Searching for quantum optimal controls under severe constraints

Riviello, Gregory; Tibbetts, Katharine Moore; Brif, Constantin; Long, Ruixing; Wu, Re-Bing; Ho, Tak-San; Rabitz, Herschel

doi:10.1103/PhysRevA.91.043401

Searching for quantum optimal controls under severe constraints

Journal Article · Mon Apr 06 00:00:00 EDT 2015 · Physical Review A - Atomic, Molecular, and Optical Physics

DOI:https://doi.org/10.1103/PhysRevA.91.043401· OSTI ID:1340253

Riviello, Gregory ^[1]; Tibbetts, Katharine Moore ^[2]; Brif, Constantin ^[3]; Long, Ruixing ^[1]; Wu, Re-Bing ^[4]; Ho, Tak-San ^[1]; Rabitz, Herschel ^[1]

Princeton Univ., NJ (United States). Dept. of Chemistry
Princeton Univ., NJ (United States). Dept. of Chemistry; Temple Univ., Philadelphia, PA (United States). Dept. of Chemistry
Sandia National Lab. (SNL-CA), Livermore, CA (United States). Dept. of Scalable & Secure Systems Research
Tsinghua Univ., Beijing (China). Center for Quantum Information Science and Technology, Dept. of Automation

The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, but certain control constraints can still prevent successful optimization of the objective. Using optimal control simulations, we show that the most severe field constraints are those that limit essential control resources, such as the number of control variables, the control duration, and the field strength. Proper management of these resources is an issue of great practical importance for optimization in the laboratory. For each resource, we show that constraints exceeding quantifiable limits can introduce artificial traps to the control landscape and prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helps to eliminate artificial traps and facilitate successful optimization.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); Army Research Office; NSFC

Grant/Contract Number:: AC04-94AL85000; FG02-02ER15344

OSTI ID:: 1340253

Alternate ID(s):: OSTI ID: 1179324

Report Number(s):: SAND--2014-19558J; 642791

Journal Information:: Physical Review A - Atomic, Molecular, and Optical Physics, Journal Name: Physical Review A - Atomic, Molecular, and Optical Physics Journal Issue: 4 Vol. 91; ISSN 1050-2947; ISSN PLRAAN

