,17 @@ Install via pip pip install [-e] [--user] . ``` +## Access to published data + +### Setup + +The publication data is stored in PostgreSQL format which can be interfaced through `qlpdb`. +This repository provides a dump file which populates an empty PostgreSQL database with the publication data. +To access the data, you have +1. To install and setup `psql` +2. Specify the connection information in `qlpdb/db-config.yaml` +3. Run `make initdb` in `qlpdb` + ## Compile the doc Run once to get dependencies ```bash diff --git a/qlpdb/Makefile b/qlpdb/Makefile new file mode 100644 index 0000000..2b60d6e --- /dev/null +++ b/qlpdb/Makefile @@ -0,0 +1,25 @@ +CREATEDB=createdb +PSQL=psql +CHECKSUM=shasum -a 512 + +DBNAME:= $(shell sed -n 's/^NAME:[[:blank:]]*\(..*\)/\1/p' db-config.yaml) +USER:= $(shell sed -n 's/^USER:[[:blank:]]*\(..*\)/\1/p' db-config.yaml) + +initdb: data/qlp-dump.sql + $(info Creating db $(DBNAME)) + $(CREATEDB) $(DBNAME) + + $(info Creating user $(USER) (if not exists)) + $(PSQL) -d $(DBNAME) -tc "SELECT 1 FROM pg_user WHERE usename = '$(USER)';" | grep -q 1 || \ + $(PSQL) -d $(DBNAME) -c "CREATE USER $(USER);" + + $(info Loading dump file. This might take a while) + $(PSQL) $(DBNAME) < data/qlp-dump.sql + +data/qlp-dump.sql: data.tar.gz + $(info Extracting data) + tar -xvf data.tar.gz + $(info Checksum) + cat data/sha512.txt + $(info local checksum) + $(CHECKSUM) data/qlp-dump.sql From 26954257cac709c9081d20e0d9412422caa34f32 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Fri, 9 Oct 2020 18:12:16 +0200 Subject: [PATCH 02/28] Tracking data.tar.gz --- .gitattributes | 1 + 1 file changed, 1 insertion(+) create mode 100644 .gitattributes diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..7d58636 --- /dev/null +++ b/.gitattributes @@ -0,0 +1 @@ +qlpdb/data.tar.gz filter=lfs diff=lfs merge=lfs -text From 024b30212f864e0888074ff5087de26e8f91804d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Fri, 9 Oct 2020 18:12:45 +0200 Subject: [PATCH 03/28] Tracking data dump --- qlpdb/data.tar.gz | 3 +++ 1 file changed, 3 insertions(+) create mode 100644 qlpdb/data.tar.gz diff --git a/qlpdb/data.tar.gz b/qlpdb/data.tar.gz new file mode 100644 index 0000000..3d0c07f --- /dev/null +++ b/qlpdb/data.tar.gz @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4eecb0e3dce0a11402326fbe1b4c5b755103e55550920dd909dd7ea1e597681d +size 126214836 From f748b38ffdf10247facfb6297d8ed3ab57b050af Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Fri, 9 Oct 2020 18:19:29 +0200 Subject: [PATCH 04/28] Added example db-config --- qlpdb/db-config.example.yaml | 3 +++ 1 file changed, 3 insertions(+) create mode 100644 qlpdb/db-config.example.yaml diff --git a/qlpdb/db-config.example.yaml b/qlpdb/db-config.example.yaml new file mode 100644 index 0000000..03b8b46 --- /dev/null +++ b/qlpdb/db-config.example.yaml @@ -0,0 +1,3 @@ +ENGINE: django.db.backends.postgresql +NAME: qlp-publication +USER: admin From 37708d866cca9c0a559fbf313263c67dce911468 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Fri, 9 Oct 2020 18:21:56 +0200 Subject: [PATCH 05/28] Ignored data dir --- qlpdb/.gitignore | 1 + 1 file changed, 1 insertion(+) diff --git a/qlpdb/.gitignore b/qlpdb/.gitignore index b340d9c..a0c6fff 100644 --- a/qlpdb/.gitignore +++ b/qlpdb/.gitignore @@ -1 +1,2 @@ db-config*.yaml +data/ From 7b0d9428b07b212402d1790efb2c1f7f0c74b521 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Fri, 9 Oct 2020 18:54:48 +0200 Subject: [PATCH 06/28] Updated requirements --- qlpdb/requirements.txt | 1 + 1 file changed, 1 insertion(+) diff --git a/qlpdb/requirements.txt b/qlpdb/requirements.txt index c3aa11b..05586d6 100644 --- a/qlpdb/requirements.txt +++ b/qlpdb/requirements.txt @@ -3,4 +3,5 @@ django-bootstrap4 django-widget-tweaks espressodb plotly +jupyter dwave-ocean-sdk From 24c380d4c66c55198b0ebef42485682ee5957a5d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Mon, 12 Oct 2020 18:48:09 +0200 Subject: [PATCH 07/28] Templated EspressoDB readme for project --- README.md | 100 ++++++++++++++++++++++++++++++++++++++++-------------- 1 file changed, 75 insertions(+), 25 deletions(-) diff --git a/README.md b/README.md index b850084..db32b34 100644 --- a/README.md +++ b/README.md @@ -1,37 +1,87 @@ -# qlp +# Integer Programming from Quantum Annealing and Open Quantum Systems -Module for converting set of inequalities to matrix which can be implemented on a quantum annealer. +This repository contains software and data associated with publication [Integer Programming from Quantum Annealing and Open Quantum Systems [2009.11970]](https://arxiv.org/abs/2009.11970). -## Description +It contains Python code mapping [Integer Linear Programming problems](https://en.wikipedia.org/wiki/Integer_programming), in particular the [Minimum Dominating Set](https://mathworld.wolfram.com/MinimumDominatingSet.html) Problem, to [QUBOs or Ising Hamiltonians utilized as input for Quantum Annealers](https://docs.dwavesys.com/docs/latest/c_gs_3.html#qubo). +It furthermore contains code which simulates the quantum hardware. -The module `qlp` converts a set of `sympy` equations to a `numpy` matrix which corresponds to a constrained minimization problem. -## Install -Install via pip -```bash -pip install [-e] [--user] . -``` +## What does EspressoDB provide? + +EspressoDB provides an easy to use database interface which helps you make educated decisions fast. + +Once you have created your Python project (e.g., `my_project`) with EspressoDB + +* you can use it in all your Python apps to query your data. For example, + ```python + from qlp.mds.graph_tools as generate_nn_graph + from qlp.mds.qubo import get_mds_qubo -## Access to published data + # generate line graph of length 4: o-o-o-o + graph, tag = gt.generate_nn_graph(4) + # Generate mds qubo + qubo = get_mds_qubo( + graph, # The graph as a set of edges + directed=False, # no directed edges + penalty=2 # strength of penalty term + ) + ``` + The solution to the MDS problem is given by the vector bit `psi` which minimizes + ```python + E = psi.T@qubo@psi + ``` +* you can generate web views which summarize your tables and data. + ![Docpage example](https://raw.githubusercontent.com/callat-qcd/espressodb/master/doc-src/_static/webview-example.png) + Because the web pages use a Python API as well, you can completely customize views with code you have already developed. + E.g., you can automate plots and display summaries in your browser. + If you want to, you can also make your web app public (with different layers of accessibility) and share results with others. -### Setup -The publication data is stored in PostgreSQL format which can be interfaced through `qlpdb`. -This repository provides a dump file which populates an empty PostgreSQL database with the publication data. -To access the data, you have -1. To install and setup `psql` -2. Specify the connection information in `qlpdb/db-config.yaml` -3. Run `make initdb` in `qlpdb` +See also the [Documentation](https://espressodb.readthedocs.io/en/latest/) for more detailed usage instructions. -## Compile the doc -Run once to get dependencies +## How to install it? + +### Install the computation module +The repository source code can be installed via pip: ```bash -pip install [-e] [--user] . -pip install -r requirements-dev.txt +pip install [--user] . ``` -Compile the docs + +### Install the data module + +To interface with the publication data, you also have to install the data module `qlpdb` ```bash -cd docs -make html -open build/html/index.html +cd qlpdb +pip install [--user] . ``` + +### Access publication data + +This repository contains all the data presented in [2009.11970]](https://arxiv.org/abs/2009.11970). +To access this data you must host a [PostgreSQL database](https://www.postgresql.org/about/) (usage of `JSON` and `ArrayFields`). +We provide more information in the [`qlpdb/README.md`](qlpdb/README.md). + + +## What's the story behind it? + +EspressoDB was developed when we created [LatteDB](https://www.github.com/callat-qcd/lattedb) -- a database for organizing Lattice Quantum Chromodynamics research. +We intended to create a database for several purposes, e.g. to optimize the scheduling of architecture-dependent many-node jobs and to help in the eventual analysis process. +For this reason, we started to abstract our thinking of how to organize physics objects. + +It was the goal to have easily shareable and completely reproducible snapshots of our workflow while being flexible and not restricting ourselves too much -- in the end science is full of surprises. +The challenges we encountered were: +1. How can we program a table structure which can be easily extended in the future? +2. How do we write a database such that users not familiar with the database concept can start using this tool with minimal effort? + +The core module of LatteDB, EspressoDB, is trying to address those challenges. + +## Who is responsible for it? +* [@cchang5](https://github.com/cchang5) +* [@cchang5](https://github.com/cchang5) +* [@ckoerber](https://www.ckoerber.com) + +Feel free to reach out for questions. + +## License + +BSD 3-Clause License. See also the [LICENSE](LICENSE.md) file. From ce5cc20fb6c2615f365fa723a2068e2d3a5e0c60 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Mon, 12 Oct 2020 19:15:55 +0200 Subject: [PATCH 08/28] Updated readme --- README.md | 116 ++++++++++++++++++++++++++++++++++-------------------- 1 file changed, 73 insertions(+), 43 deletions(-) diff --git a/README.md b/README.md index db32b34..e1f5890 100644 --- a/README.md +++ b/README.md @@ -2,42 +2,22 @@ This repository contains software and data associated with publication [Integer Programming from Quantum Annealing and Open Quantum Systems [2009.11970]](https://arxiv.org/abs/2009.11970). -It contains Python code mapping [Integer Linear Programming problems](https://en.wikipedia.org/wiki/Integer_programming), in particular the [Minimum Dominating Set](https://mathworld.wolfram.com/MinimumDominatingSet.html) Problem, to [QUBOs or Ising Hamiltonians utilized as input for Quantum Annealers](https://docs.dwavesys.com/docs/latest/c_gs_3.html#qubo). +It contains Python code for mapping [Integer Linear Programming problems](https://en.wikipedia.org/wiki/Integer_programming), in particular the [Minimum Dominating Set](https://mathworld.wolfram.com/MinimumDominatingSet.html) Problem, to [QUBOs or Ising Hamiltonians utilized as input for Quantum Annealers](https://docs.dwavesys.com/docs/latest/c_gs_3.html#qubo). It furthermore contains code which simulates the quantum hardware. -## What does EspressoDB provide? +## How to use this repository? -EspressoDB provides an easy to use database interface which helps you make educated decisions fast. +This repository contains two modules -Once you have created your Python project (e.g., `my_project`) with EspressoDB - -* you can use it in all your Python apps to query your data. For example, - ```python - from qlp.mds.graph_tools as generate_nn_graph - from qlp.mds.qubo import get_mds_qubo - - # generate line graph of length 4: o-o-o-o - graph, tag = gt.generate_nn_graph(4) - # Generate mds qubo - qubo = get_mds_qubo( - graph, # The graph as a set of edges - directed=False, # no directed edges - penalty=2 # strength of penalty term - ) - ``` - The solution to the MDS problem is given by the vector bit `psi` which minimizes - ```python - E = psi.T@qubo@psi - ``` -* you can generate web views which summarize your tables and data. - ![Docpage example](https://raw.githubusercontent.com/callat-qcd/espressodb/master/doc-src/_static/webview-example.png) - Because the web pages use a Python API as well, you can completely customize views with code you have already developed. - E.g., you can automate plots and display summaries in your browser. - If you want to, you can also make your web app public (with different layers of accessibility) and share results with others. +1. `qlp` used for computations and +2. `qlpdb` for accessing and storing computation data +### Access publication data -See also the [Documentation](https://espressodb.readthedocs.io/en/latest/) for more detailed usage instructions. +This repository contains all the data presented in [2009.11970]](https://arxiv.org/abs/2009.11970). +To access this data you must host a [PostgreSQL database](https://www.postgresql.org/about/) (usage of `JSON` and `ArrayFields`). +We provide more information in the [`qlpdb/README.md`](qlpdb/README.md). ## How to install it? @@ -55,30 +35,80 @@ cd qlpdb pip install [--user] . ``` -### Access publication data +## Usage + +### `qlp` + +The module `qlp` contains two major components + +* The first submodule, `mds`, was used to map the Minimum Dominating Set Problem to annealing Hardware: + ```python + from qlp.mds.graph_tools as generate_nn_graph + from qlp.mds.qubo import get_mds_qubo + + # generate line graph of length 4: o-o-o-o + graph, tag = gt.generate_nn_graph(4) + # Generate mds qubo + qubo = get_mds_qubo( + graph, # The graph as a set of edges + directed=False, # no directed edges + penalty=2 # strength of penalty term + ) + ``` + The solution to the MDS problem is given by the bit vector `psi` which minimizes + ```python + E = psi.T@qubo@psi + ``` + The QUBO serves as input for the annealing hardware. +* the second submodule, `tdse`, simulates the time dependent Schrödinger equation for given input (Ising) Hamiltonians: + ```python + from qlp.mds.mds_qlpdb import QUBO_to_Ising, graph_summary + from qlp.tdse import TDSE + + Jij, hi, c = QUBO_to_Ising(qubo.todense().tolist()) + ising_params = { + "Jij": [list(row) for row in Jij], + "hi": list(hi), + "c": c, + "energyscale": annealing_time * 1000.0, + "qubo_constant": penalty * nvertices, + "penalty": penalty, + } + graph_params = graph_summary(tag, graph, qubo) + ... + # Initialize the solver + tdse = TDSE( + graph_params, # Graph parameters + ising_params, # Ising Hamiltonian parameters + offset_params, # how is the annealing curve implemented + solver_params, # numerical parameters for solving the time dependent equation + ) + # Compute the starting wave density + rho = tdse.init_densitymatrix( + temp, # full counting decoherence parameters + temp_local, # local decoherence parameters + initial_wavefunction="transverse", + ) + tdse.gamma = gamma # set FC decoherence rate + tdse.gamma_local = gamma_local # set local decoherence rate + # Solve time dependent Schrödinger equation + sol_densitymatrix = tdse.solve_mixed(rho) + ``` + +See also the [`notebooks`](notebooks) folder, especially the [`notebooks/runs`](notebooks/runs) for reproducing computations. + +### `qlpdb` -This repository contains all the data presented in [2009.11970]](https://arxiv.org/abs/2009.11970). -To access this data you must host a [PostgreSQL database](https://www.postgresql.org/about/) (usage of `JSON` and `ArrayFields`). -We provide more information in the [`qlpdb/README.md`](qlpdb/README.md). -## What's the story behind it? -EspressoDB was developed when we created [LatteDB](https://www.github.com/callat-qcd/lattedb) -- a database for organizing Lattice Quantum Chromodynamics research. -We intended to create a database for several purposes, e.g. to optimize the scheduling of architecture-dependent many-node jobs and to help in the eventual analysis process. -For this reason, we started to abstract our thinking of how to organize physics objects. -It was the goal to have easily shareable and completely reproducible snapshots of our workflow while being flexible and not restricting ourselves too much -- in the end science is full of surprises. -The challenges we encountered were: -1. How can we program a table structure which can be easily extended in the future? -2. How do we write a database such that users not familiar with the database concept can start using this tool with minimal effort? -The core module of LatteDB, EspressoDB, is trying to address those challenges. ## Who is responsible for it? * [@cchang5](https://github.com/cchang5) -* [@cchang5](https://github.com/cchang5) * [@ckoerber](https://www.ckoerber.com) +* [@lastyoru](https://github.com/lastyoru) Feel free to reach out for questions. From 32459b3e44382fcca308689cd6269696d203c495 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Mon, 12 Oct 2020 19:26:51 +0200 Subject: [PATCH 09/28] Further doc updates --- README.md | 37 +++++++++++++++++++++++++------------ 1 file changed, 25 insertions(+), 12 deletions(-) diff --git a/README.md b/README.md index e1f5890..69d2aa3 100644 --- a/README.md +++ b/README.md @@ -6,20 +6,13 @@ It contains Python code for mapping [Integer Linear Programming problems](https: It furthermore contains code which simulates the quantum hardware. -## How to use this repository? +## How to install it? This repository contains two modules 1. `qlp` used for computations and 2. `qlpdb` for accessing and storing computation data -### Access publication data - -This repository contains all the data presented in [2009.11970]](https://arxiv.org/abs/2009.11970). -To access this data you must host a [PostgreSQL database](https://www.postgresql.org/about/) (usage of `JSON` and `ArrayFields`). -We provide more information in the [`qlpdb/README.md`](qlpdb/README.md). - -## How to install it? ### Install the computation module The repository source code can be installed via pip: @@ -35,6 +28,12 @@ cd qlpdb pip install [--user] . ``` +### Access publication data + +This repository contains all the data presented in [2009.11970]](https://arxiv.org/abs/2009.11970). +To access this data you must host a [PostgreSQL database](https://www.postgresql.org/about/) (usage of `JSON` and `ArrayFields`). +We provide more information in the [`qlpdb/README.md`](qlpdb/README.md). + ## Usage ### `qlp` @@ -99,11 +98,25 @@ See also the [`notebooks`](notebooks) folder, especially the [`notebooks/runs`]( ### `qlpdb` +`qlpdb` is an [(ORM)](https://en.wikipedia.org/wiki/Object–relational_mapping) framework for database structures to Python objects using [EspressoDB](https://espressodb.readthedocs.io/en/latest/) / [Django](https://www.djangoproject.com). - - - - +Once the database [is properly set up](qlpdb/README.md), you can launch a local web server for inspecting data and browsing the documentation (viewable in any browser) +```bash +cd qlpdb +python manage.py runserver +``` +and query data in Python code +```python +from qlpdb.tdse.models import Tdse +... +solutions = Tdse.objects.filter( + graph__tag=graph_params["tag"], + offset__contains=convert_params(offset_params), + ising__contains=convert_params(ising_params), + solver__contains=solver_params, + wave__contains=wave_params, +) +``` ## Who