An iterative algorithm for Hamiltonian identification of quantum systems

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

doi:10.1109/cdc.2016.7798641

Cited by 5 publications

(2 citation statements)

References 21 publications

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“…The direct solution to Problem 3 is difficult [39] and we split it into two sub-problems (which is the reason we name our method Two-Step Optimization):…”

Section: A Solution To Problem 3: Two-step Optimization (Tso)mentioning

confidence: 99%

A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis

Wang

Dong

et al. 2018

IEEE Trans. Automat. Contr.

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100

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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 Index Terms-Quantum system, Hamiltonian identification, process tomography, computational complexity.

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“…The direct solution to Problem 3 is difficult [39] and we split it into two sub-problems (which is the reason we name our method Two-Step Optimization):…”

Section: A Solution To Problem 3: Two-step Optimization (Tso)mentioning

confidence: 99%

A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis

Wang

Dong

et al. 2018

IEEE Trans. Automat. Contr.

Self Cite

100

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“…For example, Sone and Cappellaro [9] employed the Gröbner basis to investigate the Hamiltonian identifiability of a many-body spin system assisted by measuring a single quantum probe. Based on quantum process tomography, Wang et al [7] designed a general iterative identification method for time-independent Hamiltonians, which is then improved in [8] as a two-step optimization QHI method. Bonnabel et al [10] proposed a symmetry-preserving observer-based quantum Hamiltonian identification and proved an exponential convergence result for 2-level systems with the atom-laser frequency detuning and coupling constant being the unknown parameters.…”

Section: Introductionmentioning

confidence: 99%

An approximate quantum Hamiltonian identification algorithm using a Taylor expansion of the matrix exponential function

Wang

Dong

Petersen

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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An approximate quantum Hamiltonian identification algorithm is presented with the assumption that the system initial state and observation matrix can be set appropriately. We sample the system with a fixed period and using the sampled data we estimate the Hamiltonian based on a Taylor expansion of the matrix exponential function. We prove the estimation error is linear in the variance of the additive Gaussian noise. We also propose a heuristic formula to find the order of magnitude of the optimal sampling period. Two numerical examples are presented to validate the theoretical results on robustness analysis.

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An Approximate Algorithm for Quantum Hamiltonian Identification with Complexity Analysis

et al. 2017

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An iterative algorithm for Hamiltonian identification of quantum systems

Cited by 5 publications

References 21 publications

A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis

A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis

An approximate quantum Hamiltonian identification algorithm using a Taylor expansion of the matrix exponential function

An Approximate Algorithm for Quantum Hamiltonian Identification with Complexity Analysis

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