A quantum compiler design method by using linear combinations of permutations
Abstract
A matrix can be converted into a doubly stochastic matrix by using two diagonal matrices. And a doubly stochastic matrix can be written as a sum of permutation matrices. In this paper, we describe a method to write a given generic matrix in terms of quantum gates based on the block encoding. In particular, we first show how to convert a matrix into doubly stochastic matrices and by using Birkhoff's algorithm, we express that matrix in terms of a linear combination of permutations which can be mapped to quantum circuits. We then discuss a few optimization techniques that can be applied in a possibly future quantum compiler software based on the method described here.
Cite
@article{arxiv.2404.18226,
title = {A quantum compiler design method by using linear combinations of permutations},
author = {Ammar Daskin},
journal= {arXiv preprint arXiv:2404.18226},
year = {2024}
}
Comments
related code https://github.com/adaskin/stochastic-matrix-into-permutations/