An Efficient and Fast Quantum State Estimator With Sparse Disturbance

被引：18

作者：

Zhang, Jiaojiao ^{[1
]}

Cong, Shuang ^{[1
]}

Ling, Qing ^{[2
]}

Li, Kezhi ^{[3
]}

机构：

[1] Univ Sci & Technol China, Dept Automat, Hefei 230027, Anhui, Peoples R China

[2] Sun Yat Sen Univ, Sch Data & Comp Sci, Guangzhou 510006, Guangdong, Peoples R China

[3] Imperial Coll London, Dept Elect & Elect Engn, London SW5 7AZ, England

来源：

IEEE TRANSACTIONS ON CYBERNETICS | 2019年 / 49卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Alternating direction method of multipliers (ADMM); quantum state estimation (QSE); robust principal component analysis (RPCA); THRESHOLDING ALGORITHM; MATRICES; RANK;

D O I：

10.1109/TCYB.2018.2828498

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：2546 / 2555

页数：10