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IEEE Conference on Decision and Control (CDC)

An iterative algorithm for Hamiltonian identification of quantum systems

Yuanlong Wang, Bo Qi, Daoyi Dong, Ian R. Petersen

Published Dec 1, 2016• 6 citations
Publisher

Abstract

Identifying parameters in the system Hamiltonian is a vitally important task in the development of quantum technology. This paper investigates the problem of Hamiltonian identification for closed quantum systems and develops a new algorithm to achieve the task of identifying the Hamiltonian. Under the framework of standard quantum process tomography and without prior assumptions, we first convert the problem of Hamiltonian identification into an optimization problem and then design an iterative algorithm to numerically solve this problem. Numerical results for a two-qubit system are presented to show the effectiveness of the proposed algorithm through analyzing the mean squared error.

DOI
10.1109/cdc.2016.7798641

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Identification of the Hamiltonian is vital for characterizing the dynamical evolution of a quantum system. The dimension of a multi-qubit system increases exponentially with the qubit number, which usually leads to daunting computational complexity for general Hamiltonian identification algorithms. In this paper, we design an efficient quantum Hamiltonian identification method based on periodical sampling. The computational complexity is O(M2 + MN2), where M is the number of unknown parameters to be identified in the Hamiltonian and N is the length of the sampling data. Numerical results with different data lengths demonstrate the effectiveness of the proposed identification algorithm.
Identifying an unknown unitary quantum process is a fundamental task in the development of quantum technology. In this paper, we propose an efficient identification algorithm for estimating unitary processes. In the method, input pure states are used and a fast quantum state tomography algorithm is developed to reconstruct the output states. Then the information of the output states is used to estimate the unitary process. The identification algorithm has computational complexity O(d3) for a d-dimensional system. Numerical results show that the proposed identification algorithm is much more efficient than the maximum likelihood estimation method and works well for input mixed states with high purity. An analytical upper bound for the identification error is also provided, and numerical simulations and experimental results on quantum optical systems verify the theoretical results.
Identifying the Hamiltonian of an unknown quantum system is a critical task in the area of quantum information. In this article, we propose a systematic Hamiltonian identification approach via quantum ensemble multiclass classification (HI-QEMC). This approach is implemented by a three-step iterative refining process, i.e., parameter interval guess, verification, and judgment. In the parameter interval guess step, the parameter interval is divided into several sub-intervals and the true Hamiltonian parameter is guessed in one of them. In the parameter interval verification step, cross verification is applied to verify the accuracy of the guess. In the parameter interval judgment step, an adaptive interval judgment (AIJ) algorithm is designed to determine the sub-interval containing the true Hamiltonian parameter. Numerical results on two typical quantum systems, i.e., two-level quantum systems and three-level quantum systems, demonstrate the effectiveness and superior performance of the proposed approach for quantum Hamiltonian identification.
Parameter identification of quantum systems is a fundamental task in developing practical quantum technology. In this article, we study the identification of time-varying decoherence rates for open quantum systems. Given the measurement data of local observables, this can be formulated as an optimization problem. We expand the unknown decoherence rates into Fourier series and take the expansion coefficients as optimization variables. We then convert it into a minimax problem and apply a sequential linear programming technique to solve it. Numerical study on a two-qubit quantum system with a time-varying decoherence rate demonstrates the effectiveness of our algorithm.