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Landscape for optimal control of quantum-mechanical unitary transformations Rabitz, Herschel; Hsieh, Michael; Rosenthal, Carey Physical Review A, Vol. 72, Issue 5 https://doi.org/10.1103/PhysRevA.72.052337	journal	November 2005
Optimal control, geometry, and quantum computing Nielsen, Michael A.; Dowling, Mark R.; Gu, Mile Physical Review A, Vol. 73, Issue 6 https://doi.org/10.1103/PhysRevA.73.062323	journal	June 2006
Topology of optimally controlled quantum mechanical transition probability landscapes Rabitz, H.; Ho, T. -S.; Hsieh, M. Physical Review A, Vol. 74, Issue 1 https://doi.org/10.1103/PhysRevA.74.012721	journal	July 2006
Analysis of femtosecond quantum control mechanisms with colored double pulses Vogt, Gerhard; Nuernberger, Patrick; Selle, Reimer Physical Review A, Vol. 74, Issue 3 https://doi.org/10.1103/PhysRevA.74.033413	journal	September 2006
Laboratory observation of quantum control level sets Roslund, Jonathan; Roth, Matthias; Rabitz, Herschel Physical Review A, Vol. 74, Issue 4 https://doi.org/10.1103/PhysRevA.74.043414	journal	October 2006
Shortest paths for efficient control of indirectly coupled qubits Khaneja, Navin; Heitmann, Björn; Spörl, Andreas Physical Review A, Vol. 75, Issue 1 https://doi.org/10.1103/PhysRevA.75.012322	journal	January 2007
Optimal quantum control of Bose-Einstein condensates in magnetic microtraps Hohenester, Ulrich; Rekdal, Per Kristian; Borzì, Alfio Physical Review A, Vol. 75, Issue 2 https://doi.org/10.1103/PhysRevA.75.023602	journal	February 2007
Time-optimal unitary operations Carlini, Alberto; Hosoya, Akio; Koike, Tatsuhiko Physical Review A, Vol. 75, Issue 4 https://doi.org/10.1103/PhysRevA.75.042308	journal	April 2007
Multiobjective genetic approach for optimal control of photoinduced processes Bonacina, Luigi; Extermann, Jérôme; Rondi, Ariana Physical Review A, Vol. 76, Issue 2 https://doi.org/10.1103/PhysRevA.76.023408	journal	August 2007
Optimal control landscape for the generation of unitary transformations Hsieh, Michael; Rabitz, Herschel Physical Review A, Vol. 77, Issue 4 https://doi.org/10.1103/PhysRevA.77.042306	journal	April 2008
Optimal control of atom transport for quantum gates in optical lattices De Chiara, G.; Calarco, T.; Anderlini, M. Physical Review A, Vol. 77, Issue 5 https://doi.org/10.1103/PhysRevA.77.052333	journal	May 2008
Protecting coherence in optimal control theory: State-dependent constraint approach Palao, José P.; Kosloff, Ronnie; Koch, Christiane P. Physical Review A, Vol. 77, Issue 6 https://doi.org/10.1103/PhysRevA.77.063412	journal	June 2008
State-independent control theory for weakly dissipative quantum systems Wenin, M.; Pötz, W. Physical Review A, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevA.78.012358	journal	July 2008
Optimal control of entangling operations for trapped-ion quantum computing Nebendahl, V.; Häffner, H.; Roos, C. F. Physical Review A, Vol. 79, Issue 1 https://doi.org/10.1103/PhysRevA.79.012312	journal	January 2009
Landscape of unitary transformations in controlled quantum dynamics Ho, Tak-San; Dominy, Jason; Rabitz, Herschel Physical Review A, Vol. 79, Issue 1 https://doi.org/10.1103/PhysRevA.79.013422	journal	January 2009
Gradient algorithm applied to laboratory quantum control Roslund, Jonathan; Rabitz, Herschel Physical Review A, Vol. 79, Issue 5 https://doi.org/10.1103/PhysRevA.79.053417	journal	May 2009
Optimal control of the silicon-based donor-electron-spin quantum computing Tsai, Dong-Bang; Chen, Po-Wen; Goan, Hsi-Sheng Physical Review A, Vol. 79, Issue 6 https://doi.org/10.1103/PhysRevA.79.060306	journal	June 2009
Monotonically convergent optimal control theory of quantum systems with spectral constraints on the control field Lapert, M.; Tehini, R.; Turinici, G. Physical Review A, Vol. 79, Issue 6 https://doi.org/10.1103/PhysRevA.79.063411	journal	June 2009
Experimental quantum control landscapes: Inherent monotonicity and artificial structure Roslund, Jonathan; Rabitz, Herschel Physical Review A, Vol. 80, Issue 1 https://doi.org/10.1103/PhysRevA.80.013408	journal	July 2009
Constructing general unitary maps from state preparations Merkel, Seth T.; Brennen, Gavin; Jessen, Poul S. Physical Review A, Vol. 80, Issue 2 https://doi.org/10.1103/PhysRevA.80.023424	journal	August 2009
Accelerated optimization and automated discovery with covariance matrix adaptation for experimental quantum control Roslund, Jonathan; Shir, Ofer M.; Bäck, Thomas Physical Review A, Vol. 80, Issue 4 https://doi.org/10.1103/PhysRevA.80.043415	journal	October 2009
Optimal control of number squeezing in trapped Bose-Einstein condensates Grond, Julian; von Winckel, Gregory; Schmiedmayer, Jörg Physical Review A, Vol. 80, Issue 5 https://doi.org/10.1103/PhysRevA.80.053625	journal	November 2009
Coherent control of atomic transport in spinor optical lattices Mischuck, Brian; Deutsch, Ivan H.; Jessen, Poul S. Physical Review A, Vol. 81, Issue 2 https://doi.org/10.1103/PhysRevA.81.023403	journal	February 2010
Optimal control landscape for the generation of unitary transformations with constrained dynamics Hsieh, Michael; Wu, Rebing; Rabitz, Herschel Physical Review A, Vol. 81, Issue 6 https://doi.org/10.1103/PhysRevA.81.062352	journal	June 2010
