A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis

Quantum Hamiltonian identification (QHI) is important for characterizing the dynamics of quantum systems, calibrating quantum devices, and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) QHI algorithm is developed within the framework of quantum process tom...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 63; no. 5; pp. 1388 - 1403
Main Authors: Yuanlong Wang, Daoyi Dong, Bo Qi, Jun Zhang, Petersen, Ian R., Yonezawa, Hidehiro
Format: Journal Article
Language:English
Published: IEEE 01.05.2018
Subjects:
Computational complexity
Electronic mail
Estimation error
Hamiltonian identification
Heuristic algorithms
process tomography
Quantum computing
quantum system
Tomography
Upper bound
ISSN:0018-9286, 1558-2523
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Quantum Hamiltonian identification (QHI) is important for characterizing the dynamics of quantum systems, calibrating quantum devices, and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) QHI algorithm is developed within the framework of quantum process tomography. In the identification method, different probe states are input into quantum systems and the output states are estimated using the quantum state tomography protocol via linear regression estimation. The time-independent system Hamiltonian is reconstructed based on the experimental data for the output states. The Hamiltonian identification method has computational complexity O(d 6 ), where d is the dimension of the system Hamiltonian. An error upper bound O( d 3 /√N ) is also established, where N is the resource number for the tomography of each output state, and several numerical examples demonstrate the effectiveness of the proposed TSO Hamiltonian identification method.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2017.2747507