An approximate quantum Hamiltonian identification algorithm using a Taylor expansion of the matrix exponential function
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Dong, D
Petersen, IR
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Melbourne, Australia
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Abstract
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.
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2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
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© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
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Theory of computation
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Wang, Y; Dong, D; Petersen, IR, An approximate quantum Hamiltonian identification algorithm using a Taylor expansion of the matrix exponential function, 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, 2017, pp. 5523-5528