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An Efficient and Fast Quantum State Estimator With Sparse Disturbance.

Jiaojiao Zhang, Shuang Cong, Qing Ling

    IEEE Transactions on Cybernetics
    |July 12, 2018
    PubMed
    Summary
    This summary is machine-generated.

    Researchers developed an efficient algorithm to recover quantum states from noisy measurements. This method accurately reconstructs low-rank density matrices using robust principal component analysis (RPCA) and an inexact alternating direction method of multipliers (I-ADMM).

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    Area of Science:

    • Quantum information science
    • Quantum state estimation
    • Quantum computing

    Background:

    • Pure quantum states are represented by low-rank density matrices, which must be positive semidefinite, unit-trace, and Hermitian.
    • Quantum state estimation involves recovering these matrices from linear measurements, often corrupted by sparse noise.
    • Existing methods struggle with accuracy and efficiency when dealing with noisy and incomplete quantum state data.

    Purpose of the Study:

    • To develop an efficient and accurate method for recovering low-rank quantum density matrices from limited, noisy linear measurements.
    • To formulate the quantum state estimation problem as a constrained robust principal component analysis (RPCA) problem.
    • To propose and analyze an inexact alternating direction method of multipliers (I-ADMM) for solving this constrained RPCA problem.

    Main Methods:

    • Formulation of quantum state estimation as a robust principal component analysis (RPCA) problem with positive semidefinite and unit-trace Hermitian constraints.
    • Development of an efficient and fast inexact alternating direction method of multipliers (I-ADMM) algorithm.
    • Solving subproblems inexactly to obtain closed-form solutions and proving the global convergence of the I-ADMM.

    Main Results:

    • The proposed I-ADMM algorithm demonstrates global convergence, providing theoretical guidelines for parameter selection.
    • Numerical experiments show successful recovery of 5-qubit state density matrices with high accuracy (6 ×10-4 error, 99.38% fidelity).
    • The method achieves this performance using only 30% compressive sensing measurements and completes recovery in under a second on a laptop.

    Conclusions:

    • The I-ADMM is a highly efficient and accurate algorithm for quantum state estimation, outperforming existing methods.
    • The algorithm effectively recovers low-rank density matrices from sparse, noisy linear measurements.
    • This work provides a robust computational tool for quantum information processing and experimental quantum state reconstruction.