General unifying features of controlled quantum phenomena Pechen, Alexander; Brif, Constantin; Wu, Rebing Physical Review A, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevA.82.030101	journal	September 2010
Time complexity and gate complexity Koike, Tatsuhiko; Okudaira, Yosuke Physical Review A, Vol. 82, Issue 4 https://doi.org/10.1103/PhysRevA.82.042305	journal	October 2010
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Optimal control of the electronic current density: Application to one- and two-dimensional one-electron systems Kammerlander, David; Castro, Alberto; Marques, Miguel A. L. Physical Review A, Vol. 83, Issue 4 https://doi.org/10.1103/PhysRevA.83.043413	journal	April 2011
Role of controllability in optimizing quantum dynamics Wu, Re-Bing; Hsieh, Michael A.; Rabitz, Herschel Physical Review A, Vol. 83, Issue 6 https://doi.org/10.1103/PhysRevA.83.062306	journal	June 2011
Exploring quantum control landscapes: Topology, features, and optimization scaling Moore, Katharine W.; Rabitz, Herschel Physical Review A, Vol. 84, Issue 1 https://doi.org/10.1103/PhysRevA.84.012109	journal	July 2011
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Time-optimal monotonically convergent algorithm with an application to the control of spin systems Lapert, M.; Salomon, J.; Sugny, D. Physical Review A, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevA.85.033406	journal	March 2012
Coherent optimal control of photosynthetic molecules Caruso, F.; Montangero, S.; Calarco, T. Physical Review A, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevA.85.042331	journal	April 2012
Singularities of quantum control landscapes Wu, Re-Bing; Long, Ruixing; Dominy, Jason Physical Review A, Vol. 86, Issue 1 https://doi.org/10.1103/PhysRevA.86.013405	journal	July 2012
Strong-field-ionization suppression by light-field control Räsänen, Esa; Madsen, Lars Bojer Physical Review A, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevA.86.033426	journal	September 2012
Exploring the tradeoff between fidelity and time optimal control of quantum unitary transformations Moore Tibbetts, Katharine W.; Brif, Constantin; Grace, Matthew D. Physical Review A, Vol. 86, Issue 6 https://doi.org/10.1103/PhysRevA.86.062309	journal	December 2012
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Steering the optimization pathway in the control landscape using constraints Palao, José P.; Reich, Daniel M.; Koch, Christiane P. Physical Review A, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevA.88.053409	journal	November 2013
Searching for quantum optimal control fields in the presence of singular critical points Riviello, Gregory; Brif, Constantin; Long, Ruixing Physical Review A, Vol. 90, Issue 1 https://doi.org/10.1103/PhysRevA.90.013404	journal	July 2014
Characterization of control noise effects in optimal quantum unitary dynamics Hocker, David; Brif, Constantin; Grace, Matthew D. Physical Review A, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevA.90.062309	journal	December 2014
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Minimization of environment-induced decoherence in quantum subsystems and application to solid-state-based quantum gates Wenin, M.; Pötz, W. Physical Review B, Vol. 78, Issue 16 https://doi.org/10.1103/PhysRevB.78.165118	journal	October 2008
Optimal control of a leaking qubit Rebentrost, P.; Wilhelm, F. K. Physical Review B, Vol. 79, Issue 6 https://doi.org/10.1103/PhysRevB.79.060507	journal	February 2009
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Monotonic Convergent Optimal Control Theory with Strict Limitations on the Spectrum of Optimized Laser Fields Gollub, Caroline; Kowalewski, Markus; de Vivie-Riedle, Regina Physical Review Letters, Vol. 101, Issue 7 https://doi.org/10.1103/PhysRevLett.101.073002	journal	August 2008
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Quantum Control of Tightly Competitive Product Channels Roth, Matthias; Guyon, Laurent; Roslund, Jonathan Physical Review Letters, Vol. 102, Issue 25 https://doi.org/10.1103/PhysRevLett.102.253001	journal	June 2009
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Selective Bond Dissociation and Rearrangement with Optimally Tailored, Strong-Field Laser Pulses Levis, Robert J.; Menkir, Getahun M.; Rabitz, Herschel Science, Vol. 292, Issue 5517, p. 709-713 https://doi.org/10.1126/science.1059133	journal	March 2001
Deciphering the Reaction Dynamics Underlying Optimal Control Laser Fields Daniel, Chantal; Full, Jurgen; Gonzalez, Leticia Science, Vol. 299, Issue 5606, p. 536-539 https://doi.org/10.1126/science.1078517	journal	January 2003
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Coherent Control of Retinal Isomerization in Bacteriorhodopsin Prokhorenko, V. I. Science, Vol. 313, Issue 5791 https://doi.org/10.1126/science.1130747	journal	September 2006
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Frequency domain quantum optimal control under multiple constraints Shu, Chuan-Cun; Ho, Tak-San; Xing, Xi Physical Review A, Vol. 93, Issue 3 https://doi.org/10.1103/physreva.93.033417	journal	March 2016
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