A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis

TL;DR

This paper introduces a two-step optimization algorithm for quantum Hamiltonian identification, analyzing its computational complexity and error bounds, with numerical validation demonstrating its effectiveness.

Contribution

The paper develops a novel two-step optimization method for quantum Hamiltonian identification within quantum process tomography, including complexity and error analysis.

Findings

Computational complexity is O(d^6) for a system of dimension d.

Error upper bound is O(d^3/N^{1/2}) with N being the number of resources.

Numerical examples confirm the effectiveness of the proposed method.

Abstract

Quantum Hamiltonian identification 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) quantum Hamiltonian identification algorithm is developed within the framework of quantum process tomography. In the identification method, different probe states are inputted 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^(1/2))$ 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.