is responsible for it? * [@cchang5](https://github.com/cchang5) From 17526820eb51cd393652d6de4821cb440917e553 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 12:53:32 +0200 Subject: [PATCH 10/28] Added dockerfiles for postgres --- README.md | 10 +++++----- qlpdb/Dockerfile.postgres | 22 ++++++++++++++++++++++ qlpdb/db-config.example.yaml | 3 ++- qlpdb/docker-compose.yml | 11 +++++++++++ 4 files changed, 40 insertions(+), 6 deletions(-) create mode 100644 qlpdb/Dockerfile.postgres create mode 100644 qlpdb/docker-compose.yml diff --git a/README.md b/README.md index 69d2aa3..8b827ad 100644 --- a/README.md +++ b/README.md @@ -15,7 +15,7 @@ This repository contains two modules ### Install the computation module -The repository source code can be installed via pip: +The `qlp` module can be installed via pip: ```bash pip install [--user] . ``` @@ -30,8 +30,8 @@ pip install [--user] . ### Access publication data -This repository contains all the data presented in [2009.11970]](https://arxiv.org/abs/2009.11970). -To access this data you must host a [PostgreSQL database](https://www.postgresql.org/about/) (usage of `JSON` and `ArrayFields`). +This repository contains all the data presented in [[2009.11970]](https://arxiv.org/abs/2009.11970). +To access this data you must host a [PostgreSQL database](https://www.postgresql.org/about/) (other database formats are not sufficient because we have implemented `JSON` and `ArrayFields`). We provide more information in the [`qlpdb/README.md`](qlpdb/README.md). ## Usage @@ -94,11 +94,11 @@ The module `qlp` contains two major components sol_densitymatrix = tdse.solve_mixed(rho) ``` -See also the [`notebooks`](notebooks) folder, especially the [`notebooks/runs`](notebooks/runs) for reproducing computations. +See also the [`notebooks`](notebooks) folder, especially the [`notebooks/runs`](notebooks/runs), for reproducing computations. ### `qlpdb` -`qlpdb` is an [(ORM)](https://en.wikipedia.org/wiki/Object–relational_mapping) framework for database structures to Python objects using [EspressoDB](https://espressodb.readthedocs.io/en/latest/) / [Django](https://www.djangoproject.com). +`qlpdb` is an [(ORM)](https://en.wikipedia.org/wiki/Object–relational_mapping) framework for mapping database structures to Python objects using [EspressoDB](https://espressodb.readthedocs.io/en/latest/) / [Django](https://www.djangoproject.com). Once the database [is properly set up](qlpdb/README.md), you can launch a local web server for inspecting data and browsing the documentation (viewable in any browser) ```bash diff --git a/qlpdb/Dockerfile.postgres b/qlpdb/Dockerfile.postgres new file mode 100644 index 0000000..5e430a3 --- /dev/null +++ b/qlpdb/Dockerfile.postgres @@ -0,0 +1,22 @@ +# Load in python image +FROM postgres + +# Who to contact +MAINTAINER Christopher Körber + +# Environment variables and dirs used +ENV WORKDIR=/work + +# Create dirs +RUN mkdir -p $WORKDIR +RUN mkdir -p /docker-entrypoint-initdb.d + +# Copy data file +COPY data.tar.gz $WORKDIR + +# Set workdir +WORKDIR $WORKDIR + +# Extract data +RUN tar -xzf data.tar.gz +RUN mv data/qlp-dump.sql /docker-entrypoint-initdb.d diff --git a/qlpdb/db-config.example.yaml b/qlpdb/db-config.example.yaml index 03b8b46..f8f737e 100644 --- a/qlpdb/db-config.example.yaml +++ b/qlpdb/db-config.example.yaml @@ -1,3 +1,4 @@ ENGINE: django.db.backends.postgresql -NAME: qlp-publication +NAME: qlpdb USER: admin +PASSWORD: postges diff --git a/qlpdb/docker-compose.yml b/qlpdb/docker-compose.yml new file mode 100644 index 0000000..6e768e2 --- /dev/null +++ b/qlpdb/docker-compose.yml @@ -0,0 +1,11 @@ +version: '3' + +services: + db: + build: + context: . + dockerfile: Dockerfile.postgres + environment: + - POSTGRES_DB=qlpdb + - POSTGRES_USER=admin + - POSTGRES_PASSWORD=postgres From bf8630123d588691dcf2c88850c6e5fcbcdfd895 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 15:17:02 +0200 Subject: [PATCH 11/28] Added docker compose setup in favor of readme --- .dockerignore | 9 ++++++++ Dockerfile | 45 ++++++++++++++++++++++++++++++++++++ docker-compose.yml | 22 ++++++++++++++++++ qlpdb/.dockerignore | 2 ++ qlpdb/Dockerfile.postgres | 2 ++ qlpdb/Makefile | 25 -------------------- qlpdb/db-config.example.yaml | 3 ++- qlpdb/docker-compose.yml | 11 --------- qlpdb/requirements.txt | 4 ++++ qlpdb/settings.yaml | 2 +- 10 files changed, 87 insertions(+), 38 deletions(-) create mode 100644 .dockerignore create mode 100644 Dockerfile create mode 100644 docker-compose.yml create mode 100644 qlpdb/.dockerignore delete mode 100644 qlpdb/Makefile delete mode 100644 qlpdb/docker-compose.yml diff --git a/.dockerignore b/.dockerignore new file mode 100644 index 0000000..d1f7a40 --- /dev/null +++ b/.dockerignore @@ -0,0 +1,9 @@ +qlpdb/data/ +qlpdb/media/ +.git +.github +docs +notebooks +Notes +paper +*.egg-info diff --git a/Dockerfile b/Dockerfile new file mode 100644 index 0000000..e69ba75 --- /dev/null +++ b/Dockerfile @@ -0,0 +1,45 @@ +# Load in python image +FROM python:3.7-buster + +# Who to contact +MAINTAINER Christopher Körber + +# Environment variables and dirs used +ENV APP_DIR=/opt/app + +# Create dirs +RUN mkdir -p $APP_DIR +RUN mkdir -p $APP_DIR/qlp +RUN mkdir -p $APP_DIR/qlpdb +RUN mkdir -p $APP_DIR/.pip_cache + +# Install requirements +RUN pip install --upgrade pip --cache-dir $APP_DIR/.pip_cache + +## Install qlp +WORKDIR $APP_DIR/qlp +COPY requirements.txt . +COPY README.md . +COPY setup.py . +COPY qlp qlp +RUN pip install -r requirements.txt --cache-dir $APP_DIR/.pip_cache +RUN pip install . + +# Install qlpdb +# DO NOT COPY FILES LIKE db-config.yaml or settings.yaml if they contain secrete passwords +WORKDIR $APP_DIR/qlpdb +COPY qlpdb/requirements.txt . +COPY qlpdb/setup.py . +COPY qlpdb/settings.yaml . +COPY qlpdb/db-config.example.yaml db-config.yaml +COPY qlpdb/README.md . +COPY qlpdb/manage.py . +COPY qlpdb/qlpdb qlpdb +RUN pip install -r requirements.txt --cache-dir $APP_DIR/.pip_cache +RUN pip install . + +# Port to expose +EXPOSE 8000 + +# Run entrypoint script +CMD ["python", "manage.py", "runserver"] diff --git a/docker-compose.yml b/docker-compose.yml new file mode 100644 index 0000000..d192543 --- /dev/null +++ b/docker-compose.yml @@ -0,0 +1,22 @@ +version: '3' + +services: + db: + build: + context: qlpdb + dockerfile: Dockerfile.postgres + environment: + - POSTGRES_DB=qlpdb + - POSTGRES_USER=admin + - POSTGRES_PASSWORD=postgres + ports: + - "5432:5432" + expose: + - "5432" + qlpdb: + build: . + ports: + - "8000:8000" + depends_on: + - db + command: python manage.py runserver 0.0.0.0:8000 diff --git a/qlpdb/.dockerignore b/qlpdb/.dockerignore new file mode 100644 index 0000000..acb3016 --- /dev/null +++ b/qlpdb/.dockerignore @@ -0,0 +1,2 @@ +data/ +media/ diff --git a/qlpdb/Dockerfile.postgres b/qlpdb/Dockerfile.postgres index 5e430a3..77ef18d 100644 --- a/qlpdb/Dockerfile.postgres +++ b/qlpdb/Dockerfile.postgres @@ -19,4 +19,6 @@ WORKDIR $WORKDIR # Extract data RUN tar -xzf data.tar.gz + +# Add it to postgres image entrypoints (automatic loading of data on init) RUN mv data/qlp-dump.sql /docker-entrypoint-initdb.d diff --git a/qlpdb/Makefile b/qlpdb/Makefile deleted file mode 100644 index 2b60d6e..0000000 --- a/qlpdb/Makefile +++ /dev/null @@ -1,25 +0,0 @@ -CREATEDB=createdb -PSQL=psql -CHECKSUM=shasum -a 512 - -DBNAME:= $(shell sed -n 's/^NAME:[[:blank:]]*\(..*\)/\1/p' db-config.yaml) -USER:= $(shell sed -n 's/^USER:[[:blank:]]*\(..*\)/\1/p' db-config.yaml) - -initdb: data/qlp-dump.sql - $(info Creating db $(DBNAME)) - $(CREATEDB) $(DBNAME) - - $(info Creating user $(USER) (if not exists)) - $(PSQL) -d $(DBNAME) -tc "SELECT 1 FROM pg_user WHERE usename = '$(USER)';" | grep -q 1 || \ - $(PSQL) -d $(DBNAME) -c "CREATE USER $(USER);" - - $(info Loading dump file. This might take a while) - $(PSQL) $(DBNAME) < data/qlp-dump.sql - -data/qlp-dump.sql: data.tar.gz - $(info Extracting data) - tar -xvf data.tar.gz - $(info Checksum) - cat data/sha512.txt - $(info local checksum) - $(CHECKSUM) data/qlp-dump.sql diff --git a/qlpdb/db-config.example.yaml b/qlpdb/db-config.example.yaml index f8f737e..e4c2add 100644 --- a/qlpdb/db-config.example.yaml +++ b/qlpdb/db-config.example.yaml @@ -1,4 +1,5 @@ ENGINE: django.db.backends.postgresql NAME: qlpdb USER: admin -PASSWORD: postges +PASSWORD: postgres +HOST: db diff --git a/qlpdb/docker-compose.yml b/qlpdb/docker-compose.yml deleted file mode 100644 index 6e768e2..0000000 --- a/qlpdb/docker-compose.yml +++ /dev/null @@ -1,11 +0,0 @@ -version: '3' - -services: - db: - build: - context: . - dockerfile: Dockerfile.postgres - environment: - - POSTGRES_DB=qlpdb - - POSTGRES_USER=admin - - POSTGRES_PASSWORD=postgres diff --git a/qlpdb/requirements.txt b/qlpdb/requirements.txt index 05586d6..74b154a 100644 --- a/qlpdb/requirements.txt +++ b/qlpdb/requirements.txt @@ -1,7 +1,11 @@ Django django-bootstrap4 django-widget-tweaks +django-picklefield espressodb plotly jupyter dwave-ocean-sdk +psycopg2 +matplotlib +qlp diff --git a/qlpdb/settings.yaml b/qlpdb/settings.yaml index b66b843..35562a3 100644 --- a/qlpdb/settings.yaml +++ b/qlpdb/settings.yaml @@ -4,5 +4,5 @@ PROJECT_APPS: - qlpdb.experiment - qlpdb.data - qlpdb.tdse -ALLOWED_HOSTS: [] +ALLOWED_HOSTS: ["*"] DEBUG: True From 630faeca509cea5493b3b81bc13e7a34af5af68c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 15:36:41 +0200 Subject: [PATCH 12/28] Updated user fields related to espressodb --- qlpdb/.gitignore | 2 +- .../migrations/0004_auto_20201013_1333.py | 21 +++++++++++++++++++ .../migrations/0010_auto_20201013_1333.py | 21 +++++++++++++++++++ .../migrations/0003_auto_20201013_1333.py | 21 +++++++++++++++++++ .../migrations/0010_auto_20201013_1333.py | 21 +++++++++++++++++++ 5 files changed, 85 insertions(+), 1 deletion(-) create mode 100644 qlpdb/qlpdb/data/migrations/0004_auto_20201013_1333.py create mode 100644 qlpdb/qlpdb/experiment/migrations/0010_auto_20201013_1333.py create mode 100644 qlpdb/qlpdb/graph/migrations/0003_auto_20201013_1333.py create mode 100644 qlpdb/qlpdb/tdse/migrations/0010_auto_20201013_1333.py diff --git a/qlpdb/.gitignore b/qlpdb/.gitignore index a0c6fff..bb0cb12 100644 --- a/qlpdb/.gitignore +++ b/qlpdb/.gitignore @@ -1,2 +1,2 @@ db-config*.yaml -data/ +/data/ diff --git a/qlpdb/qlpdb/data/migrations/0004_auto_20201013_1333.py b/qlpdb/qlpdb/data/migrations/0004_auto_20201013_1333.py new file mode 100644 index 0000000..641e8e8 --- /dev/null +++ b/qlpdb/qlpdb/data/migrations/0004_auto_20201013_1333.py @@ -0,0 +1,21 @@ +# Generated by Django 3.1.2 on 2020-10-13 13:33 + +from django.conf import settings +from django.db import migrations, models +import django.db.models.deletion + + +class Migration(migrations.Migration): + + dependencies = [ + migrations.swappable_dependency(settings.AUTH_USER_MODEL), + ('data', '0003_data_chain_break_fraction'), + ] + + operations = [ + migrations.AlterField( + model_name='data', + name='user', + field=models.ForeignKey(blank=True, help_text='User who updated this object. Set on save by connection to database. Anonymous if not found.', null=True, on_delete=django.db.models.deletion.CASCADE, to=settings.AUTH_USER_MODEL), + ), + ] diff --git a/qlpdb/qlpdb/experiment/migrations/0010_auto_20201013_1333.py b/qlpdb/qlpdb/experiment/migrations/0010_auto_20201013_1333.py new file mode 100644 index 0000000..ae391ef --- /dev/null +++ b/qlpdb/qlpdb/experiment/migrations/0010_auto_20201013_1333.py @@ -0,0 +1,21 @@ +# Generated by Django 3.1.2 on 2020-10-13 13:33 + +from django.conf import settings +from django.db import migrations, models +import django.db.models.deletion + + +class Migration(migrations.Migration): + + dependencies = [ + migrations.swappable_dependency(settings.AUTH_USER_MODEL), + ('experiment', '0009_auto_20200416_0521'), + ] + + operations = [ + migrations.AlterField( + model_name='experiment', + name='user', + field=models.ForeignKey(blank=True, help_text='User who updated this object. Set on save by connection to database. Anonymous if not found.', null=True, on_delete=django.db.models.deletion.CASCADE, to=settings.AUTH_USER_MODEL), + ), + ] diff --git a/qlpdb/qlpdb/graph/migrations/0003_auto_20201013_1333.py b/qlpdb/qlpdb/graph/migrations/0003_auto_20201013_1333.py new file mode 100644 index 0000000..bca30e9 --- /dev/null +++ b/qlpdb/qlpdb/graph/migrations/0003_auto_20201013_1333.py @@ -0,0 +1,21 @@ +# Generated by Django 3.1.2 on 2020-10-13 13:33 + +from django.conf import settings +from django.db import migrations, models +import django.db.models.deletion + + +class Migration(migrations.Migration): + + dependencies = [ + migrations.swappable_dependency(settings.AUTH_USER_MODEL), + ('graph', '0002_auto_20200311_2252'), + ] + + operations = [ + migrations.AlterField( + model_name='graph', + name='user', + field=models.ForeignKey(blank=True, help_text='User who updated this object. Set on save by connection to database. Anonymous if not found.', null=True, on_delete=django.db.models.deletion.CASCADE, to=settings.AUTH_USER_MODEL), + ), + ] diff --git a/qlpdb/qlpdb/tdse/migrations/0010_auto_20201013_1333.py b/qlpdb/qlpdb/tdse/migrations/0010_auto_20201013_1333.py new file mode 100644 index 0000000..53aedbc --- /dev/null +++ b/qlpdb/qlpdb/tdse/migrations/0010_auto_20201013_1333.py @@ -0,0 +1,21 @@ +# Generated by Django 3.1.2 on 2020-10-13 13:33 + +from django.conf import settings +from django.db import migrations, models +import django.db.models.deletion + + +class Migration(migrations.Migration): + + dependencies = [ + migrations.swappable_dependency(settings.AUTH_USER_MODEL), + ('tdse', '0009_auto_20200502_0754'), + ] + + operations = [ + migrations.AlterField( + model_name='tdse', + name='user', + field=models.ForeignKey(blank=True, help_text='User who updated this object. Set on save by connection to database. Anonymous if not found.', null=True, on_delete=django.db.models.deletion.CASCADE, to=settings.AUTH_USER_MODEL), + ), + ] From d48feaa9640d90cd2a99be1af3ca41975efceb93 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 15:37:58 +0200 Subject: [PATCH 13/28] Updated JSON fields related to Django --- .../migrations/0011_auto_20201013_1336.py | 18 ++++++++++ qlpdb/qlpdb/experiment/models.py | 2 +- .../migrations/0011_auto_20201013_1336.py | 33 +++++++++++++++++++ qlpdb/qlpdb/tdse/models.py | 2 +- qlpdb/requirements.txt | 4 +-- 5 files changed, 55 insertions(+), 4 deletions(-) create mode 100644 qlpdb/qlpdb/experiment/migrations/0011_auto_20201013_1336.py create mode 100644 qlpdb/qlpdb/tdse/migrations/0011_auto_20201013_1336.py diff --git a/qlpdb/qlpdb/experiment/migrations/0011_auto_20201013_1336.py b/qlpdb/qlpdb/experiment/migrations/0011_auto_20201013_1336.py new file mode 100644 index 0000000..792857a --- /dev/null +++ b/qlpdb/qlpdb/experiment/migrations/0011_auto_20201013_1336.py @@ -0,0 +1,18 @@ +# Generated by Django 3.1.2 on 2020-10-13 13:36 + +from django.db import migrations, models + + +class Migration(migrations.Migration): + + dependencies = [ + ('experiment', '0010_auto_20201013_1333'), + ] + + operations = [ + migrations.AlterField( + model_name='experiment', + name='settings', + field=models.JSONField(help_text='Store DWave machine parameters'), + ), + ] diff --git a/qlpdb/qlpdb/experiment/models.py b/qlpdb/qlpdb/experiment/models.py index eedddda..13ad038 100644 --- a/qlpdb/qlpdb/experiment/models.py +++ b/qlpdb/qlpdb/experiment/models.py @@ -4,7 +4,7 @@ from django.db import models from espressodb.base.models import Base -from django.contrib.postgres.fields import JSONField +from django.db.models import JSONField from django.db.models import Count, Avg diff --git a/qlpdb/qlpdb/tdse/migrations/0011_auto_20201013_1336.py b/qlpdb/qlpdb/tdse/migrations/0011_auto_20201013_1336.py new file mode 100644 index 0000000..4224f08 --- /dev/null +++ b/qlpdb/qlpdb/tdse/migrations/0011_auto_20201013_1336.py @@ -0,0 +1,33 @@ +# Generated by Django 3.1.2 on 2020-10-13 13:36 + +from django.db import migrations, models + + +class Migration(migrations.Migration): + + dependencies = [ + ('tdse', '0010_auto_20201013_1333'), + ] + + operations = [ + migrations.AlterField( + model_name='tdse', + name='ising', + field=models.JSONField(help_text='Ising parameters: Jij, hi, c, energyscale'), + ), + migrations.AlterField( + model_name='tdse', + name='offset', + field=models.JSONField(help_text='Offset parameters: normalized time, offset, hi_for_offset, offset_min, offset_range, fill_value, anneal_curve'), + ), + migrations.AlterField( + model_name='tdse', + name='solver', + field=models.JSONField(help_text='Solver parameters: method, rtol, atol'), + ), + migrations.AlterField( + model_name='tdse', + name='wave', + field=models.JSONField(help_text='Wavefunction: type (mixed or pure), temp, initial wavefunction (True or transverse)'), + ), + ] diff --git a/qlpdb/qlpdb/tdse/models.py b/qlpdb/qlpdb/tdse/models.py index bbd4fc7..fe844c4 100644 --- a/qlpdb/qlpdb/tdse/models.py +++ b/qlpdb/qlpdb/tdse/models.py @@ -4,7 +4,7 @@ import numpy as np from django.db import models from espressodb.base.models import Base -from django.contrib.postgres.fields import JSONField +from django.db.models import JSONField from django.contrib.postgres.fields import ArrayField diff --git a/qlpdb/requirements.txt b/qlpdb/requirements.txt index 74b154a..0c71626 100644 --- a/qlpdb/requirements.txt +++ b/qlpdb/requirements.txt @@ -1,8 +1,8 @@ -Django +Django>=3.1 django-bootstrap4 django-widget-tweaks django-picklefield -espressodb +espressodb>=1.2 plotly jupyter dwave-ocean-sdk From 9d068b97bc992b4b2989841a2827ab5acc464325 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 15:38:11 +0200 Subject: [PATCH 14/28] Compose now migrates as well --- docker-compose.