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arXiv · 2506.21455

An Iterative Methodology for Unitary Quantum Channel Search

Matthew M. Lin·Hao-Wei Huang·Bing-Ze Lu
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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.

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Matthew M. Lin, Hao-Wei Huang, Bing-Ze Lu. 2025-06-26. An Iterative Methodology for Unitary Quantum Channel Search. https://doi.org/10.1016/j.laa.2026.01.0170024-3795

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