Incoherent control of locally controllable quantum systems.

An incoherent control scheme for state control of locally controllable quantum systems is proposed. This scheme includes three steps: (1) amplitude amplification of the initial state by a suitable unitary transformation, (2) projective measurement of the amplified state, and (3) final optimization by a unitary controlled transformation. The first step increases the amplitudes of some desired eigenstates and the corresponding probability of observing these eigenstates, the second step projects, with high probability, the amplified state into a desired eigenstate, and the last step steers this eigenstate into the target state. Within this scheme, two control algorithms are presented for two classes of quantum systems. As an example, the incoherent control scheme is applied to the control of a hydrogen atom by an external field. The results support the suggestion that projective measurements can serve as an effective control and local controllability information can be used to design control laws for quantum systems. Thus, this scheme establishes a subtle connection between control design and controllability analysis of quantum systems and provides an effective engineering approach in controlling quantum systems with partial controllability information.

[1]  Herschel Rabitz,et al.  Observation-assisted optimal control of quantum dynamics. , 2007, The Journal of chemical physics.

[2]  R. Romano,et al.  Incoherent control and entanglement for two-dimensional coupled systems (8 pages) , 2006 .

[3]  Paul Brumer,et al.  Laser control of product quantum state populations in unimolecular reactions , 1986 .

[4]  A. G. White,et al.  Experimental verification of decoherence-free subspaces. , 2000, Science.

[5]  Stuart A. Rice,et al.  Interfering for the good of a chemical reaction , 2001, Nature.

[6]  A. Y. Khapalov,et al.  Local controllability for a “swimming” model. , 2007, 2007 46th IEEE Conference on Decision and Control.

[7]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[8]  Karine Beauchard,et al.  Local controllability of a 1-D Schrödinger equation , 2005 .

[9]  Herschel Rabitz,et al.  Quantum wavefunction controllability , 2001 .

[10]  Herschel Rabitz,et al.  Quantum control by von Neumann measurements , 2006 .

[11]  Samuel H. Tersigni,et al.  On using shaped light pulses to control the selectivity of product formation in a chemical reaction: An application to a multiple level system , 1990 .

[12]  Constantin Brif,et al.  Controllability of open quantum systems with Kraus-map dynamics , 2006, quant-ph/0611215.

[13]  J. C. Bevington,et al.  Chemical Reviews , 1970, Nature.

[14]  M. L. Ladron de Guevara,et al.  Measurement-driven quantum evolution , 2006 .

[15]  Herschel Rabitz,et al.  Wavefunction controllability for finite-dimensional bilinear quantum systems , 2003 .

[16]  Jiangbin Gong,et al.  Measurement-assisted coherent control. , 2004, The Journal of chemical physics.

[17]  Constantin Brif,et al.  Optimal control of quantum gates and suppression of decoherence in a system of interacting two-level particles , 2007, quant-ph/0702147.

[18]  Coherent control in a decoherence-free subspace of a collective multilevel system , 2006, quant-ph/0611084.

[19]  Herschel Rabitz.  The role of theory in the laboratory control of quantum dynamics phenomena , 2003 .

[20]  Daniel A. Lidar,et al.  Decoherence-Free Subspaces for Quantum Computation , 1998, quant-ph/9807004.

[21]  Tzyh Jong Tarn,et al.  Incoherent Control of Quantum Systems With Wavefunction-Controllable Subspaces via Quantum Reinforcement Learning , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[22]  Steven Chu,et al.  Cold atoms and quantum control , 2002, Nature.

[23]  Karine Beauchard,et al.  Controllability of a quantum particle in a moving potential well , 2006 .

[24]  Kompa,et al.  Whither the future of controlling quantum phenomena? , 2000, Science.

[25]  S. Lloyd,et al.  Coherent quantum feedback , 2000 .

[26]  Ramakrishna,et al.  Controllability of molecular systems. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[27]  Domenico D'Alessandro,et al.  Notions of controllability for bilinear multilevel quantum systems , 2003, IEEE Trans. Autom. Control..

[28]  G. Farkas,et al.  Local controllability of reactions , 1998 .

[29]  T. Tarn,et al.  On the controllability of quantum‐mechanical systems , 1983 .

[30]  Tzyh Jong Tarn,et al.  Quantum Reinforcement Learning , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[31]  Herschel Rabitz,et al.  Coherent Control of Quantum Dynamics: The Dream Is Alive , 1993, Science.

[32]  Gilles Brassard,et al.  Quantum Counting , 1998, ICALP.

[33]  Paul Brumer,et al.  Principles of the Quantum Control of Molecular Processes , 2003 .

[34]  Lov K. Grover.  Quantum Computers Can Search Rapidly by Using Almost Any Transformation , 1998 .

[35]  Ramakrishna,et al.  Relation between quantum computing and quantum controllability. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[36]  R. Mitrić,et al.  Theoretical exploration of ultrafast dynamics in atomic clusters: analysis and control. , 2005, Chemical reviews.

[37]  A. Mandilara,et al.  Probabilistic quantum control via indirect measurement , 2005 .

[38]  A. I. Solomon,et al.  Complete controllability of quantum systems , 2000, quant-ph/0010031.

[39]  Marcos Dantus,et al.  Experimental coherent laser control of physicochemical processes. , 2004, Chemical reviews.

[40]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[41]  Stuart A. Rice,et al.  Optical Control of Molecular Dynamics , 2000 .

[42]  M Sugawara.  Quantum dynamics driven by continuous laser fields under measurements: towards measurement-assisted quantum dynamics control. , 2005, The Journal of chemical physics.

[43]  V. I. Man'ko,et al.  Quantum control and the Strocchi map , 2003 .

[44]  Domenico D'Alessandro,et al.  Environment-mediated control of a quantum system. , 2006, Physical review letters.

[45]  Constantin Brif,et al.  Fidelity of optimally controlled quantum gates with randomly coupled multiparticle environments , 2007, 0712.2935.

[46]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[47]  Jonathan P Dowling,et al.  Quantum technology: the second quantum revolution , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[48]  D G Cory,et al.  Principles of control for decoherence-free subsystems. , 2006, The Journal of chemical physics.

[49]  H. Rabitz,et al.  Teaching lasers to control molecules. , 1992, Physical review letters.

[50]  C. Altafini,et al.  QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC) 2357 Controllability properties for finite dimensional quantum Markovian master equations , 2002, quant-ph/0211194.

[51]  Herschel Rabitz,et al.  Teaching the environment to control quantum systems , 2006 .

[52]  Tzyh-Jong Tarn,et al.  Smooth controllability of infinite-dimensional quantum-mechanical systems (11 pages) , 2006 .

[53]  P. Høyer.  Arbitrary phases in quantum amplitude amplification , 2000, quant-ph/0006031.