TysonRayJones / DensePauliDecomposer

Decomposing dense matrices into dense Pauli tensors

Tyson Jones

• Department of Materials, University of Oxford
• Institute of Physics, EPFL
• Quantum Motion Technologies Ltd

This repository contains a Python implementation of the algorithm presented by this manuscript for decomposing an arbitrary complex matrix into a weighted sum of Pauli strings. Our main algorithm is defined as function calcPauliCoeffFast() in our_method.py, with an optimised implementation defined as calcPauliCoeffFaster(). We include benchmarking in benchmarking.py against the PauliDecomposer with code modified from its source repo.

If this code is useful to you, feel free to cite

@misc{jones2024decomposing,
      title={Decomposing dense matrices into dense Pauli tensors}, 
      author={Tyson Jones},
      year={2024},
      eprint={2401.16378},
      archivePrefix={arXiv},
      primaryClass={quant-ph}
}

Usage

Using our algorithm requires a single import:

from our_method import calcPauliCoeffFaster

Given a complex matrix G with dimension 2^N-by-2^N, instantiated as a list-of-lists or as a numpy ndarray, you can call

c = calcPauliCoeffFaster(n, G, N)

to compute the complex coefficient c of the n-th Pauli tensor.

To compute a 4^N-length list of all coefficients, you can call

c_all = get_all_coefficients(G)

but beware that this loop has not been explicitly parallelised.

To perform the benchmarking, simply run

python3 benchmarking.py

which will log to file results.txt in a format which can be passed by Mathematica's Get[] function. Benchmarking can be interrupted at any time, preserving the results so far. To change the benchmarked configuration, edit the variables at the bottom of benchmarking.py.

License

This repository is licensed under the terms of the MIT license.