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docker-compose.yml b/docker-compose.yml index d192543..9f8cc4b 100644 --- a/docker-compose.yml +++ b/docker-compose.yml @@ -19,4 +19,4 @@ services: - "8000:8000" depends_on: - db - command: python manage.py runserver 0.0.0.0:8000 + command: "python manage.py migrate && python manage.py runserver 0.0.0.0:8000" From f2ffa030634a71c443d30f5afc60cca1b3851eea Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 16:17:40 +0200 Subject: [PATCH 15/28] Updated readme --- docker-compose.yml | 2 +- qlpdb/README.md | 59 ++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 60 insertions(+), 1 deletion(-) diff --git a/docker-compose.yml b/docker-compose.yml index 9f8cc4b..7690bc2 100644 --- a/docker-compose.yml +++ b/docker-compose.yml @@ -19,4 +19,4 @@ services: - "8000:8000" depends_on: - db - command: "python manage.py migrate && python manage.py runserver 0.0.0.0:8000" + command: "python manage.py runserver 0.0.0.0:8000" diff --git a/qlpdb/README.md b/qlpdb/README.md index e69de29..4654286 100644 --- a/qlpdb/README.md +++ b/qlpdb/README.md @@ -0,0 +1,59 @@ +# qlpdb + +Data module for publication [2009.11970]](https://arxiv.org/abs/2009.11970). +It allows interfacing, searching and saving database structures through Python objects. + + +## Requirements + +The implemented data structures require a [PostgreSQL database](https://www.postgresql.org/about/) (`JSON` and `ArrayFields`). +Thus, you first have to setup a [PostgreSQL database server](https://www.postgresql.org/docs/9.1/server-start.html). + +If you prefer a shortcut, we also specify a high-level [Docker setup](https://docs.docker.com/get-docker/). + +## Docker +Once you have [started Docker](https://docs.docker.com/get-started/), you can install the repository software and initialize data structures by running +```bash +docker-compose build +``` +in the repository root directory. +Note that this might take a while. + +In case data structures have changed, you have to run once +```bash +docker-compose run qlpdb python manage.py migrate +``` + +Finally, to launch the database interface, you can run +```bash +docker-compose up +``` +This data server can be access through any web browser at the address +``` +http://localhost:8000 +``` + +## Details +The data is stored in a `sql` dump file which is contained in the `data.tar.gz`. +We also provide a `SHA-512` checksum for verifying the data integrity. + +You can create a custom PostgreSQL database and user for loading in the dump file +```bash +psql [-U {USER}] {DBNAME} < data/qlp-dump.sql +``` + +Next, after `pip` installing `qlpdb`, you have to specify the connection information. +This is done by creating and adjusting the `db-config.yaml` file in the `qlpdb` directory. +We provide the example file `db-config.example.yaml` in the same directory. +See also the [EspressoDB docs](https://espressodb.readthedocs.io/en/latest/Usage.html?highlight=db-config#configure-your-project). + +**NOTE: Do not commit or share this file in case the database credentials are sensitive.** + +After credentials are matched to the database, you may have to update data structures by running +```bash +python manage.py migrate +``` +and can launch the data browser by running +```bash +python manage.py runserver +``` From fb95eb90c2cadc77608343ec3d12fd143e79de5e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 16:19:40 +0200 Subject: [PATCH 16/28] Removed slack latex compile webhook --- .github/workflows/compile-tex.yaml | 7 ------- 1 file changed, 7 deletions(-) diff --git a/.github/workflows/compile-tex.yaml b/.github/workflows/compile-tex.yaml index 58ff8e4..28a1090 100644 --- a/.github/workflows/compile-tex.yaml +++ b/.github/workflows/compile-tex.yaml @@ -16,10 +16,3 @@ jobs: with: name: main.pdf path: paper/main.pdf - - name: Send slack notification - uses: rtCamp/action-slack-notify@v2.0.2 - env: - SLACK_WEBHOOK: https://hooks.slack.com/services/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 - SLACK_USERNAME: "CompileBot" - SLACK_TITLE: "PDF compiled!" - SLACK_MESSAGE: "I was able to compile the most recent pdf. You can check it out here: https://github.com/cchang5/quantum_linear_programming/actions." From 0ed93e453501dcc6f8519d7f2fef05086ead97f6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 16:21:58 +0200 Subject: [PATCH 17/28] Added build container action --- .github/workflows/docker-build.yaml | 12 ++++++++++++ 1 file changed, 12 insertions(+) create mode 100644 .github/workflows/docker-build.yaml diff --git a/.github/workflows/docker-build.yaml b/.github/workflows/docker-build.yaml new file mode 100644 index 0000000..9bee93c --- /dev/null +++ b/.github/workflows/docker-build.yaml @@ -0,0 +1,12 @@ +name: Build qlp & qlpdb and load data +on: [push] +jobs: + build_latex: + runs-on: ubuntu-latest + steps: + - name: Set up Git repository + uses: actions/checkout@v1 + - name: Build the stack + run: | + docker-compose build + docker-compose run qlpdb python manage.py migrate From d6a067d997e4eb6d715ebdcf16c6353917a29194 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 16:23:00 +0200 Subject: [PATCH 18/28] Updated name --- .github/workflows/docker-build.yaml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/docker-build.yaml b/.github/workflows/docker-build.yaml index 9bee93c..d711d86 100644 --- a/.github/workflows/docker-build.yaml +++ b/.github/workflows/docker-build.yaml @@ -1,7 +1,7 @@ name: Build qlp & qlpdb and load data on: [push] jobs: - build_latex: + docker_compose: runs-on: ubuntu-latest steps: - name: Set up Git repository From 3efd40df1d7304004a7bba70ea4cfaf78117bbf7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 19:33:41 +0200 Subject: [PATCH 19/28] Updating data unzip (exclude gzip) --- qlpdb/Dockerfile.postgres | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/qlpdb/Dockerfile.postgres b/qlpdb/Dockerfile.postgres index 77ef18d..bbffdb3 100644 --- a/qlpdb/Dockerfile.postgres +++ b/qlpdb/Dockerfile.postgres @@ -18,7 +18,7 @@ COPY data.tar.gz $WORKDIR WORKDIR $WORKDIR # Extract data -RUN tar -xzf data.tar.gz +RUN tar -xvf data.tar.gz # Add it to postgres image entrypoints (automatic loading of data on init) RUN mv data/qlp-dump.sql /docker-entrypoint-initdb.d From 2e7d886d7ba95dafa80318d1781b1906aff1e88a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 19:45:09 +0200 Subject: [PATCH 20/28] Adding lfs pull before unzipping --- .github/workflows/docker-build.yaml | 2 ++ qlpdb/Dockerfile.postgres | 2 +- 2 files changed, 3 insertions(+), 1 deletion(-) diff --git a/.github/workflows/docker-build.yaml b/.github/workflows/docker-build.yaml index d711d86..668937a 100644 --- a/.github/workflows/docker-build.yaml +++ b/.github/workflows/docker-build.yaml @@ -6,6 +6,8 @@ jobs: steps: - name: Set up Git repository uses: actions/checkout@v1 + - name: Git LFS Pull + run: git lfs pull - name: Build the stack run: | docker-compose build diff --git a/qlpdb/Dockerfile.postgres b/qlpdb/Dockerfile.postgres index bbffdb3..9e060ac 100644 --- a/qlpdb/Dockerfile.postgres +++ b/qlpdb/Dockerfile.postgres @@ -18,7 +18,7 @@ COPY data.tar.gz $WORKDIR WORKDIR $WORKDIR # Extract data -RUN tar -xvf data.tar.gz +RUN tar -xvzf data.tar.gz # Add it to postgres image entrypoints (automatic loading of data on init) RUN mv data/qlp-dump.sql /docker-entrypoint-initdb.d From ed3bd41e462cb18821743b5d67ca7098bf2f6b1d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 19:51:49 +0200 Subject: [PATCH 21/28] Updated the readme to include lfs --- qlpdb/README.md | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/qlpdb/README.md b/qlpdb/README.md index 4654286..ace6d20 100644 --- a/qlpdb/README.md +++ b/qlpdb/README.md @@ -3,6 +3,12 @@ Data module for publication [2009.11970]](https://arxiv.org/abs/2009.11970). It allows interfacing, searching and saving database structures through Python objects. +The data itself is stored using [`git lfs`](https://git-lfs.github.com). +To make sure you have the most recent version, run +```bash +git pull +git lfs pull +``` ## Requirements From 04e895590d684f57645c90a4ffdaf8246eead722 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 19:57:11 +0200 Subject: [PATCH 22/28] Restructure db connection workflow --- .github/workflows/docker-build.yaml | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/.github/workflows/docker-build.yaml b/.github/workflows/docker-build.yaml index 668937a..8a60c75 100644 --- a/.github/workflows/docker-build.yaml +++ b/.github/workflows/docker-build.yaml @@ -9,6 +9,8 @@ jobs: - name: Git LFS Pull run: git lfs pull - name: Build the stack - run: | - docker-compose build - docker-compose run qlpdb python manage.py migrate + run: docker-compose build + - name: Up the service + run: docker-compose up + - name: Check DB connection + run: docker-compose run qlpdb python manage.py migrate From 5cebb9783ff5ccefd1ec50a83b701798283aedbe Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 20:10:54 +0200 Subject: [PATCH 23/28] Detach docker up --- .github/workflows/docker-build.yaml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/docker-build.yaml b/.github/workflows/docker-build.yaml index 8a60c75..763e6e1 100644 --- a/.github/workflows/docker-build.yaml +++ b/.github/workflows/docker-build.yaml @@ -11,6 +11,6 @@ jobs: - name: Build the stack run: docker-compose build - name: Up the service - run: docker-compose up + run: docker-compose up -d - name: Check DB connection run: docker-compose run qlpdb python manage.py migrate From 3d7029099f2cc62b10d92106d04584adb146e755 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 21:09:22 +0200 Subject: [PATCH 24/28] Only verify build --- .github/workflows/docker-build.yaml | 4 ---- 1 file changed, 4 deletions(-) diff --git a/.github/workflows/docker-build.yaml b/.github/workflows/docker-build.yaml index 763e6e1..29a5d03 100644 --- a/.github/workflows/docker-build.yaml +++ b/.github/workflows/docker-build.yaml @@ -10,7 +10,3 @@ jobs: run: git lfs pull - name: Build the stack run: docker-compose build - - name: Up the service - run: docker-compose up -d - - name: Check DB connection - run: docker-compose run qlpdb python manage.py migrate From b99813637ecd1a832626e939bbdde38e1befe4e8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 21:57:03 +0200 Subject: [PATCH 25/28] updated data readme --- qlpdb/README.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/qlpdb/README.md b/qlpdb/README.md index ace6d20..887c1ce 100644 --- a/qlpdb/README.md +++ b/qlpdb/README.md @@ -20,10 +20,14 @@ If you prefer a shortcut, we also specify a high-level [Docker setup](https://do ## Docker Once you have [started Docker](https://docs.docker.com/get-started/), you can install the repository software and initialize data structures by running ```bash -docker-compose build +docker-compose build # install dependencies +docker compose run db # load in data and start db ``` in the repository root directory. +The data has been loaded in once you see the message `database system is ready to accept connections`. Note that this might take a while. +You can now end this process (`Ctrl-c`). +This only needs to be executed once. In case data structures have changed, you have to run once ```bash From fe2ea233ff8c7703454ba43845a064c5deff2632 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Christopher=20K=C3=B6rber?= Date: Tue, 13 Oct 2020 22:07:46 +0200 Subject: [PATCH 26/28] Updated readme files --- README.md | 24 ++++++++++++------------ qlpdb/README.md | 10 +++++----- 2 files changed, 17 insertions(+), 17 deletions(-) diff --git a/README.md b/README.md index 8b827ad..1d07765 100644 --- a/README.md +++ b/README.md @@ -1,14 +1,14 @@ # Integer Programming from Quantum Annealing and Open Quantum Systems -This repository contains software and data associated with publication [Integer Programming from Quantum Annealing and Open Quantum Systems [2009.11970]](https://arxiv.org/abs/2009.11970). +This repository contains software and data associated with the publication [Integer Programming from Quantum Annealing and Open Quantum Systems [2009.11970]](https://arxiv.org/abs/2009.11970). -It contains Python code for mapping [Integer Linear Programming problems](https://en.wikipedia.org/wiki/Integer_programming), in particular the [Minimum Dominating Set](https://mathworld.wolfram.com/MinimumDominatingSet.html) Problem, to [QUBOs or Ising Hamiltonians utilized as input for Quantum Annealers](https://docs.dwavesys.com/docs/latest/c_gs_3.html#qubo). -It furthermore contains code which simulates the quantum hardware. +It contains Python code for mapping [Integer Linear Programming problems](https://en.wikipedia.org/wiki/Integer_programming), notably the [Minimum Dominating Set](https://mathworld.wolfram.com/MinimumDominatingSet.html) Problem, to [QUBOs or Ising Hamiltonians utilized as input for Quantum Annealers](https://docs.dwavesys.com/docs/latest/c_gs_3.html#qubo). +It furthermore contains code that simulates the quantum hardware. ## How to install it? -This repository contains two modules +This repository contains two modules: 1. `qlp` used for computations and 2. `qlpdb` for accessing and storing computation data @@ -31,14 +31,14 @@ pip install [--user] . ### Access publication data This repository contains all the data presented in [[2009.11970]](https://arxiv.org/abs/2009.11970). -To access this data you must host a [PostgreSQL database](https://www.postgresql.org/about/) (other database formats are not sufficient because we have implemented `JSON` and `ArrayFields`). -We provide more information in the [`qlpdb/README.md`](qlpdb/README.md). +To access this data, you must host a [PostgreSQL database](https://www.postgresql.org/about/) (other database formats are not sufficient because we have implemented `JSON` and `ArrayFields`). +We provide more information on the [`qlpdb/README.md`](qlpdb/README.md). ## Usage ### `qlp` -The module `qlp` contains two major components +The module `qlp` contains two major components: * The first submodule, `mds`, was used to map the Minimum Dominating Set Problem to annealing Hardware: ```python @@ -54,12 +54,12 @@ The module `qlp` contains two major components penalty=2 # strength of penalty term ) ``` - The solution to the MDS problem is given by the bit vector `psi` which minimizes + The solution to the MDS problem is given by the bit vector `psi`, which minimizes ```python E = psi.T@qubo@psi ``` The QUBO serves as input for the annealing hardware. -* the second submodule, `tdse`, simulates the time dependent Schrödinger equation for given input (Ising) Hamiltonians: +* the second submodule, `tdse`, simulates the time-dependent Schrödinger equation for given input (Ising) Hamiltonians: ```python from qlp.mds.mds_qlpdb import QUBO_to_Ising, graph_summary from qlp.tdse import TDSE @@ -80,7 +80,7 @@ The module `qlp` contains two major components graph_params, # Graph parameters ising_params, # Ising Hamiltonian parameters offset_params, # how is the annealing curve implemented - solver_params, # numerical parameters for solving the time dependent equation + solver_params, # numerical parameters for solving the time-dependent equation ) # Compute the starting wave density rho = tdse.init_densitymatrix( @@ -90,7 +90,7 @@ The module `qlp` contains two major components ) tdse.gamma = gamma # set FC decoherence rate tdse.gamma_local = gamma_local # set local decoherence rate - # Solve time dependent Schrödinger equation + # Solve time-dependent Schrödinger equation sol_densitymatrix = tdse.solve_mixed(rho) ``` @@ -100,7 +100,7 @@ See also the [`notebooks`](notebooks) folder, especially the [`notebooks/runs`]( `qlpdb` is an [(ORM)](https://en.wikipedia.org/wiki/Object–relational_mapping) framework for mapping database structures to Python objects using [EspressoDB](https://espressodb.readthedocs.io/en/latest/) / [Django](https://www.djangoproject.com). -Once the database [is properly set up](qlpdb/README.md), you can launch a local web server for inspecting data and browsing the documentation (viewable in any browser) +Once the database [is appropriately set up](qlpdb/README.md), you can launch a local web server for inspecting data and browsing the documentation (viewable in any browser) ```bash cd qlpdb python manage.py runserver diff --git a/qlpdb/README.md b/qlpdb/README.md index 887c1ce..ba86990 100644 --- a/qlpdb/README.md +++ b/qlpdb/README.md @@ -1,7 +1,7 @@ # qlpdb Data module for publication [2009.11970]](https://arxiv.org/abs/2009.11970). -It allows interfacing, searching and saving database structures through Python objects. +It allows interfacing, searching, and saving database structures through Python objects. The data itself is stored using [`git lfs`](https://git-lfs.github.com). To make sure you have the most recent version, run @@ -13,7 +13,7 @@ git lfs pull ## Requirements The implemented data structures require a [PostgreSQL database](https://www.postgresql.org/about/) (`JSON` and `ArrayFields`). -Thus, you first have to setup a [PostgreSQL database server](https://www.postgresql.org/docs/9.1/server-start.html). +Thus, you first have to set up a [PostgreSQL database server](https://www.postgresql.org/docs/9.1/server-start.html). If you prefer a shortcut, we also specify a high-level [Docker setup](https://docs.docker.com/get-docker/). @@ -38,14 +38,14 @@ Finally, to launch the database interface, you can run ```bash docker-compose up ``` -This data server can be access through any web browser at the address +This data server can be accessed through any web browser at the address ``` http://localhost:8000 ``` ## Details -The data is stored in a `sql` dump file which is contained in the `data.tar.gz`. -We also provide a `SHA-512` checksum for verifying the data integrity. +The data is stored in a `.sql` dump file, which is contained in the `data.tar.gz`. +We also provide an `SHA-512` checksum for verifying the data integrity. You can create a custom PostgreSQL database and user for loading in the dump file ```bash From d7c77a5135d5e78c88962770e58e8b545c18e6b2 Mon Sep 17 00:00:00 2001 From: Jason Chang Date: Thu, 12 Nov 2020 14:16:31 -0500 Subject: [PATCH 27/28] update title --- notebooks/brute_force_solver.ipynb | 122 +-- notebooks/d-wave_benchmark.ipynb | 6 +- notebooks/devel.ipynb | 6 +- notebooks/example-problem.ipynb | 6 +- notebooks/hamming-graph.ipynb | 40 +- notebooks/mds-directed-example.ipynb | 6 +- notebooks/mds-qlpdb_implicit_embedding.ipynb | 6 +- notebooks/minimum-dominating-set.ipynb | 328 +------ notebooks/tdse_notebook.ipynb | 23 +- paper/.gitignore | 2 + paper/Cover_Letter.docx | Bin 0 -> 433587 bytes paper/Cover_Letter.pdf | Bin 0 -> 272839 bytes paper/v1/DWave_scaling.pdf | Bin 0 -> 19386 bytes paper/v1/MDS_mds0.pdf | Bin 0 -> 40407 bytes paper/v1/MDS_mds1.pdf | Bin 0 -> 39437 bytes paper/v1/MDS_mds2.pdf | Bin 0 -> 39004 bytes paper/v1/NN2_offset_scaling.pdf | Bin 0 -> 12563 bytes paper/v1/NN2_offset_scaling_extended.pdf | Bin 0 -> 14405 bytes paper/v1/anneal_schedule.pdf | Bin 0 -> 17410 bytes paper/v1/anneal_schedule_extended.pdf | Bin 0 -> 17363 bytes paper/v1/final_state_distribution.pdf | Bin 0 -> 14930 bytes paper/v1/linear_graph.pdf | Bin 0 -> 63231 bytes paper/v1/main.aux | 159 ++++ paper/v1/main.bbl | 429 +++++++++ paper/v1/main.blg | 69 ++ paper/v1/main.log | 892 +++++++++++++++++++ paper/v1/main.out | 27 + paper/v1/main.pdf | Bin 0 -> 773964 bytes paper/v1/main.tex | 698 +++++++++++++++ paper/v1/mainNotes.bib | 0 paper/v1/time_dependent_probability.pdf | Bin 0 -> 23297 bytes paper/v1/vacuum_probability.pdf | Bin 0 -> 16240 bytes qlpdb/db-config.example.yaml | 3 - 33 files changed, 2383 insertions(+), 439 deletions(-) create mode 100644 paper/Cover_Letter.docx create mode 100644 paper/Cover_Letter.pdf create mode 100644 paper/v1/DWave_scaling.pdf create mode 100644 paper/v1/MDS_mds0.pdf create mode 100644 paper/v1/MDS_mds1.pdf create mode 100644 paper/v1/MDS_mds2.pdf create mode 100644 paper/v1/NN2_offset_scaling.pdf create mode 100644 paper/v1/NN2_offset_scaling_extended.pdf create mode 100644 paper/v1/anneal_schedule.pdf create mode 100644 paper/v1/anneal_schedule_extended.pdf create mode 100644 paper/v1/final_state_distribution.pdf create mode 100644 paper/v1/linear_graph.pdf create mode 100644 paper/v1/main.aux create mode 100644 paper/v1/main.bbl create mode 100644 paper/v1/main.blg create mode 100644 paper/v1/main.log create mode 100644 paper/v1/main.out create mode 100644 paper/v1/main.pdf create mode 100644 paper/v1/main.tex create mode 100644 paper/v1/mainNotes.bib create mode 100644 paper/v1/time_dependent_probability.pdf create mode 100644 paper/v1/vacuum_probability.pdf delete mode 100644 qlpdb/db-config.example.yaml diff --git a/notebooks/brute_force_solver.ipynb b/notebooks/brute_force_solver.ipynb index 000d0bd..42f0702 100644 --- a/notebooks/brute_force_solver.ipynb +++ b/notebooks/brute_force_solver.