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Abstract:

The core problem in optimal control theory applied to quantum systems is to determine the temporal shape of an applied field in order to maximize the expected value of some physical observable. The complexity of this procedure is given by the structural and topological features of the quantum control landscape (QCL) - i.e. the functional which maps the control field into a given value of the observable. In this work, we analyze the rich structure of the QCL in the paradigmatic Landau-Zener two-level model, and focus in particular on characterizing the QCL when the total evolution time is severely constrained. By studying several features of the optimized solutions, such as their abundance, spatial distribution and fidelities, we are able to rationalize several geometrical and topological aspects of the QCL of this simple model and identify the effects produced by different types of constraint. © 2018 IOP Publishing Ltd.

Registro:

Documento: Artículo
Título:Quantum control landscape for a two-level system near the quantum speed limit
Autor:Larocca, M.; Poggi, P.M.; Wisniacki, D.A.
Filiación:Departamento de Física 'J. J. Giambiagi', IFIBA, FCEyN, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Center for Quantum Information and Control, University of New Mexico, Albuquerque, NM 87131, United States
Palabras clave:control landscape; quantum optimal control; quantum speed limit
Año:2018
Volumen:51
Número:38
DOI: http://dx.doi.org/10.1088/1751-8121/aad657
Título revista:Journal of Physics A: Mathematical and Theoretical
Título revista abreviado:J. Phys. Math. Theor.
ISSN:17518113
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17518113_v51_n38_p_Larocca

Referencias:

