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arXiv · 2404.18226

A quantum compiler design method by using linear combinations of permutations

Ammar Daskin
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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.

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Ammar Daskin. 2024-04-28. A quantum compiler design method by using linear combinations of permutations. https://arxiv.org/abs/2404.18226

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