An Iterative Methodology for Unitary Quantum Channel Search
Numerical Analysis
2025-06-27 v1 Numerical Analysis
Quantum Physics
Abstract
In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal solution obtained from our method using one pair with a specific structure will generate an equivalent class, significantly reducing the dimension of the searching space. Furthermore, we prove that the unitary matrices describing the same channel differ by a complex number with modulus 1. We rigorously prove our proposed algorithm can ultimately identify a critical point, which is also a local minimum of the established objective function.
Cite
@article{arxiv.2506.21455,
title = {An Iterative Methodology for Unitary Quantum Channel Search},
author = {Matthew M. Lin and Hao-Wei Huang and Bing-Ze Lu},
journal= {arXiv preprint arXiv:2506.21455},
year = {2025}
}