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 7, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -12,7 +12,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -55,22 +55,21 @@ }, { "cell_type": "code", - "execution_count": 95, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ - "# Dwave assume Ising\n", - "h = np.array([-3.0, 10.5, 2.5, 6.0, 6.0])\n", - "J = np.array([[ 0, 0, 8, -4, -4],\n", - " [ 0, 0,-16, -4, -4],\n", - " [ 0, 0, 0, 0, 0],\n", - " [ 0, 0, 0, 0, 0],\n", - " [ 0, 0, 0, 0, 0]])" + "#Ising\n", + "h = np.array([ 1.5, 1.5, -1., -1. ])\n", + "J = np.array([[ 0., 2., -1., -1.],\n", + " [ 0., 0., -1., -1.],\n", + " [ 0., 0., 0., 0.],\n", + " [ 0., 0., 0., 0.]])" ] }, { "cell_type": "code", - "execution_count": 96, + "execution_count": 5, "metadata": { "scrolled": true }, @@ -78,14 +77,13 @@ { "data": { "text/plain": [ - "array([[ -6., 0., 32., -16., -16.],\n", - " [ 0., 69., -64., -16., -16.],\n", - " [ 0., 0., 21., 0., 0.],\n", - " [ 0., 0., 0., 28., 0.],\n", - " [ 0., 0., 0., 0., 28.]])" + "array([[ 3., 8., -4., -4.],\n", + " [ 0., 3., -4., -4.],\n", + " [ 0., 0., 2., 0.],\n", + " [ 0., 0., 0., 2.]])" ] }, - "execution_count": 96, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -97,41 +95,7 @@ }, { "cell_type": "code", - "execution_count": 154, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ 0. 0. 0. 2. -4.]\n", - " [ 0. 0. 0. -1. -1.]\n", - " [ 0. 0. 0. -1. -1.]\n", - " [ 0. 0. 0. 0. 0.]\n", - " [ 0. 0. 0. 0. 0.]] [-0.75 1. 1. -1.5 -0.75]\n" - ] - } - ], - "source": [ - "# DWave assume QUBO\n", - "Q = [[2.5, 0.0, 0.0, 8.0, -16.0], [0.0, 6.0, 0.0, -4.0, -4.0], [0.0, 0.0, 6.0, -4.0, -4.0], [0.0, 0.0, 0.0, -3.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.5]]\n", - "J, h, _ = transform.QUBO_to_Ising(Q)\n", - "print(J, h)" - ] - }, - { - "cell_type": "code", - "execution_count": 137, - "metadata": {}, - "outputs": [], - "source": [ - "# Hand craft\n", - "Q = [[-3.0, 8.0, -4.0, -4.0], [0.0, -3.0, -4.0, -4.0], [0.0, 0.0, 6.0, 0.0], [0.0, 0.0, 0.0, 6.0]]" - ] - }, - { - "cell_type": "code", - "execution_count": 146, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -140,7 +104,7 @@ }, { "cell_type": "code", - "execution_count": 147, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -149,47 +113,31 @@ }, { "cell_type": "code", - "execution_count": 148, + "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[[-2.0, array([0., 0., 0., 1., 0.])],\n", - " [-2.0, array([1., 0., 0., 0., 1.])],\n", - " [-1.3333333333333321, array([1., 1., 1., 1., 1.])],\n", - " [-0.6666666666666665, array([0., 0., 1., 1., 0.])],\n", - " [-0.6666666666666665, array([0., 1., 0., 1., 0.])],\n", - " [-0.6666666666666661, array([1., 0., 1., 0., 1.])],\n", - " [-0.6666666666666661, array([1., 1., 0., 0., 1.])],\n", - " [0.0, array([0., 0., 0., 0., 0.])],\n", - " [8.881784197001252e-16, array([1., 0., 1., 1., 1.])],\n", - " [8.881784197001252e-16, array([1., 1., 0., 1., 1.])],\n", - " [0.6666666666666674, array([0., 1., 1., 1., 0.])],\n", - " [0.6666666666666679, array([1., 1., 1., 0., 1.])],\n", - " [1.333333333333334, array([1., 0., 0., 1., 1.])],\n", - " [1.6666666666666667, array([1., 0., 0., 0., 0.])],\n", - " [2.333333333333334, array([0., 1., 1., 1., 1.])],\n", - " [3.666666666666667, array([0., 0., 1., 1., 1.])],\n", - " [3.666666666666667, array([0., 1., 0., 1., 1.])],\n", - " [4.0, array([0., 0., 1., 0., 0.])],\n", - " [4.0, array([0., 1., 0., 0., 0.])],\n", - " [5.0, array([0., 0., 0., 1., 1.])],\n", - " [5.0, array([1., 0., 0., 1., 0.])],\n", - " [5.666666666666667, array([1., 0., 1., 0., 0.])],\n", - " [5.666666666666667, array([1., 1., 0., 0., 0.])],\n", - " [6.333333333333334, array([1., 0., 1., 1., 0.])],\n", - " [6.333333333333334, array([1., 1., 0., 1., 0.])],\n", - " [7.0, array([0., 0., 0., 0., 1.])],\n", - " [7.666666666666668, array([1., 1., 1., 1., 0.])],\n", - " [8.0, array([0., 1., 1., 0., 0.])],\n", - " [8.333333333333334, array([0., 0., 1., 0., 1.])],\n", - " [8.333333333333334, array([0., 1., 0., 0., 1.])],\n", - " [9.666666666666668, array([0., 1., 1., 0., 1.])],\n", - " [9.666666666666668, array([1., 1., 1., 0., 0.])]]" + "[[-1.0, array([0., 1., 1., 1.])],\n", + " [-1.0, array([1., 0., 1., 1.])],\n", + " [0.0, array([0., 0., 0., 0.])],\n", + " [1.0, array([0., 1., 0., 1.])],\n", + " [1.0, array([0., 1., 1., 0.])],\n", + " [1.0, array([1., 0., 0., 1.])],\n", + " [1.0, array([1., 0., 1., 0.])],\n", + " [2.0, array([0., 0., 0., 1.])],\n", + " [2.0, array([0., 0., 1., 0.])],\n", + " [2.0, array([1., 1., 1., 1.])],\n", + " [3.0, array([0., 1., 0., 0.])],\n", + " [3.0, array([1., 0., 0., 0.])],\n", + " [4.0, array([0., 0., 1., 1.])],\n", + " [8.0, array([1., 1., 0., 1.])],\n", + " [8.0, array([1., 1., 1., 0.])],\n", + " [14.0, array([1., 1., 0., 0.])]]" ] }, - "execution_count": 148, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } diff --git a/notebooks/d-wave_benchmark.ipynb b/notebooks/d-wave_benchmark.ipynb index 72bc5d7..de680f7 100644 --- a/notebooks/d-wave_benchmark.ipynb +++ b/notebooks/d-wave_benchmark.ipynb @@ -1419,9 +1419,9 @@ ], "metadata": { "kernelspec": { - "display_name": "quantum_linear_programming", + "display_name": "Python 3", "language": "python", - "name": "quantum_linear_programming" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -1433,7 +1433,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.4" + "version": "3.8.3" } }, "nbformat": 4, diff --git a/notebooks/devel.ipynb b/notebooks/devel.ipynb index 63405d4..f3d2e25 100644 --- a/notebooks/devel.ipynb +++ b/notebooks/devel.ipynb @@ -410,9 +410,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qlp", + "display_name": "Python 3", "language": "python", - "name": "qlp" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -424,7 +424,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.5" + "version": "3.8.3" } }, "nbformat": 4, diff --git a/notebooks/example-problem.ipynb b/notebooks/example-problem.ipynb index b0f2255..ca80a47 100644 --- a/notebooks/example-problem.ipynb +++ b/notebooks/example-problem.ipynb @@ -47737,9 +47737,9 @@ ], "metadata": { "kernelspec": { - "display_name": "quantum_linear_programming", + "display_name": "Python 3", "language": "python", - "name": "quantum_linear_programming" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -47751,7 +47751,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.4" + "version": "3.8.3" } }, "nbformat": 4, diff --git a/notebooks/hamming-graph.ipynb b/notebooks/hamming-graph.ipynb index 8c0ed2f..4e6bf5a 100644 --- a/notebooks/hamming-graph.ipynb +++ b/notebooks/hamming-graph.ipynb @@ -16,7 +16,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -29,21 +29,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 30, "metadata": {}, "outputs": [], "source": [ - "d = 3\n", - "q = 2\n", + "d = 1\n", + "q = 5\n", "kq = complete_graph(q)\n", "graph, name = gt.generate_hamming_graph(d, q, v_as_string=True)" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 31, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "gt.get_plot(kq.edges)\n", "plt.show()" @@ -51,9 +62,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 32, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "fig, ax = plt.subplots(figsize=(3, 2), dpi=200)\n", "gt.get_plot_mpl(graph, ax=ax, seed=1)\n", @@ -111,7 +133,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.5" + "version": "3.8.3" } }, "nbformat": 4, diff --git a/notebooks/mds-directed-example.ipynb b/notebooks/mds-directed-example.ipynb index c9b6725..be3b283 100644 --- a/notebooks/mds-directed-example.ipynb +++ b/notebooks/mds-directed-example.ipynb @@ -237,9 +237,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qlp", + "display_name": "Python 3", "language": "python", - "name": "qlp" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -251,7 +251,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.5" + "version": "3.8.3" } }, "nbformat": 4, diff --git a/notebooks/mds-qlpdb_implicit_embedding.ipynb b/notebooks/mds-qlpdb_implicit_embedding.ipynb index e93346e..62f9f86 100644 --- a/notebooks/mds-qlpdb_implicit_embedding.ipynb +++ b/notebooks/mds-qlpdb_implicit_embedding.ipynb @@ -2255,9 +2255,9 @@ ], "metadata": { "kernelspec": { - "display_name": "qlp", + "display_name": "Python 3", "language": "python", - "name": "quantum_linear_programming" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -2269,7 +2269,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.6" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/notebooks/minimum-dominating-set.ipynb b/notebooks/minimum-dominating-set.ipynb index 635928a..4316504 100644 --- a/notebooks/minimum-dominating-set.ipynb +++ b/notebooks/minimum-dominating-set.ipynb @@ -20,319 +20,15 @@ "metadata": {}, "outputs": [ { - "data": { - "text/html": [ - "\n", - "
\n", - " \n", - " Loading BokehJS ...\n", - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "application/javascript": [ - "\n", - "(function(root) {\n", - " function now() {\n", - " return new Date();\n", - " }\n", - "\n", - " var force = true;\n", - "\n", - " if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n", - " root._bokeh_onload_callbacks = [];\n", - " root._bokeh_is_loading = undefined;\n", - " }\n", - "\n", - " var JS_MIME_TYPE = 'application/javascript';\n", - " var HTML_MIME_TYPE = 'text/html';\n", - " var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n", - " var CLASS_NAME = 'output_bokeh rendered_html';\n", - "\n", - " /**\n", - " * Render data to the DOM node\n", - " */\n", - " function render(props, node) {\n", - " var script = document.createElement(\"script\");\n", - " node.appendChild(script);\n", - " }\n", - "\n", - " /**\n", - " * Handle when an output is cleared or removed\n", - " */\n", - " function handleClearOutput(event, handle) {\n", - " var cell = handle.cell;\n", - "\n", - " var id = cell.output_area._bokeh_element_id;\n", - " var server_id = cell.output_area._bokeh_server_id;\n", - " // Clean up Bokeh references\n", - " if (id != null && id in Bokeh.index) {\n", - " Bokeh.index[id].model.document.clear();\n", - " delete Bokeh.index[id];\n", - " }\n", - "\n", - " if (server_id !== undefined) {\n", - " // Clean up Bokeh references\n", - " var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n", - " cell.notebook.kernel.execute(cmd, {\n", - " iopub: {\n", - " output: function(msg) {\n", - " var id = msg.content.text.trim();\n", - " if (id in Bokeh.index) {\n", - " Bokeh.index[id].model.document.clear();\n", - " delete Bokeh.index[id];\n", - " }\n", - " }\n", - " }\n", - " });\n", - " // Destroy server and session\n", - " var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n", - " cell.notebook.kernel.execute(cmd);\n", - " }\n", - " }\n", - "\n", - " /**\n", - " * Handle when a new output is added\n", - " */\n", - " function handleAddOutput(event, handle) {\n", - " var output_area = handle.output_area;\n", - " var output = handle.output;\n", - "\n", - " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n", - " if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n", - " return\n", - " }\n", - "\n", - " var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n", - "\n", - " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n", - " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n", - " // store reference to embed id on output_area\n", - " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n", - " }\n", - " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n", - " var bk_div = document.createElement(\"div\");\n", - " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n", - " var script_attrs = bk_div.children[0].attributes;\n", - " for (var i = 0; i < script_attrs.length; i++) {\n", - " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n", - " }\n", - " // store reference to server id on output_area\n", - " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n", - " }\n", - " }\n", - "\n", - " function register_renderer(events, OutputArea) {\n", - "\n", - " function append_mime(data, metadata, element) {\n", - " // create a DOM node to render to\n", - " var toinsert = this.create_output_subarea(\n", - " metadata,\n", - " CLASS_NAME,\n", - " EXEC_MIME_TYPE\n", - " );\n", - " this.keyboard_manager.register_events(toinsert);\n", - " // Render to node\n", - " var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n", - " render(props, toinsert[toinsert.length - 1]);\n", - " element.append(toinsert);\n", - " return toinsert\n", - " }\n", - "\n", - " /* Handle when an output is cleared or removed */\n", - " events.on('clear_output.CodeCell', handleClearOutput);\n", - " events.on('delete.Cell', handleClearOutput);\n", - "\n", - " /* Handle when a new output is added */\n", - " events.on('output_added.OutputArea', handleAddOutput);\n", - "\n", - " /**\n", - " * Register the mime type and append_mime function with output_area\n", - " */\n", - " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n", - " /* Is output safe? */\n", - " safe: true,\n", - " /* Index of renderer in `output_area.display_order` */\n", - " index: 0\n", - " });\n", - " }\n", - "\n", - " // register the mime type if in Jupyter Notebook environment and previously unregistered\n", - " if (root.Jupyter !== undefined) {\n", - " var events = require('base/js/events');\n", - " var OutputArea = require('notebook/js/outputarea').OutputArea;\n", - "\n", - " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n", - " register_renderer(events, OutputArea);\n", - " }\n", - " }\n", - "\n", - " \n", - " if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n", - " root._bokeh_timeout = Date.now() + 5000;\n", - " root._bokeh_failed_load = false;\n", - " }\n", - "\n", - " var NB_LOAD_WARNING = {'data': {'text/html':\n", - " \"
\\n\"+\n", - " \"

\\n\"+\n", - " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n", - " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n", - " \"

\\n\"+\n", - " \"
    \\n\"+\n", - " \"
  • re-rerun `output_notebook()` to attempt to load from CDN again, or
  • \\n\"+\n", - " \"
  • use INLINE resources instead, as so:
  • \\n\"+\n", - " \"
\\n\"+\n", - " \"\\n\"+\n", - " \"from bokeh.resources import INLINE\\n\"+\n", - " \"output_notebook(resources=INLINE)\\n\"+\n", - " \"\\n\"+\n", - " \"
\"}};\n", - "\n", - " function display_loaded() {\n", - " var el = document.getElementById(\"1001\");\n", - " if (el != null) {\n", - " el.textContent = \"BokehJS is loading...\";\n", - " }\n", - " if (root.Bokeh !== undefined) {\n", - " if (el != null) {\n", - " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n", - " }\n", - " } else if (Date.now() < root._bokeh_timeout) {\n", - " setTimeout(display_loaded, 100)\n", - " }\n", - " }\n", - "\n", - "\n", - " function run_callbacks() {\n", - " try {\n", - " root._bokeh_onload_callbacks.forEach(function(callback) {\n", - " if (callback != null)\n", - " callback();\n", - " });\n", - " } finally {\n", - " delete root._bokeh_onload_callbacks\n", - " }\n", - " console.debug(\"Bokeh: all callbacks have finished\");\n", - " }\n", - "\n", - " function load_libs(css_urls, js_urls, callback) {\n", - " if (css_urls == null) css_urls = [];\n", - " if (js_urls == null) js_urls = [];\n", - "\n", - " root._bokeh_onload_callbacks.push(callback);\n", - " if (root._bokeh_is_loading > 0) {\n", - " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n", - " return null;\n", - " }\n", - " if (js_urls == null || js_urls.length === 0) {\n", - " run_callbacks();\n", - " return null;\n", - " }\n", - " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n", - " root._bokeh_is_loading = css_urls.length + js_urls.length;\n", - "\n", - " function on_load() {\n", - " root._bokeh_is_loading--;\n", - " if (root._bokeh_is_loading === 0) {\n", - " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n", - " run_callbacks()\n", - " }\n", - " }\n", - "\n", - " function on_error() {\n", - " console.error(\"failed to load \" + url);\n", - " }\n", - "\n", - " for (var i = 0; i < css_urls.length; i++) {\n", - " var url = css_urls[i];\n", - " const element = document.createElement(\"link\");\n", - " element.onload = on_load;\n", - " element.onerror = on_error;\n", - " element.rel = \"stylesheet\";\n", - " element.type = \"text/css\";\n", - " element.href = url;\n", - " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n", - " document.body.appendChild(element);\n", - " }\n", - "\n", - " for (var i = 0; i < js_urls.length; i++) {\n", - " var url = js_urls[i];\n", - " var element = document.createElement('script');\n", - " element.onload = on_load;\n", - " element.onerror = on_error;\n", - " element.async = false;\n", - " element.src = url;\n", - " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n", - " document.head.appendChild(element);\n", - " }\n", - " };var element = document.getElementById(\"1001\");\n", - " if (element == null) {\n", - " console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1001' but no matching script tag was found. \")\n", - " return false;\n", - " }\n", - "\n", - " function inject_raw_css(css) {\n", - " const element = document.createElement(\"style\");\n", - " element.appendChild(document.createTextNode(css));\n", - " document.body.appendChild(element);\n", - " }\n", - "\n", - " \n", - " var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.4.0.min.js\"];\n", - " var css_urls = [];\n", - " \n", - "\n", - " var inline_js = [\n", - " function(Bokeh) {\n", - " Bokeh.set_log_level(\"info\");\n", - " },\n", - " function(Bokeh) {\n", - " \n", - " \n", - " }\n", - " ];\n", - "\n", - " function run_inline_js() {\n", - " \n", - " if (root.Bokeh !== undefined || force === true) {\n", - " \n", - " for (var i = 0; i < inline_js.length; i++) {\n", - " inline_js[i].call(root, root.Bokeh);\n", - " }\n", - " if (force === true) {\n", - " display_loaded();\n", - " }} else if (Date.now() < root._bokeh_timeout) {\n", - " setTimeout(run_inline_js, 100);\n", - " } else if (!root._bokeh_failed_load) {\n", - " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n", - " root._bokeh_failed_load = true;\n", - " } else if (force !== true) {\n", - " var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n", - " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n", - " }\n", - "\n", - " }\n", - "\n", - " if (root._bokeh_is_loading === 0) {\n", - " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n", - " run_inline_js();\n", - " } else {\n", - " load_libs(css_urls, js_urls, function() {\n", - " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n", - " run_inline_js();\n", - " });\n", - " }\n", - "}(window));" - ], - "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n function now() {\n return new Date();\n }\n\n var force = true;\n\n if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n root._bokeh_onload_callbacks = [];\n root._bokeh_is_loading = undefined;\n }\n\n \n\n \n if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n var NB_LOAD_WARNING = {'data': {'text/html':\n \"
