Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors

Ma, Andrew; Magann, Alicia B.; Ho, Tak-San; Rabitz, Herschel

doi:10.1103/physreva.102.013115

Title: Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors

Abstract

This paper presents a method for performing approximate optimal control simulations for quantum systems with multiple coupled degrees of freedom. In this work, the time evolution is simulated using the first-order Magnus expansion in the interaction picture, where the couplings between different degrees of freedom are treated as the perturbation. A numerical implementation procedure is presented that leverages upon pairwise couplings and the separability of the zeroth-order time evolution operator to achieve a reduced computational cost, which is analyzed with respect to the number of degrees of freedom. The formulation is compatible with gradient-free methods to optimize the control field, and a stochastic hill climbing algorithm is adopted for this purpose. As illustrations, optimal control simulations are performed for systems of two and three dipole-dipole-coupled molecular rotors under the influence of a control field. For the two-rotor system, the field is optimized to achieve either orientation or entanglement objectives. For the three-rotor system, the field is optimized either to orient all three rotors in the same direction or to orient one rotor in a particular direction while the other two rotors point in the opposite direction.

Authors:

^[1];

^[1]

Princeton Univ., NJ (United States)

Publication Date:: Thu Jul 30 00:00:00 EDT 2020

Research Org.:: Princeton Univ., NJ (United States); Krell Institute, Ames, IA (United States)

Sponsoring Org.:: USDOE Office of Science (SC); US Army Research Office (ARO)

OSTI Identifier:: 1800043

Grant/Contract Number:: FG02-02ER15344; FG02-97ER25308; W911NF-16-1- 0014

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review A

Additional Journal Information:: Journal Volume: 102; Journal Issue: 1; Journal ID: ISSN 2469-9926

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Optics; Physics

Citation Formats


                    Ma, Andrew, Magann, Alicia B., Ho, Tak-San, and Rabitz, Herschel. Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors.  United States: N. p., 2020. 
Web.  doi:10.1103/physreva.102.013115.

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                    Ma, Andrew, Magann, Alicia B., Ho, Tak-San, & Rabitz, Herschel. Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors.  United States.  https://doi.org/10.1103/physreva.102.013115

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                    Ma, Andrew, Magann, Alicia B., Ho, Tak-San, and Rabitz, Herschel. Thu .  
"Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors".  United States.  https://doi.org/10.1103/physreva.102.013115.  https://www.osti.gov/servlets/purl/1800043.

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@article{osti_1800043,

  title        = {Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors},

  author       = {Ma, Andrew and Magann, Alicia B. and Ho, Tak-San and Rabitz, Herschel},

  abstractNote = {This paper presents a method for performing approximate optimal control simulations for quantum systems with multiple coupled degrees of freedom. In this work, the time evolution is simulated using the first-order Magnus expansion in the interaction picture, where the couplings between different degrees of freedom are treated as the perturbation. A numerical implementation procedure is presented that leverages upon pairwise couplings and the separability of the zeroth-order time evolution operator to achieve a reduced computational cost, which is analyzed with respect to the number of degrees of freedom. The formulation is compatible with gradient-free methods to optimize the control field, and a stochastic hill climbing algorithm is adopted for this purpose. As illustrations, optimal control simulations are performed for systems of two and three dipole-dipole-coupled molecular rotors under the influence of a control field. For the two-rotor system, the field is optimized to achieve either orientation or entanglement objectives. For the three-rotor system, the field is optimized either to orient all three rotors in the same direction or to orient one rotor in a particular direction while the other two rotors point in the opposite direction.},

  doi          = {10.1103/physreva.102.013115},

  journal      = {Physical Review A},

  number       = 1,

  volume       = 102,

  place        = {United States},

  year         = {Thu Jul 30 00:00:00 EDT 2020},

  month        = {Thu Jul 30 00:00:00 EDT 2020}

}

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Title: Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors

Abstract

Citation Formats

Optimally controlled quantum molecular dynamics: A perturbation formulation and the existence of multiple solutions journal, February 1993

Optimization schemes for selective molecular cleavage with tailored ultrashort laser pulses journal, November 2011

Computing matrix functions journal, May 2010

Control of quantum phenomena: past, present and future journal, July 2010

Effect of intrinsic decoherence on entanglement of three polar molecules with two-dimensional rotation journal, March 2019

A numerical study of large sparse matrix exponentials arising in Markov chains journal, January 1999

Optimal Control Technique for Many-Body Quantum Dynamics journal, May 2011

Quantum optimal control within the rotating-wave approximation journal, September 2015

Quantum control of I2 wave packet localization in solid argon matrix journal, February 2000

Wavepacket dancing: Achieving chemical selectivity by shaping light pulses journal, December 1989

Free-time and fixed end-point optimal control theory in quantum mechanics: Application to entanglement generation journal, January 2009

Quantum error correction in a solid-state hybrid spin register journal, February 2014

Optimal control of selective vibrational excitation in harmonic linear chain molecules journal, June 1988

Locally optimized control pulses with nonlinear interactions journal, October 2019

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators journal, October 1950

Optimal control of the local electromagnetic response of nanostructured materials: Optimal detectors and quantum disguises. journal, June 2009

