Optimizing Mixed Quantum Channels via Projected Gradient Dynamics

TL;DR

This paper introduces a novel optimization method using projected gradient dynamics on the Stiefel manifold and simplex to efficiently identify mixed quantum channels from limited input-output data.

Contribution

It develops a new approach for quantum channel identification that guarantees convergence and handles multiple data pairs, improving over traditional full characterization methods.

Findings

Method guarantees convergence via Zariski topology

Numerical results show flexibility across scenarios

Efficiently identifies quantum channels with limited data

Abstract

Designing a mixed quantum channel is challenging due to the complexity of the transformations and the probabilistic mixtures of more straightforward channels involved. Fully characterizing a quantum channel generally requires preparing a complete set of input states, such as a basis for the state space, and measuring the corresponding output states. In this work, we begin by investigating a single input-output pair using projected gradient dynamics. This approach applies optimization flows constrained to the Stiefel manifold and the probabilistic simplex to identify the original quantum channel. The convergence of the flow is guaranteed by its relationship to the Zariski topology. We present numerical investigations of models adapted to various scenarios, including those with multiple input-output pairs, highlighting the flexibility and efficiency of our proposed method.