A quantum compiler design method by using linear combinations of permutations
<|reference_start|>A quantum compiler design method by using linear combinations of permutations: 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.<|reference_end|>
@article{daskin2024a,
    title={A quantum compiler design method by using linear combinations of
  permutations},
    author={Ammar Daskin},
    journal={arXiv preprint arXiv:2404.18226},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.18226},
    primaryClass={quant-ph cs.PL}
}