\\n\"+\n \"

\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"

\\n\"+\n \"
    \\n\"+\n \"
  • re-rerun `output_notebook()` to attempt to load from CDN again, or
  • \\n\"+\n \"
  • use INLINE resources instead, as so:
  • \\n\"+\n \"
\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\n\n function display_loaded() {\n var el = document.getElementById(\"1001\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null || js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n function on_load() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n run_callbacks()\n }\n }\n\n function on_error() {\n console.error(\"failed to load \" + url);\n }\n\n for (var i = 0; i < css_urls.length; i++) {\n var url = css_urls[i];\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error;\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n }\n\n for (var i = 0; i < js_urls.length; i++) {\n var url = js_urls[i];\n var element = document.createElement('script');\n element.onload = on_load;\n element.onerror = on_error;\n element.async = false;\n element.src = url;\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.head.appendChild(element);\n }\n };var element = document.getElementById(\"1001\");\n if (element == null) {\n console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1001' but no matching script tag was found. \")\n return false;\n }\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n \n var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.4.0.min.js\"];\n var css_urls = [];\n \n\n var inline_js = [\n function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\n function(Bokeh) {\n \n \n }\n ];\n\n function run_inline_js() {\n \n if (root.Bokeh !== undefined || force === true) {\n \n for (var i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }\n if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n\n }\n\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(css_urls, js_urls, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));" - }, - "metadata": {}, - "output_type": "display_data" + "ename": "ModuleNotFoundError", + "evalue": "No module named 'bokeh'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnetworkx\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mbokeh\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mio\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mshow\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moutput_notebook\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 12\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mbokeh\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodels\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mPlot\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRange1d\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mMultiLine\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mCircle\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mHoverTool\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mbokeh\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodels\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraphs\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mfrom_networkx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'bokeh'" + ] } ], "source": [ @@ -1594,9 +1290,9 @@ ], "metadata": { "kernelspec": { - "display_name": "quantum_linear_programming", + "display_name": "Python 3", "language": "python", - "name": "quantum_linear_programming" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -1608,7 +1304,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.4" + "version": "3.8.3" } }, "nbformat": 4, diff --git a/notebooks/tdse_notebook.ipynb b/notebooks/tdse_notebook.ipynb index 14a85db..ba49741 100644 --- a/notebooks/tdse_notebook.ipynb +++ b/notebooks/tdse_notebook.ipynb @@ -9,7 +9,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -61,7 +61,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -86,7 +86,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -126,21 +126,25 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "{'tag': 'NN(2)', 'total_vertices': 2, 'total_edges': 1, 'total_qubits': 5, 'max_edges': 1, 'adjacency': [[0, 1]], 'adjacency_hash': '2864ee150babb3f03de5e76a1733df4b'}\n", - "[[6.5, 0.0, -4.0, -16.0, -4.0], [0.0, -3.0, -4.0, 8.0, -4.0], [0.0, 0.0, 6.0, 0.0, 0.0], [0.0, 0.0, 0.0, 6.5, 0.0], [0.0, 0.0, 0.0, 0.0, 6.0]]\n", - "[ 2.75 1.5 -1. -1.25 -1. ]\n" + "{'tag': 'NN(2)', 'total_vertices': 2, 'total_edges': 1, 'total_qubits': 4, 'max_edges': 1, 'adjacency': [[0, 1]], 'adjacency_hash': '2864ee150babb3f03de5e76a1733df4b'}\n", + "[[-3.0, 8.0, -4.0, -4.0], [0.0, -3.0, -4.0, -4.0], [0.0, 0.0, 6.0, 0.0], [0.0, 0.0, 0.0, 6.0]]\n", + "[[ 0. 2. -1. -1.]\n", + " [ 0. 0. -1. -1.]\n", + " [ 0. 0. 0. 0.]\n", + " [ 0. 0. 0. 0.]]\n", + "[ 1.5 1.5 -1. -1. ]\n" ] } ], "source": [ - "embed = True # nvertices = [2, 3] available\n", + "embed = False # nvertices = [2, 3] available\n", "embedding = None\n", "\n", "if embed:\n", @@ -153,6 +157,7 @@ "graph_params = graph_summary(tag, graph, qubo)\n", "print(graph_params)\n", "print(qubo.todense().tolist())\n", + "print(Jij)\n", "print(hi)" ] }, @@ -467,7 +472,7 @@ "\n", "# brute force solving time-dependent schrodinger equation to simulate quantum annealing for small systems\n", "result = dict()\n", - "offset_min_list = [-0.05]\n", + "offset_min_list = [0.05]\n", "Aoffset = 0\n", "\n", "for offset_min in offset_min_list:\n", diff --git a/paper/.gitignore b/paper/.gitignore index 097b9f6..903fb49 100644 --- a/paper/.gitignore +++ b/paper/.gitignore @@ -2,3 +2,5 @@ main.dvi main.fdb_latexmk main.fls main.xdv +~$ver_Letter.docx + diff --git a/paper/Cover_Letter.docx b/paper/Cover_Letter.docx new file mode 100644 index 0000000000000000000000000000000000000000..76000b0072d08e7475bcd2e39266ab092e7455da GIT binary patch literal 433587 zcmeFW)c}g_c{`n^m9&rhL^P;Sl>rY3 zHf=$pmBEFi{t041>hkrHOgY3sv=b@$zDU(KKrC@goH}9mFcX4sPZZPbgWgS$%nc%L zYC7Ahg9A)VIyUX~@uR00^L#8CM^%@N8Vgd;oHAkPTe!-Otn?16R?xkZRYmbVIKG5E zVZvR`yFr%y`?^_=X9h{9HF5eQOS$U`ni{?HylA+KIFvW8nRkVgiMyQo213iTS20Pf zme3t3F+Ze?rq6NF{zf2PswIJkI?SAmq^@p=qq-r4%y;)R(yaRckL!*Kipw?&V 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Mappings to QUBO}{section*.12}% 13 +\BOOKMARK [3][-]{section*.14}{Minimum Dominating Set QUBO}{section*.13}% 14 +\BOOKMARK [3][-]{section*.15}{Integer Quadratic Optimization}{section*.13}% 15 +\BOOKMARK [2][-]{section*.16}{ILP on the D-Wave}{section*.12}% 16 +\BOOKMARK [3][-]{section*.17}{Comment on ILP QUBO Penalty Term}{section*.16}% 17 +\BOOKMARK [3][-]{section*.18}{Minor Embedding}{section*.16}% 18 +\BOOKMARK [2][-]{section*.19}{Simulation of a Quantum Annealer}{section*.12}% 19 +\BOOKMARK [3][-]{section*.20}{The Lindblad Equation}{section*.19}% 20 +\BOOKMARK [3][-]{section*.21}{Annealing Schedule and Offsets}{section*.19}% 21 +\BOOKMARK [3][-]{section*.22}{Pure Transverse Field Simulation}{section*.19}% 22 +\BOOKMARK [1][-]{section*.23}{DATA AVAILABILITY}{section*.2}% 23 +\BOOKMARK [1][-]{section*.24}{ACKNOWLEDGEMENTS}{section*.2}% 24 +\BOOKMARK [1][-]{section*.25}{AUTHOR CONTRIBUTIONS}{section*.2}% 25 +\BOOKMARK [1][-]{section*.26}{ADDITIONAL INFORMATION}{section*.2}% 26 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All authors contributed to writing and editing of the final manuscript. +%======================================================================================== +\section{CORRESPONDING AUTHOR} +%======================================================================================== +Correspondence to chiachang@berkeley.edu. + %======================================================================================== \section{ADDITIONAL INFORMATION} %======================================================================================== diff --git a/paper/v2/DWave_scaling.pdf b/paper/v2/DWave_scaling.pdf new file mode 100644 index 0000000000000000000000000000000000000000..835df25e67bdb99f61862dac5e30206472587d16 GIT binary patch literal 19386 zcmeHvcQ}^c|2Wwzn-CtWGN0wK_lkJzP{^Lyn~-ED$&Bn#M#|nKvJ(m^D>Ac3MvCu! zQ}1`{`dnSV>-XR1qw93e{kqRNuX)aSo!5QN!=WyxzzgT&C**iE3Ms55ghOBuM^jru zF);{K-Neem6@maDnh>bAx03|~Dr@3qV&`ZDk&qy?a4-ie3jNSP-plR0mYa#21%&^& 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/dev/null +++ b/paper/v2/main.out @@ -0,0 +1,28 @@ +\BOOKMARK [0][-]{section*.2}{Integer Programming with Quantum Annealing from an Open Quantum System}{}% 2 +\BOOKMARK [1][-]{section*.1}{Abstract}{section*.2}% 1 +\BOOKMARK [1][-]{section*.3}{INTRODUCTION}{section*.2}% 3 +\BOOKMARK [1][-]{section*.4}{RESULTS}{section*.2}% 4 +\BOOKMARK [2][-]{section*.5}{QUBO Formulation of ILP}{section*.4}% 5 +\BOOKMARK [2][-]{section*.6}{Annealer Results for the Dominating Set}{section*.4}% 6 +\BOOKMARK [2][-]{section*.7}{Simulation Results}{section*.4}% 7 +\BOOKMARK [1][-]{section*.8}{Discussion}{section*.2}% 8 +\BOOKMARK [2][-]{section*.9}{Dynamics of Time Evolution}{section*.8}% 9 +\BOOKMARK [2][-]{section*.10}{Idealized Quantum Annealing}{section*.8}% 10 +\BOOKMARK [2][-]{section*.11}{Final Remarks}{section*.8}% 11 +\BOOKMARK [1][-]{section*.12}{METHODS}{section*.2}% 12 +\BOOKMARK [2][-]{section*.13}{Additional Mappings to QUBO}{section*.12}% 13 +\BOOKMARK [3][-]{section*.14}{Minimum Dominating Set QUBO}{section*.13}% 14 +\BOOKMARK [3][-]{section*.15}{Integer Quadratic Optimization}{section*.13}% 15 +\BOOKMARK [2][-]{section*.16}{ILP on the D-Wave}{section*.12}% 16 +\BOOKMARK [3][-]{section*.17}{Comment on ILP QUBO Penalty Term}{section*.16}% 17 +\BOOKMARK [3][-]{section*.18}{Minor Embedding}{section*.16}% 18 +\BOOKMARK [2][-]{section*.19}{Simulation of a Quantum Annealer}{section*.12}% 19 +\BOOKMARK [3][-]{section*.20}{The Lindblad Equation}{section*.19}% 20 +\BOOKMARK [3][-]{section*.21}{Annealing Schedule and Offsets}{section*.19}% 21 +\BOOKMARK [3][-]{section*.22}{Pure Transverse Field Simulation}{section*.19}% 22 +\BOOKMARK [1][-]{section*.23}{DATA AVAILABILITY}{section*.2}% 23 +\BOOKMARK [1][-]{section*.24}{ACKNOWLEDGEMENTS}{section*.2}% 24 +\BOOKMARK [1][-]{section*.25}{AUTHOR CONTRIBUTIONS}{section*.2}% 25 +\BOOKMARK [1][-]{section*.26}{CORRESPONDING AUTHOR}{section*.2}% 26 +\BOOKMARK [1][-]{section*.27}{ADDITIONAL INFORMATION}{section*.2}% 27 +\BOOKMARK 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zDpQr}6?OF;7fH2Lv;V9dC}-tEYoFmR^Gw%bEY|UduCg4JbTZ^ZX_@UA}mqZ^$wh6rC_d$3J7nq=fjkSSs7?Ep73yNH&0$?R(ro1{+`5eo&=~RvG@`0Idy5X6J}M9`I#cVwn>ku;~>A!Twgl! z2d^|B{y6cynQ^?G9+w=G9M(0U<|Zc!j|-cHmy|K=Hqi@D#oY6UjO?$btma=i9Ua|? zYD|ufC`1J(MPKbi1t%Ym<(_HEudcO8p0*gRPk?`eSgX69%V^Re*BJB}+}o(I@GQkr zQIZq!8D)qc=GCA}l5_EA?jr8MNTDroK>iRx5CJG0n#zUWL6Qpd&%DkH{K1^;VexFU z19eS?tfEtf=PiylD6^F5pgcvf%X9=hN8Of*l&!bUxSjH%&icu1tW$;c6<+E-Cb=z- za@P!D3WY9cO@PK;bsRV+51R*cHdwda*8Jj^Sm0zH4z6q$T%8j- zeDT`JCoasbMJT;$_mj} \sqrt{B_{i}(t)B_{j}(t)} J_{ij} \sigma^z_i \sigma^z_j , +\end{align} +where $A_i(t)$ and $B_{i}(t)$ are site-dependent annealing schedule functions. +The site dependency takes into account of the annealing offsets. +The simulation takes two decoherance models into account. +Full-counting statistics and local decoherence. + +For full-counting statistics, the Lindblad operator is +\begin{align} +\mathcal{L}_{\textrm{fc}}(\rho (t), H(t)) = & \Gamma_{\textrm{fc}} \sum_{j, i0$, $S_{ij}=|E_i \rangle \langle E_j|$ denotes the many-body lowering operator and $\Gamma_{fc} = 1/T_{fc}$ is the full-counting decoherence rate for coherence time $T_{fc}$. +That is, due to the interaction with the classical thermal bath, there is a probability that the system hops from each higher-energy many-body state to a lower-energy many-body state. +The probability of the inverse process is given by a Boltzmann factor. + +To model the local decoherence of each qubits in the non-interacting limit, we also consider the amplitude damping for non-interacting qubits. +For the local decoherance model, the Lindblad operator is +\begin{align} +\mathcal{L}_{\textrm{loc}}(\rho (t), H(t)) = & \Gamma_{\textrm{loc}} \sum_j \left(2L_j \rho(t) L_j^\dagger - \{ L^\dagger_j L_j, \rho(t) \} \right)\notag \\ +& + e^{- 2 \beta |h_j| } \left(2L_j^\dagger \rho(t) L_j - \{ L_j L_j^\dagger, \rho(t) \} \right) , +\end{align} +where $j$ is the index for qubit. +$L_j= \sigma^{+}_j=|1\rangle \langle 0|$ for $h_j>0$ and $L_j= \sigma^{-}_j=|0\rangle \langle 1|$ for $h_j<0$. +That is, each qubit is damped toward its local ground state if we ignore all the interactions. + +The initial condition is the Gibbs canonical ensemble +\begin{equation} +\rho (0) = \frac{e^{-\beta H(0)}}{\mbox{Tr}\left(e^{-\beta H(0)}\right)} , +\end{equation} +where $\beta$ is the inverse temperature. +The probability to get the ground state at measurement is +\begin{align} +P = \mbox{Tr} \left( \rho (t) \pi_{\mbox{gnd}} \right) , +\end{align} +where the projection operator onto the degenerated ground states subspace is defined as $\pi_{\mbox{gnd}}=\sum_{i\in G} |\mbox{gnd}_i\rangle \langle \mbox{gnd}_i| $. +Here $\{ | \mbox{gnd}_i \rangle | i \in G \}$ forms an orthonormal basis for the degenerated ground states subspace, i.e., $\langle \mbox{gnd}_j | \mbox{gnd}_i \rangle = \delta_{ij}$. + +For the simulation results presented, we set the temperature to 22.5 milliKelvin. +The coherence time for local decoherence is set to 15$ns$, and 1$ns$ for full-counting statistics. + +%---------------------------------------------------------------------------------------- +\subsubsection{Annealing Schedule and Offsets} +\label{sec:methods:annealing-schedule} +%---------------------------------------------------------------------------------------- +In this section, we discuss the details of the annealing schedule with respect to the dimensionless normalized time $s$. +On D-Wave solvers, annealing offsets effectively advance or delay the annealing schedule of individual qubits (see E.~\eqref{eq:annealH}). +In Fig.~\ref{fig:anneal_schedule}, the default D-Wave annealing schedule is shown in black, in addition to the effects of applying negative offsets (effective time delay) to $A(s)$ and $B(s)$ in blue. +Further documentation is provided by D-Wave in Ref.~\cite{dwave_as, dwave_as_docu}. + +\begin{figure}[htb] + \centering + \includegraphics[width=\columnwidth]{./anneal_schedule.pdf} + \caption{ + Anneal schedules for amplitudes of initial Hamiltonian (dashed) and final Hamiltonian (solid). + Offset 0.0 (black) and -0.05 (purple) are displayed. + Intermediate values lie between and are suppressed for clarity. + } + \label{fig:anneal_schedule} +\end{figure} + +The coefficients $A(s)$ and $B(s)$ follow the underlying control variable $c(s)$, which is designed to grow the persistent current $I_p(s)$ linearly in time. +The effective time delay is implemented by introducing an offset as $c(s) + \delta$. +Because annealing schedules are finite, systematic errors are introduced because the final values of $A(s)$ and $B(s)$ will differ for qubits with different offsets. +Additionally, the values of the coefficients are unknown outside of $s\in [0, 1]$. +We only employ negative offsets such that this unkonwn coefficient range, approximated by a linear extrapolation, only enters at the beginning of the annealing process. + +We verify that our implementation of annealing offsets on the simulator is consistent with D-Wave by solving the following three qubit Hamiltonian +\begin{align} + \label{eq:offset_test_hamiltonian} + H^{\textrm{problem}} = + \begin{pmatrix} + -0.25 & 1 & 0 \\ + 0 & -0.25 & 0 \\ + 0 & 0 & -0.25 + \end{pmatrix} +\end{align} +which has a doubly-degenerate ground state of $(0, 1, 1)$ and $(1, 0, 1)$. An annealing offset is then applied to either qubit 0 or 1, and thus breaks the ground state degeneracy of the system. Because of the systematic error introduced when assigning an offset to a qubit, the final Hamiltonian given by Eq.~(\ref{eq:annealH}) will have small deviations from the input problem Hamiltonian. For example, we expect a negative offset to qubit 0 to Eq.~(\ref{eq:offset_test_hamiltonian}) will yield $(1, 0, 1)$ as the unique ground state given Eq.~(\ref{eq:annealH}). + +We confirm that with different combinations of annealing offsets, the degeneracy is lifted on the D-Wave results as expected by solving for the modified problem Hamiltonian spectrum, as well as dialing in annealing offset in the simulation of this three qubit test case. + + +%---------------------------------------------------------------------------------------- +\subsubsection{Pure Transverse Field Simulation} +\label{sec:methods:simulation_details} +%---------------------------------------------------------------------------------------- +To check the correctness of simulator and unit conversion, we tested a simple annealing schedule for pure transverse field, i.e. $A(s)=A(0)$ and $B(s)=0$. +The initial state is pure zero state $\rho=|00...0\rangle \langle 00...0|$. +In this case the analytical solution can be obtained for the wave function oscillation. +The time-dependent probability is $P_{0}=\cos^{2n}(s)=\cos^{2n}(t/T)$ where $n$ is the number of qubits and $T$ is the annealing time. +For annealing time $T=1/A(0)$, we expect to see perfect one-period oscillation. The energy spectrum for this system can be analytically obtained, so we also checked the Boltzmann distribution in the initial density matrix construction. The oscillation is depicted in Fig.