An improved robust ADMM algorithm for quantum state tomography

作者：Li, Kezhi; Zhang, Hui; Kuang, Sen; Meng, Fangfang; Cong, Shuang^*

来源：Quantum Information Processing, 2016, 15(6): 2343-2358.

DOI：10.1007/s11128-016-1288-x

• Quantum state estimation
• Compressive sensing
• ADMM algorithm
• Adaptive weights

In this paper, an improved adaptive weights alternating direction method of multipliers algorithm is developed to implement the optimization scheme for recovering the quantum state in nearly pure states. The proposed approach is superior to many existing methods because it exploits the low-rank property of density matrices, and it can deal with unexpected sparse outliers as well. The numerical experiments are provided to verify our statements by comparing the results to three different optimization algorithms, using both adaptive and fixed weights in the algorithm, in the cases of with and without external noise, respectively. The results indicate that the improved algorithm has better performances in both estimation accuracy and robustness to external noise. The further simulation results show that the successful recovery rate increases when more qubits are estimated, which in fact satisfies the compressive sensing theory and makes the proposed approach more promising.

• 出版日期2016-6
• 单位中国科学技术大学