Quantum process tomography is a critical task for characterizing the dynamics of quantum systems and achieving precise quantum control. In this paper, we propose a two-stage solution for both trace-preserving and non-trace-preserving quantum process tomography. Utilizing a tensor structure, our algorithm exhibits a computational complexity of O(MLd2 ) where d is the dimension of the quantum system and M, L (M ≥ d 2 , L ≥ d 2 ) represent the numbers of different input states and measurement operators, respectively. We establish an analytical error upper bound and then design the optimal input states and the optimal measurement operators, which are both based on minimizing the error upper bound and maximizing the robustness characterized by the condition number. Numerical examples and testing on IBM quantum devices are presented to demonstrate the performance and efficiency of our algorithm.

Publication:

IEEE TRANSACTIONS ON INFORMATION THEORY

http://dx.doi.org/10.1109/TIT.2024.3522005

Author:

Yuanlong Wang

Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

e-mail: wangyuanlong@amss.ac.cn

Jun Zhang

University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China

e-mail: zhangjun12@sjtu.edu.cn

Daoyi Dong

CIICADA Laboratory, School of Engineering, The Australian National University, Canberra, ACT 2601, Australia, and also with the School of Physics, The University of Melbourne, Parkville, VIC 3010, Australia

e-mail: daoyi.dong@anu.edu.au

Gary J. Mooney

School of Physics, The University of Melbourne, Parkville, VIC 3010, Australia

e-mail: mooney.g@unimelb.edu.au

Ian R. Petersen

School of Engineering, The Australian National University, Canberra, ACT 2601, Australia

e-mail: i.r.petersen@gmail.com

Hidehiro Yonezawa

RIKEN Center for Quantum Computing, Saitama 351-0198, Japan, also with the School of Engineering and Technology, University of New South Wales, Canberra, ACT 2600, Australia

Centre for Quantum Computation and Communication Technology, Australian Research Council, Canberra, ACT 2600, Australia

e-mail: hidehiro.yonezawa@riken.jp