~\ref{figcheck}, where the simulation matches the expected theoretical behavior. + + +\begin{figure} + \centering + \includegraphics[width=\columnwidth]{./vacuum_probability.pdf} + \caption{Time-dependent vacuum probability of 5 qubits system under pure transverse field.} + \label{figcheck} +\end{figure} + + +%======================================================================================== +\section{DATA AVAILABILITY} +\label{sec:open-source} +%======================================================================================== +We provide access to all the software utilized and data presented in this publication in the associated GitHub repository~\cite{github:cchang5/quantum_linear_programming}. +The utilized software is contained in two installable Python modules: +\begin{itemize}[leftmargin=*] + \itemsep0em + \item[] \texttt{qlp} for mapping MDS problems to QUBOs and performing simulations, + \item[] \texttt{qlpdb} for interfacing and documenting simulation and experiment data through EspressoDB~\cite{Chang:2019khk}. +\end{itemize} +The data itself is stored in a SQLite file and associated repository subdirectories. +We provide further documentation in the repository \texttt{readme} file. + + +%======================================================================================== +\section{ACKNOWLEDGEMENTS} +%======================================================================================== + +We thank Long Gang Pang for initial discussions. +We thank David Johnson, Vlad Papish and the rest of D-Wave Support for answering detailed questions about the D-Wave annealer. + +This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, Quantum Horizons: QIS Research and Innovation for Nuclear Science under Award Number FWP-NQISCCAWL. +Lawrence Berkeley National Laboratory (LBNL) is operated by The Regents of the University of California (UC) for the U.S. Department of Energy (DOE) under Federal Prime Agreement DE-AC02-05CH11231. +C.K. gratefully acknowledges funding through the Alexander von Humboldt Foundation through a Feodor Lynen Research Fellowship. +This work used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725. +This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. +The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. (http://energy.gov/downloads/doe-public-access-plan). + + +%======================================================================================== +\section{AUTHOR CONTRIBUTIONS} +%======================================================================================== + +Initial idea was proposed by Chang. +Ostrowski guided the ILP problem selection. +All authors contributed to the design of test cases. +Calculations and code development for the D-Wave were performed by Chang and K\"orber. +Code for numerical simulations was developed by Chen and K\"orber, and cross-checked by Chang. +Simulations were performed by Chang and Chen. +Chang, Chen, K\"orber, and Humble interpreted the results. +All authors contributed to writing and editing of the final manuscript. + +%======================================================================================== +\section{CORRESPONDING AUTHOR} +%======================================================================================== +Correspondence to chiachang@berkeley.edu. + +%======================================================================================== +\section{ADDITIONAL INFORMATION} +%======================================================================================== + +\textbf{Competing Interests:} The authors declare no competing interests. + +\bibliographystyle{apsrev4-1} +\bibliography{main.bib} +%======================================================================================== +\end{document} diff --git a/paper/v2/mainNotes.bib b/paper/v2/mainNotes.bib new file mode 100644 index 0000000..e69de29 diff --git a/paper/v2/time_dependent_probability.pdf b/paper/v2/time_dependent_probability.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8aa4eecd3bb02a7778083c7d4d93cfcc19138f3b GIT binary patch literal 23297 zcmeFZby!qg`!7!C5RyYWG)PU*p>%g6C=A`*2-1iQh%|_Vgru~J3X($#N{WQir8I&l zdiLPs`}KLhp7%VzbIx`B{y7)dV(nOK-MQC&ueCq3x%8A&1YtrVBwW?Akg8`SFbEXl 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linkcolor=blue, % color of internal links + citecolor=blue, % color of links to bibliography + filecolor=blue, % color of file links + urlcolor=blue % color of external links +} + +% disable subsections and subsubsections in the TOC +\makeatletter +\def\l@subsubsection#1#2{} +\makeatother + + +\begin{document} +\title{Integer Programming with Quantum Annealing from an Open Quantum System} + +\author{Chia~Cheng~Chang} +\affiliation{RIKEN iTHEMS, Wako, Saitama 351-0198, Japan} +\affiliation{Department of Physics, University of California, Berkeley, California 94720, USA} +\affiliation{Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA} + \author{Chih-Chieh~Chen } +\affiliation{R\&D Group, Grid Inc., Tokyo 107-0061, Japan} +\affiliation{Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA} +\author{Christopher K\"orber} +\affiliation{Institut f\"ur Theoretische Physik II, Ruhr-Universit\"at Bochum, D-44780 Bochum, Germany} +\affiliation{Department of Physics, University of California, Berkeley, California 94720, USA} +\affiliation{Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA} +\author{Travis~S.~Humble} +\affiliation{Computational Sciences and Engineering, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831, USA} +\author{Jim~Ostrowski} +\affiliation{Industrial and Systems Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA} + +\newcommand{\alert}[1]{\textbf{\color{red}{#1}}} +\renewcommand{\vec}[1]{\boldsymbol{#1}} + +\newcommand{\ghissue}[2]{ + \noindent\fbox{\parbox{0.49\textwidth}{ + \alert{[#1]}% + \\% + \href{https://github.com/cchang5/quantum\_linear\_programming/pull/#2}{See GitHub issue #2}}% + } +} + + +\begin{abstract} + While quantum computing proposes promising solutions to computational problems not accessible with classical approaches, due to current hardware constraints, most quantum algorithms are not yet capable of computing systems of practical relevance, and classical counterparts outperform them. + To practically benefit from quantum architecture, one has to identify problems and algorithms with favorable scaling and improve on corresponding limitations depending on available hardware. + For this reason, we developed an algorithm that solves integer linear programming problems, a classically NP-hard problem, on a quantum annealer, and investigated problem and hardware-specific limitations. + This work presents the formalism of how to map ILP problems to the annealing architectures, how to systematically improve computations utilizing optimized anneal schedules, and models the anneal process through a simulation. + It illustrates the effects of decoherence and many body localization for the minimum dominating set problem, and compares annealing results against numerical simulations of the quantum architecture. + We find that the algorithm outperforms random guessing but is limited to small problems and that annealing schedules can be adjusted to reduce the effects of decoherence. + Simulations qualitatively reproduce algorithmic improvements of the modified annealing schedule, suggesting the improvements have origins from quantum effects. +\end{abstract} + +\preprint{RIKEN-iTHEMS-Report-20} + +\maketitle +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\tableofcontents + +\flushbottom +\maketitle + +%======================================================================================== +\section{INTRODUCTION} +\label{sec:introduction} +%======================================================================================== +Integer Linear Programming (ILP) is an integer optimization problem subject to inequality constraints +\begin{align} + \label{eq:initial-ip-def} + \vec x_0 = \mathrm{arg} & \min\limits_{x}\left(\sum_i c_i x_i\right) +\end{align} +subject to +\begin{align} + \label{eq:ilp-constraints} + & \sum_i A_{ai}x_i +b_a \leq 0 \,, \\ + & x_i \in \mathbbm{Z} \geq 0\, , +\end{align} +where $i=1, \cdots, N$ is the number of dependent variables and $a=1, \cdots, M$ the number of constraint equations. + +In general, ILP is classically NP-complete, and as a result, heuristic methods are employed~\cite{GLOVER1986533, doi:10.1287/ijoc.1.3.190, doi:10.1287/ijoc.2.1.4}. +Standard classical heuristic algorithms follow a greedy scheme which iteratively approximates optimal solutions--starting from a random initial guess, these algorithms apply locally optimal choices at each step. +The NP-hardness of ILP can be understood by realizing that while the solution to an $n$-dimensional linear problem must lie on the vertices of the feasibility region, while the optimal integer solution may in general be at any integer solution inside the feasibility region. +While greedy algorithms do not guarantee optimal global solutions, they find approximate solutions in polynomial time, which can be utilized in further computations. ILP is a commonly tackled problem applicable to situations such as scheduling, network optimization, and graph optimization such as the minimum dominating set problem (MDS). ILP can also be used to identify reaction pathways of biological system, and has recently been explored in the context of quantum annealing~\cite{2020arXiv200713788H}. + +An important ILP application is the MDS problem, which is representatively considered in this work. +For a given a graph $G(E,V)$, defined by the set of $V$ vertices and $E$ edges, a dominating set $D$ is a specific subset of vertices $D \subseteq V$. +In particular, $D$ is a dominating set if all vertices in $V$ but not in $D$ are adjacent to at least one vertex in $D$. +This is equivalent to requiring the set of nearest-neighbor vertices of $D$ (exclusive) and $D$ cover all vertices $N(D) \cup D = V$ (an example is given by Fig.~\ref{fig:dominating_sets}a). +The set $D$ is a minimal dominating set if there is no proper subset of $D$ that is a dominating set, {\it{i.e.}}, the removal of any vertex in $D$ results in $N(D) \cup D \neq V$. +An example is given by Fig.~\ref{fig:dominating_sets}b. +The domination number of $D$ is given by the cardinality of $|D| \equiv \overline{\overline{D}}$. +The MDS is defined by $D$ with the smallest domination number. +Fig.~\ref{fig:dominating_sets}c shows an example of the MDS of $G(V, E)$ and is different from the minimal dominating set. +We emphasize that while the maximum independent set is always a minimal dominating set as exemplified by Fig.~\ref{fig:dominating_sets}b, the MDS, in general, can have a smaller domination number. +As a result, the solution to the dominating set problem can not be obtained by solving the maximum independent set problem, a well-studied problem for quantum annealers. + +\begin{figure*} + \centering + \begin{tabular}{p{0.2\textwidth}p{0.1\textwidth}p{0.2\textwidth}p{0.1\textwidth}p{0.2\textwidth}} + \includegraphics[width=0.2\textwidth]{./MDS_mds0.pdf} +&& + \includegraphics[width=0.2\textwidth]{./MDS_mds1.pdf} +&& + \includegraphics[width=0.2\textwidth]{./MDS_mds2.pdf}\\ + \centering\textbf{a} && \centering\textbf{b} && \centering\textbf{c} + \end{tabular} + \caption{Example of different dominating sets for $G(V, E)$. Vertices in the dominating set $D$ are highlighted in blue. {\textbf{a)}} A dominating set of $G$ with domination number $\overline{\overline{D}} = 2$. {\textbf{b)}} A minimal dominating set of $G$ with domination number of $\overline{\overline{D}} = 2$. {\textbf{c)}} The MDS of $G$ with domination number of $\overline{\overline{D}} = 1$.} + \label{fig:dominating_sets} +\end{figure*} + +For general graphs, existing algorithms on classical computers find MDS solutions in exponential time $\sim O( 1.5^n)$ \cite{Fomin2009, vanRooij2009} or approximate solutions in polynomial time. For example, greedy algorithms locally optimize decisions about which nodes to add to the dominating set. +Thus one is guaranteed to find a dominating set but not necessarily an MDS. + +In this work, we present a method to obtain optimal solutions to ILP by employing quantum annealing methods. + +Current implementations of quantum annealing solve the quadratic binary optimization problem (QUBO) by slowly varying a time-dependent Hamiltonian~\cite{1998PhRvE..58.5355K, 2000quant.ph..1106F, RevModPhys.80.1061}. +Through the adiabatic theorem of quantum mechanics, the annealer is initially prepared in a trivial ground state while the final Hamiltonian encodes the solution to the ILP. +Due to the explosion in research efforts towards hardware implementations of quantum annealers and future improvements to the annealing schedule~\cite{doi:10.7566/JPSJ.89.044001}, mapping ILP to QUBO provides a path forward towards obtaining optimal solutions to the class of integer optimization problems~\cite{2018Glover}. + +In the simplest model for quantum annealing, the pure state of a quantum system evolves adiabatically to prepare an eigenstate of the encoded problem Hamiltonian. The time-dependent Hamiltonian is given as +\begin{equation} + H(t) = A(t) H^{\textrm{init}} + B(t) H^{\textrm{problem}}, \label{eq:tdhamiltonian} +\end{equation} +and $H^\textrm{init}=-\sum_i\sigma^x_i$ (on the D-Wave), while $H^\textrm{problem}$ encodes the problem to be solved. In practice, and as discussed in Sec.~\ref{sec:methods:lindblad}, modeling dynamics that arise during quantum annealing requires a more robust description of the thermally populated mixed quantum states and the open dynamical processes that govern population of the sought-after eigenstate. + +The mapping of ILPs to QUBOs we propose is realized by introducing slack variables $s_a$ which turn the inequalities Eq.~\eqref{eq:ilp-constraints} to equalities +\begin{align} + \label{eq:ilp:slack} + & \sum_i A_{a i}x_i + s_a + b_a = 0, \\ + & x_i, s_a \in \mathbb{Z} \geq 0. +\end{align} +While, in general, the coefficients of the inequality constraints are not required to be integer valued, this real valued inequalities can be trivially rescaled such that $s_i \in \mathbbm{Z}$ given fixed precision coefficients $A_{ij}$ and $b_i$. +Furthermore, this formalism can be generalized to constrained quadratic optimizations \ref{sec:methods:ilp:quadratic}. + +We improve the quantum annealer's performance by utilizing annealing offsets, which effectively delay the annealing schedule on a per-qubit basis~\cite{PhysRevA.96.042322,hsu2018quantum,10.1007/978-3-030-14082-3_14,2020RPPh...83e4401H}. +Converting to the Ising representation of the the problem Hamiltonian, +\begin{equation} + \label{eq:HIsing} + H^{\textrm{problem}} \leftrightarrow H^{\textrm{Ising}} = \sum_{ij} J_{ij} \sigma^z_i \sigma^z_j + \sum_i h_i \sigma^z_i , +\end{equation} +we recognize that Eq.~(\ref{eq:HIsing}) exhibits spin-glass properties. More specifically, if the $h_i$ coefficients are randomly drawn from a Bernoulli distribution, one expects spin-localization behavior to influence the outcome of the anneal. +In the case of quantum annealing, when an algorithm is mapped to its Ising representation, the values of $h_i$ will frequently take on various values, mimicking spin-glass like behavior. +More explicitly, the spin-glass enters a glassy state when more disorder is introduced ($|h_i|$ becomes large), and as a consequence, the wavefunction experiences many body localization (MBL) effects, the many-body analog of Anderson localization~\cite{doi:10.1146/annurev-conmatphys-031214-014726,PhysRevE.90.022103,RevModPhys.91.021001,ALET2018498,PhysRevB.82.174411,PhysRevLett.109.017202}. + +Our improvement strategy is motivated by the MBL hypothesis. +As a result, we employ a modified annealing schedule that relies on partitioning the Hamiltonian into regions of relatively weak and strong external magnetic fields. + + +To understand which phenomena are relevant for describing the proposed offset study's scaling behavior, whether they are rooted in the quantum nature or related to hardware constraints, we simulate the anneal for a small MDS problem. This simulation solves the von Neumann equations accounting for different quantum decoherence models and explores whether algorithmic improvements on hardware are present in idealized systems. + +%======================================================================================== +\section{RESULTS} +\label{sec:results} +%======================================================================================== + +We first present the QUBO mapping for ILP (\ref{sec:results:qa1}), and demonstrate the methodology on an example implementation in case of the Minimal Dominating Set problem (\ref{sec:results:qa}) on the D-Wave quantum annealer. Results from quantum annealing are compared and discussed in contrast to simulations (\ref{sec:results:simulation}). + +%---------------------------------------------------------------------------------------- +\subsection{QUBO Formulation of ILP} +\label{sec:results:qa1} +%---------------------------------------------------------------------------------------- +Following Eq.~(\ref{eq:ilp:slack}), the ILP problems simplifies to solving a system of linear equations on integer valued variables. We map the integer variables $\vec z = \vec x, \vec s$ appearing in Eq.~\eqref{eq:ilp:slack} to qubits under the following transformation~\cite{Chang:2018uoc} +\begin{align} + z_i = & \sum_{r=0}^{R_i-1} 2^r \psi_{ri} + \label{eq:int_to_bin} +\end{align} +where $\psi_{ri} \in \{0, 1\}$. The number of qubits used to represent the $i$-th integer variable is allowed to vary with $R_i$. +The integer-vector qubit transformation can be expressed as a rectangular matrix. +For example, a vector of two integer variables $z_0$ and $z_1$ represented by one and two qubits respectively is given as +\begin{align} + \begin{pmatrix} + z_0 \\ + z_1 + \end{pmatrix} + = & + \begin{pmatrix} + 2^0 & 0 & 0 \\ + 0 & 2^0 & 2^1 + \end{pmatrix} + \begin{pmatrix} + \psi_{00} \\ + \psi_{01} \\ + \psi_{11} + \end{pmatrix} + \equiv T^z \begin{pmatrix} + \psi_{00} \\ + \psi_{01} \\ + \psi_{11} + \end{pmatrix} +\end{align} +If all variables are represented by the same number of qubits--$R_i$ is a constant for all $i$--then one can express the transformation as tensor product of bit vectors +\begin{align} + \mathcal{R} = & \begin{pmatrix} 2^0 & \dots & 2^{R-1}\end{pmatrix}, \\ + \mathcal{Z} = & \begin{pmatrix} z_0 & \dots & z_{N-1}\end{pmatrix}, \\ + |\mathds{1}| = & |\mathcal{Z}|, \\ + T^z = & \mathds{1}\otimes \mathcal{R}. +\end{align} + +As a result, the $\vec x$ and $\vec s$ map to the binary vector $\vec \Psi$ under the transformation +\begin{equation} + \label{eq:bit-vector-mapping} + \begin{pmatrix} + \vec x \\ \vec s + \end{pmatrix} + = + \begin{pmatrix} + T_x & 0 \\ 0 & T_s + \end{pmatrix} + \begin{pmatrix} + \vec \Psi_x \\ \vec \Psi_s + \end{pmatrix} + = + T + \vec \Psi +\end{equation} + +The integer linear optimization problem is then solved through the minimization of the quadratic objective function +\begin{align} + \label{eq:ilp-slack-bit-energy} + \chi^2(\vec \Psi) + &= + \vec c^T T_x \vec \Psi_x + p \left\| A T_x \vec \Psi_x + T_s \vec \Psi_s + \vec b \right\|^2 +\end{align} +where $p$ is an external parameter representing the strength of the penalty when violating constraints. +This parameter needs to be sufficiently large, e.g., $p \geq \vec c \cdot \vec x$, to ensure the constraints are indeed fulfilled\footnote{Depending on the problem, $p$ can be smaller as well. +For example, in the case of the MDS, $p\geq 1$ suffices.