  • Nielsen, M.A., Chuang, I.L., (2000) Quantum Computation and Quantum Information, , (Cambridge: Cambridge University Press)
  • Gisin, N., Thew, R., Quantum communication (2007) Nat. Photon., 1, p. 165
  • Georgescu, I.M., Ashhab, S., Nori, F., Quantum simulation (2014) Rev. Mod. Phys., 86, p. 153
  • Barends, R., Digitized adiabatic quantum computing with a superconducting circuit (2016) Nature, 534, p. 222
  • Yin, J., Satellite-based entanglement distribution over 1200 kilometers (2017) Science, 356, pp. 1140-1144
  • Bernien, H., Probing many-body dynamics on a 51-atom quantum simulator (2017) Nature, 551, p. 579
  • Peirce, A.P., Dahleh, M.A., Rabitz, H., Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications (1988) Phys. Rev., 37, p. 4950
  • Somlói, J., Kazakov, V.A., Tannor, D.J., Controlled dissociation of i2 via optical transitions between the x and b electronic states (1993) Chem. Phys., 172, pp. 85-98
  • Rabitz, H.A., Hsieh, M.M., Rosenthal, C.M., Quantum optimally controlled transition landscapes (2004) Science, 303, pp. 1998-2001
  • Brockett, R., Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems (1991) Linear Algebra Appl., 146, pp. 79-91
  • Shen, Z., Hsieh, M., Rabitz, H., Quantum optimal control: Hessian analysis of the control landscape (2006) J. Chem. Phys., 124
  • Hsieh, M., Wu, R., Rabitz, H., Topology of the quantum control landscape for observables (2009) J. Chem. Phys., 130
  • Moore, K.W., Rabitz, H., Exploring constrained quantum control landscapes (2012) J. Chem. Phys., 137
  • Pechen, A.N., Tannor, D.J., Quantum control landscape for a λ-atom in the vicinity of second-order traps (2012) Isr. J. Chem., 52, pp. 467-472
  • Pechen, A., Il'In, N., Trap-free manipulation in the Landau-Zener system (2012) Phys. Rev., 86
  • Zhdanov, D.V., Seideman, T., Role of control constraints in quantum optimal control (2015) Phys. Rev., 92
  • Zhdanov, D.V., (2017) Theory of Quantum Control Landscapes: Overlooked Hidden Cracks
  • Sørensen, J.J., Exploring the quantum speed limit with computer games (2016) Nature, 532, p. 210
  • Gajdacz, M., Das, K.K., Arlt, J., Sherson, J.F., Opatrný, T., Time-limited optimal dynamics beyond the quantum speed limit (2015) Phys. Rev., 92
  • Tibbetts, K.W.M., Brif, C., Grace, M.D., Donovan, A., Hocker, D.L., Ho, T.-S., Wu, R.-B., Rabitz, H., Exploring the tradeoff between fidelity and time optimal control of quantum unitary transformations (2012) Phys. Rev., 86
  • Nanduri, A., Donovan, A., Ho, T.-S., Rabitz, H., Exploring quantum control landscape structure (2013) Phys. Rev., 88
  • Zener, C., Non-adiabatic crossing of energy levels (1932) Proc. R. Soc., 137, p. 696
  • Shevchenko, S.N., Ashhab, S., Nori, F., Landau-Zener-Stückelberg interferometry (2010) Phys. Rep., 492, pp. 1-30
  • Zurek, W.H., Dorner, U., Zoller, P., Dynamics of a quantum phase transition (2005) Phys. Rev. Lett., 95
  • Konnov, A.I., Krotov, V.F., On global methods for the successive improvement of control processes (1999) Avtom. Telemekh., 60, pp. 77-88
  • Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrüggen, T., Glaser, S.J., Optimal control of coupled spin dynamics: Design of nmr pulse sequences by gradient ascent algorithms (2005) J. Magn. Reson., 172, pp. 296-305
  • Shi, S., Woody, A., Rabitz, H., Optimal control of selective vibrational excitation in harmonic linear chain molecules (1988) J. Chem. Phys., 88, pp. 6870-6883
  • Poulsen, U.V., Sklarz, S., Tannor, D., Calarco, T., Correcting errors in a quantum gate with pushed ions via optimal control (2010) Phys. Rev., 82
  • Goerz, M.H., Calarco, T., Koch, C.P., The quantum speed limit of optimal controlled phasegates for trapped neutral atoms (2011) J. Phys. B: At. Mol. Opt. Phys., 44 (15)
  • Cross, A.W., Gambetta, J.M., Optimized pulse shapes for a resonator-induced phase gate (2015) Phys. Rev., 91
  • Shore, B.W., (2011) Manipulating Quantum Structures Using Laser Pulses, , (Cambridge: Cambridge University Press)
  • Landau, L.D., (1932) Phys. Z. Sowjetunion, 2, p. 46
  • Poggi, P.M., Lombardo, F.C., Wisniacki, D.A., Controlling open quantum systems using fast transitions (2013) Phys. Rev., 87
  • Hegerfeldt, G.C., Driving at the quantum speed limit: Optimal control of a two-level system (2013) Phys. Rev. Lett., 111
  • Nanduri, A., Ho, T.-S., Rabitz, H., Quantum-control-landscape structure viewed along straight paths through the space of control fields (2016) Phys. Rev., 93
  • Nanduri, A., Shir, O.M., Donovan, A., Ho, T.-S., Rabitz, H., Exploring the complexity of quantum control optimization trajectories (2015) Phys. Chem. Chem. Phys., 17, pp. 334-347
  • Heck, R., (2017) Do Physicists Stop Searches Too Early? A Remote-science, Optimization Landscape Investigation
  • Johansson, J.R., Nation, P.D., Nori, F., Qutip 2: A python framework for the dynamics of open quantum systems (2013) Comput. Phys. Commun., 184, pp. 1234-1240
  • Johansson, J.R., Nation, P.D., Nori, F., Qutip: An open-source python framework for the dynamics of open quantum systems (2012) Comput. Phys. Commun., 183, pp. 1760-1772
  • Bukov, M., Day, A.G.R., Sels, D., Weinberg, P., Polkovnikov, A., Mehta, P., (2017) Machine Learning Meets Quantum State Preparation. The Phase Diagram of Quantum Control

Citas:

---------- APA ----------
Larocca, M., Poggi, P.M. & Wisniacki, D.A. (2018) . Quantum control landscape for a two-level system near the quantum speed limit. Journal of Physics A: Mathematical and Theoretical, 51(38).
http://dx.doi.org/10.1088/1751-8121/aad657
---------- CHICAGO ----------
Larocca, M., Poggi, P.M., Wisniacki, D.A. "Quantum control landscape for a two-level system near the quantum speed limit" . Journal of Physics A: Mathematical and Theoretical 51, no. 38 (2018).
http://dx.doi.org/10.1088/1751-8121/aad657
---------- MLA ----------
Larocca, M., Poggi, P.M., Wisniacki, D.A. "Quantum control landscape for a two-level system near the quantum speed limit" . Journal of Physics A: Mathematical and Theoretical, vol. 51, no. 38, 2018.
http://dx.doi.org/10.1088/1751-8121/aad657
---------- VANCOUVER ----------
Larocca, M., Poggi, P.M., Wisniacki, D.A. Quantum control landscape for a two-level system near the quantum speed limit. J. Phys. Math. Theor. 2018;51(38).
http://dx.doi.org/10.1088/1751-8121/aad657