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Time optimal quantum control of two-qubit systems

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Abstract

We study the optimal quantum control of heteronuclear two-qubit systems described by a Hamiltonian containing both nonlocal internal drift and local control terms. We derive an explicit formula to compute the minimum time required to steer the system from an initial state to a specified final state. As applications the minimal time to implement Controlled-NOT gate, SWAP gate and Controlled-U gate is calculated in detail. The experimental realizations of these quantum gates are explicitly presented.

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References

  1. Warren W, Rabitz H, Dahleb M. Coherent control of quantum dynamics: The dream is alive. Science, 1993, 259: 1581–1589

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Rabitz H, de Vivie-Riedle R, Motzkus M, et al. Whither the future of controlling quantum phenomena? Science, 2000, 288: 824–828

    Article  ADS  Google Scholar 

  3. Daniel C, Full J, Gonzàlez L, et al. Deciphering the reaction dynamics underlying optimal control laser fields. Science, 2003, 299: 536–539

    Article  ADS  Google Scholar 

  4. Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2000

    MATH  Google Scholar 

  5. Ernst R R, Bodenhausen G, Wokaun A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions. Oxford: Oxford University Press, 1987

    Google Scholar 

  6. Gershenfeld N A, Chuang I L. Bulk spin-resonance quantum computation. Science, 1997, 275: 350–356; Cory D G, Fahmy A, Havel T. Ensemble quantum computing by NMR spectroscopy. Proc Natl Acad Sci USA, 1997, 94: 1634–1639

    Article  MathSciNet  MATH  Google Scholar 

  7. Lapert M, Salomon J, Sugny D. Time-optimal monotonically convergent algorithm with an application to the control of spin systems. Phys Rev A, 2012, 85: 033406

    Article  ADS  Google Scholar 

  8. Tibbetts K W M, Brif C, Grace M D, et al. Exploring the tradeoff between fidelity and time optimal control of quantum unitary transformations. Phys Rev A, 2012, 86: 062309

    Article  ADS  Google Scholar 

  9. Motzoi F, Gambetta J M, Merkel S T, et al. Optimal control methods for rapidly time-varying Hamiltonians. Phys Rev A, 2011, 84: 022307

    Article  ADS  Google Scholar 

  10. Assémat E, Lapert M, Zhang Y, et al. Simultaneous time-optimal control of the inversion of two spin-1/2 particles. Phys Rev A, 2010, 82: 013415

    Article  ADS  Google Scholar 

  11. Lapert M, Zhang Y, Braun M, et al. Singular extremals for the timeoptimal control of dissipative spin 1/2 particles. Phys Rev Lett, 2010, 104: 083001

    Article  ADS  Google Scholar 

  12. Khaneja N, Brockett R, Glaser S J. Time optimal control in spin systems. Phys Rev A, 2001, 63: 032308

    Article  ADS  Google Scholar 

  13. Makhlin Y. Nonlocal properties of two-qubit gates and mixed states, and the optimization of quantum computations. Quant Inf Proc, 2002, 1: 243–252

    Article  MathSciNet  Google Scholar 

  14. Zhang J, Vala J, Sastry S, et al. Geometric theory of nonlocal two-qubit operations. Phys Rev A, 2003, 67: 042313

    Article  MathSciNet  ADS  Google Scholar 

  15. Glaser J, Schulte-Herbrüggen T, Sieveking M, et al. Unitary control in quantum ensembles: Maximizing signal intensity in coherent spectroscopy. Science, 1998, 280: 421–424

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Bin Li, ZuHuan Yu & ShaoMing Fei

  2. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China

    Bin Li

  3. Max-Planck-Institute for Mathematics in the Sciences, Leipzig, 04103, Germany

    ShaoMing Fei & XianQing Li-Jost

Authors
  1. Bin Li
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  2. ZuHuan Yu
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  3. ShaoMing Fei
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  4. XianQing Li-Jost
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Correspondence to ShaoMing Fei.

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Li, B., Yu, Z., Fei, S. et al. Time optimal quantum control of two-qubit systems. Sci. China Phys. Mech. Astron. 56, 2116–2121 (2013). https://doi.org/10.1007/s11433-013-5325-9

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  • DOI: https://doi.org/10.1007/s11433-013-5325-9

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