Efficient Self-Consistent Quantum Comb Tomography on the Product Stiefel Manifold

TL;DR

This paper introduces a scalable, self-consistent quantum comb tomography method using Riemannian optimization on the product Stiefel manifold, improving efficiency and robustness over traditional approaches.

Contribution

It unifies quantum comb, instrument set, and initial states into a single geometric framework on the product Stiefel manifold, enabling efficient unconstrained optimization.

Findings

Computational scalability demonstrated through simulations

Robustness against gate errors shown in numerical tests

Outperforms conventional isometry-based QCT methods

Abstract

Characterizing non-Markovian quantum dynamics is currently hindered by the self-inconsistency and high computational complexity of existing quantum comb tomography (QCT) methods. In this work, we propose a self-consistent framework that unifies the quantum comb, instrument set, and initial states into a single geometric entity, termed as the Comb-Instrument-State (CIS) set. We demonstrate that the CIS set naturally resides on a product Stiefel manifold, allowing the tomography problem to be solved via efficient unconstrained Riemannian optimization while automatically preserving physical constraints. Numerical simulations confirm that our approach is computationally scalable and robust against gate definition errors, significantly outperforming conventional isometry-based QCT methods. Our work indicates the potential to efficiently learn quantum comb with fewer computational resources.