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Modified Newton-Raphson GRAPE methods for optimal control of quantum systems

Modified Newton-Raphson GRAPE methods for optimal control of quantum systems
Modified Newton-Raphson GRAPE methods for optimal control of quantum systems
Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself. This leads to the possibility of using very efficient numerical optimization techniques. In particular, the Newton-Raphson method with a rational function optimization (RFO) regularized Hessian is shown in this work to require fewer system trajectory evaluations than any other algorithm in the GRAPE family. This communication describes algebraic and numerical implementation aspects (matrix exponential recycling, Hessian regularization, etc.) for the RFO Newton-Raphson version of GRAPE and reports benchmarks for common spin state control problems in magnetic resonance spectroscopy
0021-9606
204107
Goodwin, David
349b642d-bc15-4a8d-b1d7-98691a39e069
Kuprov, Ilya
bb07f28a-5038-4524-8146-e3fc8344c065
Goodwin, David
349b642d-bc15-4a8d-b1d7-98691a39e069
Kuprov, Ilya
bb07f28a-5038-4524-8146-e3fc8344c065

Goodwin, David and Kuprov, Ilya (2016) Modified Newton-Raphson GRAPE methods for optimal control of quantum systems. The Journal of Chemical Physics, 144, 204107. (doi:10.1063/1.4949534).

Record type: Article

Abstract

Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself. This leads to the possibility of using very efficient numerical optimization techniques. In particular, the Newton-Raphson method with a rational function optimization (RFO) regularized Hessian is shown in this work to require fewer system trajectory evaluations than any other algorithm in the GRAPE family. This communication describes algebraic and numerical implementation aspects (matrix exponential recycling, Hessian regularization, etc.) for the RFO Newton-Raphson version of GRAPE and reports benchmarks for common spin state control problems in magnetic resonance spectroscopy

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Accepted/In Press date: 2 May 2016
Published date: 28 May 2016
Organisations: Computational Systems Chemistry, Magnetic Resonance

Identifiers

Local EPrints ID: 396247
URI: http://eprints.soton.ac.uk/id/eprint/396247
ISSN: 0021-9606
PURE UUID: dcd0b995-f976-4258-b55a-6bea66ed371d
ORCID for Ilya Kuprov: ORCID iD orcid.org/0000-0003-0430-2682

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Date deposited: 06 Jun 2016 12:59
Last modified: 15 Mar 2024 03:43

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Contributors

Author: David Goodwin
Author: Ilya Kuprov ORCID iD

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