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

• URL: http://arxiv.org/abs/2501.14080v1
• Date: Thu, 23 Jan 2025 20:36:45 GMT
• Title: A Unified Blockwise Measurement Design for Learning Quantum Channels and Lindbladians via Low-Rank Matrix Sensing
• Authors: Quanjun Lang, Jianfeng Lu,
• Abstract summary: We propose a robust approach based on the matrix sensing techniques for quantum superoperator learning.<n>We provide theoretical guarantees for the identifiability and recovery of low-rank superoperators in the presence of noise.<n>Our approach employs alternating least squares (ALS) with acceleration for optimization in matrix sensing.
• Score: 5.266892492931388
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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