An Efficient and Fast Quantum State Estimator With Sparse Disturbance

作者：Zhang, Jiaojiao; Cong, Shuang^*; Ling, Qing; Li, Kezhi

来源：IEEE Transactions on Cybernetics, 2019, 49(7): 2546-2555.

DOI：10.1109/TCYB.2018.2828498

• Alternating direction method of multipliers (ADMM)
• quantum state estimation (QSE)
• robust principal component analysis (RPCA)

A pure or nearly pure quantum state can be described as a low-rank density matrix, which is a positive semidefinite and unit-trace Hermitian. We consider the problem of recovering such a low-rank density matrix contaminated by sparse components, from a small set of linear measurements. This quantum state estimation task can be formulated as a robust principal component analysis (RPCA) problem subject to positive semidefinite and unit-trace Hermitian constraints. We propose an efficient and fast inexact alternating direction method of multipliers (I-ADMM), in which the subproblems are solved inexactly and hence have closed-form solutions. We prove global convergence of the proposed I-ADMM, and the theoretical result provides a guideline for parameter setting. Numerical experiments show that the proposed I-ADMM can recover state density matrices of 5 qubits on a laptop in 0.69 s, with 6 x 10(-4) accuracy (99.38% fidelity) using 30% compressive sensing measurements, which outperforms existing algorithms.

• 出版日期2019-7
• 单位中国科学技术大学; 中山大学