}. +The objective function $\chi^2$ can be represented as a QUBO Hamiltonian +\begin{align} + \chi^2(\vec \Psi) = & + \vec \Psi^T + \begin{pmatrix} + Q_{xx} & Q_{xs} \\ + Q_{sx} & Q_{ss} + \end{pmatrix} + \vec \Psi + p\left \| \vec b \right\|^2, \\ + \equiv & \vec \Psi^T Q \vec \Psi + C, + \label{eq:matrix_form} +\end{align} +where +{\small +\begin{align} + \label{eq:qubo:components} + Q_{xx} = & p {T_{x}}^T \left[ A^T A + \mathrm{diag} \left(A^T \vec b + \vec b^T A\right) \right] T_x + \mathrm{diag}(\vec c) T_x, \\ + Q_{xs} = & Q_{sx}^T = p {T_{x}}^T A^T T_s, \\ + Q_{ss} = & p\left[ {T_{s}}^T T_s + \mathrm{diag}\left( {T_{s}}^T \vec b + \vec b^T T_s\right) \right]. +\end{align}} +The function $\mathrm{diag}(\vec v)$ transforms a vector $\vec v$ into a diagonal matrix, and absorbs the linear contributions of the QUBO into the diagonal elements of the quadratic representation. + +The integer solution to the original ILP is computed by $\vec x^{(0)} = T_x \vec \Psi_x^{(0)}$ and the original solution to the problem is computed by shifting the annealer extracted energy $E \equiv \chi^2(\vec \Psi^{(0)}) $ by $p \left \| \vec b \right\|^2$. +The slack components of this vector $\vec \Psi_s$ can be utilized to check if the constraints are indeed fulfilled. + +%---------------------------------------------------------------------------------------- +\subsection{Annealer Results for the Dominating Set} +\label{sec:results:qa} +%---------------------------------------------------------------------------------------- +\begin{figure}[b] + \centering + \begin{tabular}{cc} + $G(n):$ & + \raisebox{-.4\height}{\includegraphics[width=0.8\columnwidth]{./linear_graph.pdf}} + \end{tabular} + \caption{Linear graphs $G(n)$ used in this study. Nodes denote vertices of the graphs and lines are undirected edges.} +\label{fig:linear} +\end{figure} + +We demonstrate the proposed algorithm in order to obtain the MDS on a series of linear graphs $G(n)$, as shown in Fig.~\ref{fig:linear}. This type of graph is chosen because the small number of nearest-neighbor connections is more efficiently embedded into the chimera graph, allowing scaling plots to be generated when using a D-Wave quantum annealer. In particular, the number of qubits required to solve MDS scales at worse as $n_V \log_2 n_V$ where $n_V$ is the number of vertices for a generic graph before minor embedding. Details of the mapping of ILP to MDS is given in Sec.~\ref{sec:methods:mds-qubo}. + +For the graph $G(n)$ the MDS solution is known analytically, and contains both unique and degenerate solutions. In particular, the domination number for $G(n)$ is $\lceil n/3 \rceil$ while the number of MDS solutions for $n$ vertices is +\begin{align} +&1 &&\textrm{if} && n\textrm{ mod }3=0,\nonumber \\ +&2\lfloor n/3 \rfloor + 1 && \textrm{if}&& n\textrm{ mod }3=1,\nonumber \\ +&\lfloor n/3 \rfloor + 2 && \textrm{if} && n \textrm{ mod }3 = 2, +\end{align} +and gives the probability of randomly guessing the MDS of $G(n)$. + +For even the smallest graph $G(2)$, the MDS problem is not native to the chimera graph and must be embedded. Following the hypothesis of MBL, we, therefore, must look at the values of $h_i$ after embedding. The qubits split into two groups depending on the value of $h_i$ relative to $(\textrm{max}|\{h\}| + \textrm{min}|\{h\}|) / 2$ given the set of external magnetic fields $\{h\}$ defined by a specific embedding. Further detail is given in Sec.~\ref{sec:methods:minor_embedding}. We study the effects of delaying the anneal schedule of one group of qubits over the other and present the results of this study is shown in Fig.~\ref{fig:baseline}. + +Due to near-term limitations, hardware realizations of quantum annealing are unique, and possess for example, different lattice layouts (due to faulty qubits), annealing schedules, and qubit fidelity. For the following studies, we perform experiments specifically on the \texttt{DW\_2000Q\_6} solver. The annealing time is set to 500$\mu$s after performing a study on various annealing times the $G(6)$ graph. The black line (offset$=0.0$) in Fig.~\ref{fig:baseline} shows results from the baseline experiment, without modification to the D-Wave annealing schedule, and observe improvement over random guessing (dashed green). + +\begin{figure} + \centering + \includegraphics[width=\columnwidth]{./DWave_scaling.pdf} + \caption{Baseline result of D-Wave (black) compared to random guessing (dashed green). The jagged nature of random guessing reflects the degeneracy of the ground state. Negative offsets with a `s' tag (blue) are results from delays of large values of $|h_i|$, while negative offsets with the `w' label (red) delay the schedule of qubits with small values of $h_i$.} + \label{fig:baseline} +\end{figure} + +We explore one avenue towards improving the experiment results by introducing per-qubit annealing offsets into the time evolution. +The blue (red) results delay qubits' annealing subject to stronger (weaker) external fields. We observe improvement (diminishment) in the experimental results when qubits subject to stronger (weaker) final external fields are delayed in the annealing schedule, in agreement with the MBL hypothesis. The phenomena is observed across different problem sizes and hints at the possibility of a generic improvement strategy. + + +%---------------------------------------------------------------------------------------- +\subsection{Simulation Results} +%---------------------------------------------------------------------------------------- +\label{sec:results:simulation} +To understand the effects of annealing offsets, we simulate the annealing process for the $G(2)$ graph embedded in chimera topography. +We repeat the same anneal process with a shortend total annealing time of 1 $\mu s$, reducing the computational demands of the simulation, and count the number of correct ground state occurrences. +The resulting ground state probability as a function of offset measured over 100,000 observations is shown in Fig.~\ref{fig:dwave1us}. + +\begin{figure}[b] + \centering + \includegraphics[width=\columnwidth]{./NN2_offset_scaling.pdf} + \caption{The probability of finding the MDS for $G(2)$ from D-Wave (black) and simulation (dashed yellow) at annealing times of 1 $\mu s$.} + \label{fig:dwave1us} +\end{figure} + + +To solve for time evolution dynamics of quantum annealing including thermal and the decoherence effects, we solve for the master equation in Lindblad form +\begin{align} + \label{eq:sim:linblad-eq} + \partial_t \rho (t) = \frac{-i}{\hbar} [H(t) , \rho(t)] + \mathcal{L}(\rho(t), H(t)) +\end{align} +where $\hbar$ is the reduced Plank's constant, $\rho (t)$ is the density matrix at time $t$, $H(t)$ is the time-dependent Hamiltonian and $\mathcal{L}$ is the Linblad operator implementing the decoherence models. +In this work, we consider two types of decoherence models: full-counting statistics~\cite{PhysRevE.90.022103,RevModPhys.81.1665} and single-qubit amplitude damping (local damping)~\cite{10.5555/1972505,preskill1998lecture}. +The full-counting statistics term models the global decoherence to all the qubits due to the classical reservoir. +The local damping term models the decoherence of each qubit independently. +Details of the master equation are given in Sec.~\ref{sec:methods:lindblad}. +Implementation of the annealing schedule and annealing offsets for the simulation are discussed in Sec.~\ref{sec:methods:annealing-schedule}. + +The graph $G(2)$ has degenerate ground states depending on whether qubit 0 or 1 is chosen to be the MDS solution. +This degeneracy is reflected in the experimental result and provides a non-trivial benchmark for our simulation. +Fig.~\ref{fig:final_state_distribution} show the final state distribution of the three lowest-lying state. +The states $(0, 1, 0, 0, 0)$ and $(1, 0, 0, 1, 0)$ are the two degenerate ground states of the embedded Hamiltonian, while $(1, 1, 1, 1, 1)$ is the first excited state which yields an incorrect solution\footnote{According to Eq.~\eqref{eq:bit-vector-mapping}, the first two vector components represent the nodes of the graph while the following components represent the slack variables after embedding.}. +All other states receive negligible probability at the end of annealing. +The simulation (black) captures the main features of the experimental result: +\begin{enumerate} + \item Significant probability of populating both ground states (rather than populating only one) + \item Asymmetry in ground state population due to offsets and spanning approximately the correct range + \item Population of first excited state with systematically lower probability when the strong field is delayed +\end{enumerate} +The asymmetry in the ground state distribution at non-zero offset results from annealing offsets lifting the ground state degeneracy. +The non-degenerate ground state switches between the two states within the broken symmetry, depending on which qubit group is delayed. At zero offset, a slight asymmetry exists in the simulation because the Hamiltonian is only degenerate at the last moment, while the D-Wave is also subject to sampling bias~\cite{2016PhRvA..93e2320K, 2017PhRvL.118g0502M}. + +This result can be obtained by tuning three free parameters: the simulation temperature to the order of 10 milliKelvin, and the two coefficients of the two decoherence models at the order of 1 to 10 $ns$. These values are consistent with the reported D-Wave operating temperature~\cite{dwave_temp} and coherence times for flux qubits~\cite{2003Sci...299.1869C}. +Additional insights of the simulation are given in Sec.~\ref{sec:discussion:time_evolution}. + +The resulting probability of recovering the correct solution as a function of annealing offset is given in Fig.~\ref{fig:dwave1us}. +We confirm that the simulation's offset-scaling follows the experiment's scaling, which suggests that the improvements are related to quantum mechanics. +An additional study where an extended annealing schedule is employed in the simulation, which removes systematic errors introduced by annealing offsets and effects of local damping are presented in Sec.~\ref{sec:discussion:idealqa}, and further supports this observation. + +\begin{figure} + \centering + \includegraphics[width=\columnwidth]{./final_state_distribution.pdf} + \caption{Final state distribution from D-Wave (solid bars) and simulation (black outline). The colors label the type of offset The $(0, 1, 0, 0, 0)$ state is the first solution where vertex 1 is in the dominating set. The $(1, 0, 0, 1, 0)$ state is the second solution where vertex 0 is in the dominating set. The first excited state is the $(1, 1, 1, 1, 1)$ state where both vertices are in the dominating set.} + \label{fig:final_state_distribution} +\end{figure} + + +\section{Discussion} +\subsection{Dynamics of Time Evolution} +\label{sec:discussion:time_evolution} + +The time-dependent overlap with the exact Ising ground state is shown in Fig.~\ref{fig:td_prob} from applying the simulator to $G(2)$. We observe for all cases that the system undergoes what is analogous to a magnetic phase transition around $s\sim 0.4$. +After the phase transition, we can confirm that the system collapses to effectively a classical state in the sense that the density matrix becomes a diagonal matrix. +The steady increase in probability after the phase transition is a sensitive balance between the competing effects between full-counting statistics and local damping. +In our example, the full-counting statistics decoherance rate is tuned to be slightly stronger compared to the local dampening decoherance rate, effectively resulting in a final thermal annealing process after the phase transition. +If local damping were relatively larger, then the probability after the phase transition will slowly decrease as the system decoheres into its local ground state. +While we believe both effects are essential to simulate D-Wave, due to the competing effects of both decoherence models, we emphasize that a fully quantitative comparison of both decoherence models cannot be made just considering the $G(2)$ graph. +However, we emphasize that the simulation suggests that the ground state is recovered predominantly due to the quantum phase transition happing around $s\sim 0.4$. + +\begin{figure} + \centering + \includegraphics[width=\columnwidth]{./time_dependent_probability.pdf} + \caption{Time-dependent probability for resolving the ground state for simulation results presented in Sec.~\ref{sec:results:simulation}. Different offsets are labeled in the same way as Fig.~\ref{fig:baseline}.} + \label{fig:td_prob} +\end{figure} + +Finally, we comment that effects of full-counting statistics are required for the simulation to obtain the final state distribution shown in Fig.~\ref{fig:final_state_distribution}. +Because of the smallness of the $G(2)$ problem (and the utilized total annealing time of 1$\mu s$), the annealing offsets lift the ground state degeneracy in a manor that diabatic transitions do not occur--setting a discrete, fixed groundstate probability for given offsets. +Thus, if dynamical thermalization effects were absent, the simulation would populate predominantly one of the two unique ground states depending on the offsets. +Once dynamical thermalization effects are present, the final state distribution continously depends on offsets and becomes a very sensitive observable to tune the simulation temperature, which, if properly tuned, agrees well with the experimental operating temperature. + + +\subsection{Idealized Quantum Annealing} +\label{sec:discussion:idealqa} + +\begin{figure*} + \centering + \begin{tabular}{p{0.5\textwidth}p{0.5\textwidth}} + \includegraphics[width=0.5\textwidth]{./anneal_schedule_extended.pdf} + & + \includegraphics[width=0.5\textwidth]{./NN2_offset_scaling_extended.pdf}\\ + \centering \textbf{a} & \centering \textbf{b} + \end{tabular} + \centering + \caption{Extended annealing schedule and simulation result. \textbf{a)} The annealing time is increased by 10\% at both the start and end, and the initial values of $A(s)$ and $B(s)$ at non-zero offset are also not extrapolated in comparison to Fig.~\ref{fig:anneal_schedule}. Therefore, the initial and final Hamiltonian are no longer suffer systematic error at non-zero offset. \textbf{b)} The default (dashed yellow) result is one presented in Fig.~\ref{fig:dwave1us}. Results from extended schedules are presented shown with solid lines with full-counting statistics and amplitude damping (red), only full-counting-statistics (blue), and only amplitude damping (green). + } + \label{fig:anneal_schedule_ext} +\end{figure*} + +In the simulation, we also reserve the ability to remove systematic errors associated with finite annealing schedules by extending them, as shown by the red data points in Fig.~\ref{fig:anneal_schedule_ext}. With the extended schedule, all qubits start and end with the same values of $A$ and $B$ and faithfully preserves the initial and final Hamiltonians. The dependence on offset for $G(2)$ (Fig.~\ref{fig:dwave1us}) remains the same under the extended anneal schedule (Fig.~\ref{fig:anneal_schedule_ext}), confirming that the behavior is not a systematic artifact. + +The quantum system can be further idealized by including either solely the full-counting statistics model (blue) or solely the local decoherence model (green)\footnote{For problems without diabatic transitions, like the MDS problem for a $G(2)$ graph and an anneal time of $1\mu s$, removing all decoherence models results in ground state probabilities equal to unity.