Finding Quantum Operators Through Machine Learning
QuLe (rhymes with "mule") is a program for generating quantum operators (in the form of unitary matrices) that map given input states to given output states of a quantum computer (as closely as possible). When combined with unitary factorization algorithms (as included in this repository and described in our paper), QuLe enables end-to-end synthesis of quantum algorithms: starting with a set of desired input/output pairs, the end result of our pipeline can be a quantum circuit diagram that closely approximates the desired behavior.
QuLe is introduced and explained in the research paper: (Coming Soon). Please cite our paper if you find our work useful.
QuLe has been test on Windows and Linux. Compilation on Mac should be possible, but will require (1) installing a suitable compiler that supports OpenMP (e.g., brew install gcc) and using that compiler for CMake (e.g., export CC=gcc-15 && export CXX=g++-15), and (2) ensuring paths for libraries like Armadillo are specified correctly. A PR is welcomed to make Mac work smoothly out of the box.
QuLe depends on:
- Armadillo
- Boost (Note, this can often be installed more easily via package managers like
aptorbrew)
Optionally, on Windows, you may build QuLe using Intel MKL.
One prerequisites are installed, you can build QuLe simply via:
cd ./src
cmake .
make -j
Sample Usage: ./qule --matrix_type rand --alpha 0.1 --method GDLM --n 6 --num_tests 5
- Matrix type can be of type: ex_const, rand, Had (Hadamard Gate), QFT (Quantum Fourier Transform), grover
- Method can be of type: GDP (Gradient Descent Penalty), GDP*, GDLM (Gradient Descent Lagrange Multipler), DLR (Delta Learning Rule), DLR*, and New (Newtons Method). (*'s represent unitary constraint).
- alpha is the learning rate
- n is the size of the nxn matrix
- num_tests is the number of iterations to run
A few flags are listed here. We recommend browsing the source code to see the most up-to-date list of flags and their meanings.
- sequential: if set, learns in sequential mode instead of batch
- matrix_analysis: if set, prints SVD and eig info about U and X
- cond_x: set condition bound of x, default is 1000
- num_x: set the number of training examples, default is n
- each_mat: will log the data for every matrix in a test (not just the average)
- condx_upper: sets an upper bound on the condition number of randomly generated X
- condx_lower: sets a lower bound on the condition number of randomly generated X
Please open an issue or pull request to provide feedback on the project.
QuLe is licensed under the University of Illinois / NCSA Open Source License. See LICENSE.md.
If you use QuLe in your research or would otherwise like to reference it, please use the following citation:
Yuxin Huang, Benjamin E. Grossman-Ponemon, David A. B. Hyde. "Automated Synthesis of Quantum Algorithms via Classical Numerical Techniques." ACM Transactions on Quantum Computing 6:4 (2025). https://doi.org/10.1145/3757068.
Please consider sponsorship to support further development and maintenance of QuLe.
