A Unified Blockwise Measurement Design for Learning Quantum Channels and Lindbladians via Low-Rank Matrix Sensing

TL;DR

This paper introduces a blockwise measurement design and matrix sensing approach for learning quantum channels and Lindbladians, providing theoretical guarantees and efficient algorithms validated by numerical experiments.

Contribution

It presents a novel blockwise measurement scheme and theoretical analysis for low-rank quantum superoperator recovery, extending matrix sensing techniques beyond positive semidefinite cases.

Findings

Near-optimal measurement count for superoperator recovery

Theoretical guarantees under restricted isometry property (RIP)

Validated efficiency and scalability through numerical experiments

Abstract

Quantum superoperator learning is a pivotal task in quantum information science, enabling accurate reconstruction of unknown quantum operations from measurement data. We propose a robust approach based on the matrix sensing techniques for quantum superoperator learning that extends beyond the positive semidefinite case, encompassing both quantum channels and Lindbladians. We first introduce a randomized measurement design using a near-optimal number of measurements. By leveraging the restricted isometry property (RIP), we provide theoretical guarantees for the identifiability and recovery of low-rank superoperators in the presence of noise. Additionally, we propose a blockwise measurement design that restricts the tomography to the sub-blocks, significantly enhancing performance while maintaining a comparable scale of measurements. We also provide a performance guarantee for this setup. Our approach employs alternating least squares (ALS) with acceleration for optimization in matrix sensing. Numerical experiments validate the efficiency and scalability of the proposed methods.