}. We observe in both cases that the overall scaling follows the story of the MBL hypothesis. Perhaps more importantly, we observe that a simulation without local decoherence, where the relaxation is dependent on precisely the instantaneous value of $|h_i|$, exhibits the same scaling as the experiment. This result suggests that our strategy for setting annealing offsets is improving the algorithm beyond the simple explanation of qubits freezing due to single-particle amplitude damping. The simulation with only amplitude damping (green) does not fully capture the results of the experiment. We observe hints of a phase transition depending on the offset (which may be considered some measure of disorder) when dynamical thermalization effects are removed. This observation is a strong evidence for the inclusion of the full-counting statistics model. + +\subsection{Final Remarks} +\label{sec:results:final} +We want to emphasize that while the annealing offsets are motivated by the MBL hypothesis, and the results also follow those expectations, we do not have definitive proof that MBL plays a crucial role. +Observations of MBL inevitably require the study of finite-size scaling~\cite{2015PhRvB..91h1103L}, and our current simulation, while being extremely thorough and explicit, is exponentially slow to evaluate, making evaluations of even $G(3)$ unfeasible. +However, the intersection of time-dependent quantum mechanics and emergent phenomena~\cite{Goldenfeld:1992qy} is an exciting direction that is pertinent to adiabatic quantum computing. + +%======================================================================================== +\section{METHODS} +\label{sec:methods} +%======================================================================================== +%---------------------------------------------------------------------------------------- +\subsection{Additional Mappings to QUBO} +\label{sec:methods:ILP-to-QUBO} +%---------------------------------------------------------------------------------------- +%---------------------------------------------------------------------------------------- +\subsubsection{Minimum Dominating Set QUBO} +\label{sec:methods:mds-qubo} +%---------------------------------------------------------------------------------------- + +The solution to the MDS problem can be expressed as an integer optimization problem given by, +\begin{align} + f(\vec x) = & \min\left(\sum_{v \in V} x_v\right), \\ +\end{align} +subject to +\begin{align} + & x_v + \sum_{j \in \mathcal{N}(v)} x_j \geq 1, \\ + & x_v \in \{0, 1\} +\end{align} +where $\mathcal{N}(v)$ represents the set of all direct neighbors of vertex $v$ and the dimension of the dependent variable $x$ is the number of vertices $n_V \equiv \overline{\overline{V}}$. +The problem minimizes the number of vertices in $D$ with a binary variable $\vec x = \vec \Psi_x$ encoded by single qubit, subject to the constraint that at least one vertex in $\mathcal{N}(\nu)$ is in $D$. +For each vertex in $V$ we introduce slack variables +\begin{equation} + \vec s \in \left\{ \mathbb{Z}^{n_V} \, \middle| \, 0 \leq s_{v} \leq |\mathcal{N}(v)| \quad \forall v\in V \right\} \, , +\end{equation} +which is related to the qubit vector $\vec \Psi_s$ by $\vec s = T_s \vec \Psi_s$. +The inequality constraint is encoded by +\begin{align} + f(\vec \Psi_x) + = + & \min\left(\vec 1 \cdot \vec \Psi_x \right) \, , +\end{align} +subject to +\begin{align} + & + (\mathbbm{1} + J)\vec \Psi_x - T_s \Psi_s - \vec 1 = 0\,, + \\ + & + (\vec \Psi_s)_\nu \in \{ 0, 1\} +\end{align} +where the nearest-neighbor sum is expressed by the adjacency matrix $J$ (zero diagonal and symmetric for non-directional graphs). +The algorithm uses +\begin{equation} + N_q = \overline{\overline{V}} + \sum_{v \in V} \log_2 \mathcal{N}(v) +\end{equation} +qubits to encode the vertices and slack variables before embedding. +Therefore, the (logical) binary vector $\vec \Psi$ at worst scales with $n_V \log_2 n_V$ qubits for fully connected graphs. + +The target QUBO in the notation of Eq.~\eqref{eq:matrix_form} reads + {\small + \begin{align} + Q_{xx} & = \mathbbm{1} + p\left[J^T J + J^T + J - \mathrm{diag}\left(J^T \vec 1 + \vec 1^T J\right) - \mathbbm{1} \right] \,, \\ + Q_{sx} & = - p(\mathbbm{1}+J)^TT_s\,, \\ + Q_{ss} & = p\left[{T_s}^T T_s + \mathrm{diag}\left(T_s^T \vec 1 + \vec 1^T T_s\right)\right]\,, \\ + C & = p \overline{\overline{V}}\,. + \end{align}} + +%---------------------------------------------------------------------------------------- +\subsubsection{Integer Quadratic Optimization} +\label{sec:methods:ilp:quadratic} +%---------------------------------------------------------------------------------------- + +Because quantum annealing is capable of solving quadratic problems, we extend the proposed algorithm to solve integer quadratic optimization problems as well such that +\begin{align} + \vec x_0 = \mathrm{arg}\min\limits_{x}\left(\sum_{ij} x_i d_{ij} x_j + \sum_i c_i x_i\right) +\end{align} +without the introduction of auxiliary qubits. + +In this case the $Q_{xx}$ component of the QUBO, Eq.~\eqref{eq:qubo:components} obtains a new term +\begin{equation} + Q_{xx} \to Q_{xx} + T_x^T d T_x \, . +\end{equation} + +%---------------------------------------------------------------------------------------- +\subsection{ILP on the D-Wave} +\label{sec:methods:ILP-on-D-Wave} +%---------------------------------------------------------------------------------------- + +%---------------------------------------------------------------------------------------- +\subsubsection{Comment on ILP QUBO Penalty Term} +\label{sec:methods:ilp-qubo-comments} +%---------------------------------------------------------------------------------------- + +The minimal energy solution to Eq.~\eqref{eq:initial-ip-def} and Eq.~\eqref{eq:ilp-slack-bit-energy} are exactly the same if the penalty term is greater or equal to the energy gap of the first excited solution: $p \geq E_1 - E_0$. +Thus some knowledge of the problem is required. +In principle, it is possible to set the penalty term arbitrarily large, at the cost of problem resolution: large values for $p$ increase the highest available energy of the system by multiples of $p$. +After normalization of the QUBO, this corresponds to decreasing the energy gap between the ground state and the first excited state. +Thus, if solvers have finite precision, one must estimate reasonable values for $p$: for large $p$ more solutions fulfill the constraints, while for small $p$, more solutions minimize the objective function. + +%---------------------------------------------------------------------------------------- +\subsubsection{Minor Embedding} +\label{sec:methods:minor_embedding} +%---------------------------------------------------------------------------------------- +Our proposed offset strategy is motivated by the structure of the Hamiltonian being evaluated by the annealer. +As a result, details of the embedding are important. We obtain an embedding for $G(n)$ with the \texttt{embed\_qubo} function provided by the D-Wave Ocean Python package~\cite{dwave_oceans} under the \texttt{dwave.embedding} module~\cite{2008arXiv0804.4884C}. +The same embedding is used for all D-Wave solves of the same graph (independent of offset), and consequently the simulation solves the resulting embedded Hamiltonian for $G(2)$. +Additionally, solving the same graph as a function of offset on the exact same qubits removes (or at least keeps consistent) the systematic effects due to solving a problem on different physical qubits. +We note that comparisons between different graphs in Fig.~\ref{fig:baseline} are subject to this uncontrolled systematic. + +After embedding the QUBO for $G(2)$ requires 5 qubits (an increase from 4), where by construction, qubits 0 and 3 form the qubit chain. +We confirm through brute force evaluation of the eigenvalue decomposition of the 5 qubit Hamiltonian, that the embedding provided by D-Wave solves the expected ILP problem for $G(2)$, with degenerate ground states at $(0, 1, 0, 0, 0)$ and $(1, 0, 0, 1, 0)$ corresponding to whether vertex 0 or 1 is chosen for the MDS solution, and $(1, 1, 1, 1, 1)$ as the first (non-degenerate) excited state where both vertex 1 and 0 are in the set yielding a valid dominating set but not the MDS. + +The resulting Ising Hamiltonian has external field equal to $h = (2.75, 1.5, -1.0, -1.25, -1.0)$. +Following the offset strategy described in Sec.~\ref{sec:results:qa}, qubit(s) 0 (1, 2, 3, 4) are placed in the set with relatively stronger (weaker) final external fields. +This imbalance in the two groups may perhaps explain the reason why effects of delaying the weaker fields are more pronounced, since delaying the strong fields only differs from the baseline by a single qubit. + + + +%---------------------------------------------------------------------------------------- +\subsection{Simulation of a Quantum Annealer} +\label{sec:methods:simulation} +%---------------------------------------------------------------------------------------- + +%---------------------------------------------------------------------------------------- +\subsubsection{The Lindblad Equation} +\label{sec:methods:lindblad} +%---------------------------------------------------------------------------------------- + +To solve for time evolution dynamics of quantum annealing including thermal and the decoherence effects, we evaluate the master equation Eq.~\eqref{eq:sim:linblad-eq} in Lindblad form. +The explicit time-dependence of the Hamiltonian is given by +\begin{align} + \label{eq:annealH} + H(t) = & - \sum_i A_i(t)\sigma^x_i +\sum_i B_{i}(t) h_i \sigma^z_i \notag \\ + & + \sum_{i>j} \sqrt{B_{i}(t)B_{j}(t)} J_{ij} \sigma^z_i \sigma^z_j , +\end{align} +where $A_i(t)$ and $B_{i}(t)$ are site-dependent annealing schedule functions. +The site dependency takes into account of the annealing offsets. +The simulation takes two decoherance models into account. +Full-counting statistics and local decoherence. + +For full-counting statistics, the Lindblad operator is +\begin{align} +\mathcal{L}_{\textrm{fc}}(\rho (t), H(t)) = & \Gamma_{\textrm{fc}} \sum_{j, i0$, $S_{ij}=|E_i \rangle \langle E_j|$ denotes the many-body lowering operator and $\Gamma_{fc} = 1/T_{fc}$ is the full-counting decoherence rate for coherence time $T_{fc}$. +That is, due to the interaction with the classical thermal bath, there is a probability that the system hops from each higher-energy many-body state to a lower-energy many-body state. +The probability of the inverse process is given by a Boltzmann factor. + +To model the local decoherence of each qubits in the non-interacting limit, we also consider the amplitude damping for non-interacting qubits. +For the local decoherance model, the Lindblad operator is +\begin{align} +\mathcal{L}_{\textrm{loc}}(\rho (t), H(t)) = & \Gamma_{\textrm{loc}} \sum_j \left(2L_j \rho(t) L_j^\dagger - \{ L^\dagger_j L_j, \rho(t) \} \right)\notag \\ +& + e^{- 2 \beta |h_j| } \left(2L_j^\dagger \rho(t) L_j - \{ L_j L_j^\dagger, \rho(t) \} \right) , +\end{align} +where $j$ is the index for qubit. +$L_j= \sigma^{+}_j=|1\rangle \langle 0|$ for $h_j>0$ and $L_j= \sigma^{-}_j=|0\rangle \langle 1|$ for $h_j<0$. +That is, each qubit is damped toward its local ground state if we ignore all the interactions. + +The initial condition is the Gibbs canonical ensemble +\begin{equation} +\rho (0) = \frac{e^{-\beta H(0)}}{\mbox{Tr}\left(e^{-\beta H(0)}\right)} , +\end{equation} +where $\beta$ is the inverse temperature. +The probability to get the ground state at measurement is +\begin{align} +P = \mbox{Tr} \left( \rho (t) \pi_{\mbox{gnd}} \right) , +\end{align} +where the projection operator onto the degenerated ground states subspace is defined as $\pi_{\mbox{gnd}}=\sum_{i\in G} |\mbox{gnd}_i\rangle \langle \mbox{gnd}_i| $. +Here $\{ | \mbox{gnd}_i \rangle | i \in G \}$ forms an orthonormal basis for the degenerated ground states subspace, i.e., $\langle \mbox{gnd}_j | \mbox{gnd}_i \rangle = \delta_{ij}$. + +For the simulation results presented, we set the temperature to 22.5 milliKelvin. +The coherence time for local decoherence is set to 15$ns$, and 1$ns$ for full-counting statistics. + +%---------------------------------------------------------------------------------------- +\subsubsection{Annealing Schedule and Offsets} +\label{sec:methods:annealing-schedule} +%---------------------------------------------------------------------------------------- +In this section, we discuss the details of the annealing schedule with respect to the dimensionless normalized time $s$. +On D-Wave solvers, annealing offsets effectively advance or delay the annealing schedule of individual qubits (see E.~\eqref{eq:annealH}). +In Fig.~\ref{fig:anneal_schedule}, the default D-Wave annealing schedule is shown in black, in addition to the effects of applying negative offsets (effective time delay) to $A(s)$ and $B(s)$ in blue. +Further documentation is provided by D-Wave in Ref.~\cite{dwave_as, dwave_as_docu}. + +\begin{figure}[htb] + \centering + \includegraphics[width=\columnwidth]{./anneal_schedule.pdf} + \caption{ + Anneal schedules for amplitudes of initial Hamiltonian (dashed) and final Hamiltonian (solid). + Offset 0.0 (black) and -0.05 (purple) are displayed. + Intermediate values lie between and are suppressed for clarity. + } + \label{fig:anneal_schedule} +\end{figure} + +The coefficients $A(s)$ and $B(s)$ follow the underlying control variable $c(s)$, which is designed to grow the persistent current $I_p(s)$ linearly in time. +The effective time delay is implemented by introducing an offset as $c(s) + \delta$. +Because annealing schedules are finite, systematic errors are introduced because the final values of $A(s)$ and $B(s)$ will differ for qubits with different offsets. +Additionally, the values of the coefficients are unknown outside of $s\in [0, 1]$. +We only employ negative offsets such that this unkonwn coefficient range, approximated by a linear extrapolation, only enters at the beginning of the annealing process. + +We verify that our implementation of annealing offsets on the simulator is consistent with D-Wave by solving the following three qubit Hamiltonian +\begin{align} + \label{eq:offset_test_hamiltonian} + H^{\textrm{problem}} = + \begin{pmatrix} + -0.25 & 1 & 0 \\ + 0 & -0.25 & 0 \\ + 0 & 0 & -0.25 + \end{pmatrix} +\end{align} +which has a doubly-degenerate ground state of $(0, 1, 1)$ and $(1, 0, 1)$. An annealing offset is then applied to either qubit 0 or 1, and thus breaks the ground state degeneracy of the system. Because of the systematic error introduced when assigning an offset to a qubit, the final Hamiltonian given by Eq.~(\ref{eq:annealH}) will have small deviations from the input problem Hamiltonian. For example, we expect a negative offset to qubit 0 to Eq.~(\ref{eq:offset_test_hamiltonian}) will yield $(1, 0, 1)$ as the unique ground state given Eq.~(\ref{eq:annealH}). + +We confirm that with different combinations of annealing offsets, the degeneracy is lifted on the D-Wave results as expected by solving for the modified problem Hamiltonian spectrum, as well as dialing in annealing offset in the simulation of this three qubit test case. + + +%---------------------------------------------------------------------------------------- +\subsubsection{Pure Transverse Field Simulation} +\label{sec:methods:simulation_details} +%---------------------------------------------------------------------------------------- +To check the correctness of simulator and unit conversion, we tested a simple annealing schedule for pure transverse field, i.e. $A(s)=A(0)$ and $B(s)=0$. +The initial state is pure zero state $\rho=|00...0\rangle \langle 00...0|$. +In this case the analytical solution can be obtained for the wave function oscillation. +The time-dependent probability is $P_{0}=\cos^{2n}(s)=\cos^{2n}(t/T)$ where $n$ is the number of qubits and $T$ is the annealing time. +For annealing time $T=1/A(0)$, we expect to see perfect one-period oscillation. The energy spectrum for this system can be analytically obtained, so we also checked the Boltzmann distribution in the initial density matrix construction. The oscillation is depicted in Fig.~\ref{figcheck}, where the simulation matches the expected theoretical behavior. + + +\begin{figure} + \centering + \includegraphics[width=\columnwidth]{./vacuum_probability.pdf} + \caption{Time-dependent vacuum probability of 5 qubits system under pure transverse field.} + \label{figcheck} +\end{figure} + + +%======================================================================================== +\section{DATA AVAILABILITY} +\label{sec:open-source} +%======================================================================================== +We provide access to all the software utilized and data presented in this publication in the associated GitHub repository~\cite{github:cchang5/quantum_linear_programming}. +The utilized software is contained in two installable Python modules: +\begin{itemize}[leftmargin=*] + \itemsep0em + \item[] \texttt{qlp} for mapping MDS problems to QUBOs and performing simulations, + \item[] \texttt{qlpdb} for interfacing and documenting simulation and experiment data through EspressoDB~\cite{Chang:2019khk}. +\end{itemize} +The data itself is stored in a SQLite file and associated repository subdirectories. +We provide further documentation in the repository \texttt{readme} file. + + +%======================================================================================== +\section{ACKNOWLEDGEMENTS} +%======================================================================================== + +We thank Long Gang Pang for initial discussions. +We thank David Johnson, Vlad Papish and the rest of D-Wave Support for answering detailed questions about the D-Wave annealer. + +This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, Quantum Horizons: QIS Research and Innovation for Nuclear Science under Award Number FWP-NQISCCAWL. +Lawrence Berkeley National Laboratory (LBNL) is operated by The Regents of the University of California (UC) for the U.S. Department of Energy (DOE) under Federal Prime Agreement DE-AC02-05CH11231. +C.K. gratefully acknowledges funding through the Alexander von Humboldt Foundation through a Feodor Lynen Research Fellowship. +This work used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725. +This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. +The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. (http://energy.gov/downloads/doe-public-access-plan). + + +%======================================================================================== +\section{AUTHOR CONTRIBUTIONS} +%======================================================================================== + +Initial idea was proposed by Chang. +Ostrowski guided the ILP problem selection. +All authors contributed to the design of test cases. +Calculations and code development for the D-Wave were performed by Chang and K\"orber. +Code for numerical simulations was developed by Chen and K\"orber, and cross-checked by Chang. +Simulations were performed by Chang and Chen. +Chang, Chen, K\"orber, and Humble interpreted the results. +All authors contributed to writing and editing of the final manuscript. + +%======================================================================================== +\section{ADDITIONAL INFORMATION} +%======================================================================================== + +\textbf{Competing Interests:} The authors declare no competing interests. + +\bibliographystyle{apsrev4-1} +\bibliography{main.bib} +%======================================================================================== +\end{document} diff --git a/paper/v1/mainNotes.bib b/paper/v1/mainNotes.bib new file mode 100644 index 0000000..e69de29 diff --git a/paper/v1/time_dependent_probability.pdf b/paper/v1/time_dependent_probability.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8aa4eecd3bb02a7778083c7d4d93cfcc19138f3b GIT binary patch literal 23297 zcmeFZby!qg`!7!C5RyYWG)PU*p>%g6C=A`*2-1iQh%|_Vgru~J3X($#N{WQir8I&l zdiLPs`}KLhp7%VzbIx`B{y7)dV(nOK-MQC&ueCq3x%8A&1YtrVBwW?Akg8`SFbEXl zY2!j7BLflELps{~Lg2s^1BkFuu$MhVSP|)mbn|qCT)s?V?_q~&DDhhd1*~1Yc_OrX0u8oVmtsg}EeDMEb2L=T${1QOk!^6|h7a#%jR|HtG z_W;f$e-5DPsIaZSXJ2f3^n*32WQi zIU^N3gMe`{#6+PY5V(W{hK3%di{CGe8QA-J`uo@dD#YmMUn<0C^*8-t*!jh;inAM_ zB8aex8=ylads|OCK;>HY9*%xa5E#ZX2AGb%em?d{caosISN8`~MV@%a9v{#&r_;MF 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