An Iterative Methodology for Unitary Quantum Channel Search

TL;DR

This paper introduces an iterative polar decomposition-based algorithm for efficiently identifying unitary quantum channels from input-output state pairs, with proven convergence and reduced search space.

Contribution

It presents a novel iterative method for quantum channel identification that leverages polar decomposition and reduces computational complexity.

Findings

The algorithm converges to a critical point that is a local minimum.

Using a single input-output pair with specific structure reduces the search space.

Unitary matrices describing the same channel differ by a phase factor.

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.