The Magnus expansion and some of its applications journal, January 2009

Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications journal, June 1988

Implementation of quantum logic gates using polar molecules in pendular states journal, January 2013

Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators journal, January 2011

Quantum observable homotopy tracking control journal, October 2005

Realization of the CNOT quantum gate operation in six-dimensional ammonia using the OCT-MCTDH approach journal, July 2009

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms journal, February 2005

New formulations of monotonically convergent quantum control algorithms journal, May 2003

Complexity of controlling quantum many-body dynamics journal, April 2014

Quantum control of multidimensional systems Implementation within the time‐dependent Hartree approximation journal, January 1996

Control of selectivity of chemical reaction via control of wave packet evolution journal, November 1985

Controlling Qubit Networks in Polynomial Time journal, May 2018

Control of molecular orientation with combined near-single-cycle THz and optimally designed non-resonant laser pulses: Carrier-envelope phase effects journal, July 2015

Predicting Structure in Sparse Matrix Computations journal, January 1994

Femtosecond laser pulse control of multidimensional vibrational dynamics: Computational studies on the pyrazine molecule journal, July 2006

Multi-polarization quantum control of rotational motion through dipole coupling journal, February 2010

Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later journal, January 2003

Optimal molecular alignment and orientation through rotational ladder climbing journal, October 2005

Time-dependent quantum-mechanical methods for molecular dynamics journal, April 1988

Molecular alignment and orientation in short pulse laser fields journal, October 1999

Quantum phases of dipolar rotors on two-dimensional lattices journal, March 2018

Quantum optimal control theory journal, September 2007

A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator journal, July 1998

Quantum optimal control of multiple weakly interacting molecular rotors in the time-dependent Hartree approximation journal, April 2019

High-fidelity spin entanglement using optimal control journal, February 2014

Microwave Spectra of Molecules of Astrophysical Interest VI. Carbonyl Sulfide and Hydrogen Cyanide journal, January 1974

Optimally controlled quantum molecular dynamics: A perturbation formulation and the existence of multiple solutions
journal, February 1993

Optimization schemes for selective molecular cleavage with tailored ultrashort laser pulses
journal, November 2011

Computing matrix functions
journal, May 2010

Control of quantum phenomena: past, present and future
journal, July 2010

Effect of intrinsic decoherence on entanglement of three polar molecules with two-dimensional rotation
journal, March 2019

A numerical study of large sparse matrix exponentials arising in Markov chains
journal, January 1999

Optimal Control Technique for Many-Body Quantum Dynamics
journal, May 2011

Quantum optimal control within the rotating-wave approximation
journal, September 2015

Quantum control of I2 wave packet localization in solid argon matrix
journal, February 2000

Wavepacket dancing: Achieving chemical selectivity by shaping light pulses
journal, December 1989

Free-time and fixed end-point optimal control theory in quantum mechanics: Application to entanglement generation
journal, January 2009

Quantum error correction in a solid-state hybrid spin register
journal, February 2014

Optimal control of selective vibrational excitation in harmonic linear chain molecules
journal, June 1988

Locally optimized control pulses with nonlinear interactions
journal, October 2019

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
journal, October 1950

Optimal control of the local electromagnetic response of nanostructured materials: Optimal detectors and quantum disguises.
journal, June 2009

The Magnus expansion and some of its applications
journal, January 2009

Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications
journal, June 1988

Implementation of quantum logic gates using polar molecules in pendular states
journal, January 2013

Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
journal, January 2011

Quantum observable homotopy tracking control
journal, October 2005

Realization of the CNOT quantum gate operation in six-dimensional ammonia using the OCT-MCTDH approach
journal, July 2009

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms
journal, February 2005

New formulations of monotonically convergent quantum control algorithms
journal, May 2003

Complexity of controlling quantum many-body dynamics
journal, April 2014

Quantum control of multidimensional systems Implementation within the time‐dependent Hartree approximation
journal, January 1996

Control of selectivity of chemical reaction via control of wave packet evolution
journal, November 1985

Controlling Qubit Networks in Polynomial Time
journal, May 2018

Control of molecular orientation with combined near-single-cycle THz and optimally designed non-resonant laser pulses: Carrier-envelope phase effects
journal, July 2015

Predicting Structure in Sparse Matrix Computations
journal, January 1994

Femtosecond laser pulse control of multidimensional vibrational dynamics: Computational studies on the pyrazine molecule
journal, July 2006

Multi-polarization quantum control of rotational motion through dipole coupling
journal, February 2010

Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
journal, January 2003

Optimal molecular alignment and orientation through rotational ladder climbing
journal, October 2005

Time-dependent quantum-mechanical methods for molecular dynamics
journal, April 1988

Molecular alignment and orientation in short pulse laser fields
journal, October 1999

Quantum phases of dipolar rotors on two-dimensional lattices
journal, March 2018

Quantum optimal control theory
journal, September 2007

A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator
journal, July 1998

Quantum optimal control of multiple weakly interacting molecular rotors in the time-dependent Hartree approximation
journal, April 2019

High-fidelity spin entanglement using optimal control
journal, February 2014

Microwave Spectra of Molecules of Astrophysical Interest VI. Carbonyl Sulfide and Hydrogen Cyanide
journal, January 1974