A quantum compiler design method by using linear combinations of permutations

• URL: http://arxiv.org/abs/2404.18226v1
• Date: Sun, 28 Apr 2024 15:42:37 GMT
• Title: A quantum compiler design method by using linear combinations of permutations
• Authors: Ammar Daskin,
• Abstract summary: We describe a method to write a given generic matrix in terms of quantum gates based on the block encoding. We first show how to convert a matrix into doubly 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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