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Quantum information with cold atoms

Quantum information with cold atoms. Zheng-Wei Zhou( 周正威） Key Lab of Quantum Information , CAS, USTC. October, 2009. KITPC. Outline. Backgrounds on Quantum Computation(QC) Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC

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Quantum information with cold atoms

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  1. Quantum information with cold atoms Zheng-Wei Zhou(周正威） Key Lab of Quantum Information , CAS, USTC October, 2009 KITPC

  2. Outline • Backgrounds on Quantum Computation(QC) • Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC QS for highly-correlated many body models • Quantum Communication • Summary and Outlook

  3. Backgrounds on Quantum Computation(QC) Father of QC（1981－1985） R. Feynman D. Deutsch Elementary Gates for QC（1995） A. Barenco (Oxford), C. H. Bennett (IBM), R. Cleve (Calgary), D. P. DiVincenzo (IBM), N. Margolus (MIT), P. Shor (AT&T), T. Sleator (NYU), J. Smolin (UCLA), H. Weinfurter (Innsbruck) C. H. Bennett

  4. Quantum Algorithms 1994 1997

  5. Some Methods to Overcome Decoherence （1）Quantum Error Correcting Codes （Shor，Steane，Calderbank，Laflamme，Preskill，etc.）（1995－2000） （2）Decoherence-Free Subspaces （Duan, Guo, Zanardi, Whaley，Bacon, Lidar, etc.）（1997－2000） （3）Dynamical Decoupling method （Lolyd，Viola，Duan，Guo, Zanardi，etc.） （1998－1999）

  6. Standard Model for QC

  7. Beyond Standard model (I) A. Kitaev (1997) • Topological Quantum Computing

  8. Beyond Standard model (II) • One Way Quantum Computing R. Raussendorf H. Briegel (2000)

  9. E ...... t Beyond Standard model (III) • Adiabatic Quantum Computation Dorit Aharonov et. al (2004) J. Goldstone et. al (2000) Standard QC Adiabatic QC

  10. Intermediate targetsof QC——Simulating highly-correlated many body systems D. Jaksch P. Zoller D. Jaksch, C. Bruder, C.W. Gardiner, J.I. Cirac andP. Zoller (1998)

  11. Decoherence, Scalability, Energy gap, etc Standard QC model Quantum Computer Adiabatic QC Beyond Classical Computer Quantum Simulation Topological QC Once Fault-Tolerant QC can be realized…

  12. Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC QS for highly-correlated many body models

  13. Standard Model for QC

  14. 1. Register of 2-level systems (qubits) The physical origin of the confinement of cold atoms with laser light is the dipole force: Olaf Mandel, et al., Phys. Rev. Lett. 91, 010407 (2003)

  15. 2. Initialization of the qubit register

  16. However, nonideal conditions will always result in defects in that phase (i.e., missing atoms and overloaded sites). How to suppress these defects in the lattice? A possible approach is: the coherent filtering scheme. P. Rabl, et al., Phys. Rev. Lett. 91,110403, (2003)

  17. 3、4. Tools for manipulation: 1- and 2-qubit gates and readout 1-qubit As far as ultracold atoms trapped in an optical lattice is concerned, global operations on atoms are available. However, addressing individual atom becomes very difficult. So, to implement universal quantum computation, we should answer the following questions: 1: Whether global operations are enough to implement universal quantum computation? OR 2: How to addressing single qubit in this system?

  18. Cellular-automata Machine Some proposals for QC via global operations (S. Lloyd, Science 261, 1569 (1993); S. C. Benjamin, PRA 61, 020301R, 2000, PRL 88, 017904, 2002)

  19. QC via translation-invariant operations R. Raussendorf, Phys. Rev. A 72, 052301 (2005). K. G. H. Vollbrecht et al., Phys. Rev. A 73, 012324 (2006). G. Ivanyos, et al., Phys. Rev. A 72, 022339 (2005). Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006). In the above proposals, only translationally invariant global operations are required! Shortcomings: Redundant qubits (space and time overhead) Initialization Physical implementation

  20. Bose Hubbard model Ising Model PRL 81, 3108 (1998); 90, 100401(2003); 91,090402 (2003) Type I Type II PRL 91,090402 (2003) (Effective periodic magnetic field induced by left and right circularly polarized light) Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006).

  21. 1D Two-qubit operation Addressing single qubit 2D Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006).

  22. Some proposals for QC via addressing single atom Marked Qubit as Data-bus (Phys. Rev. A 70, 012306 (2004); Phys. Rev. Lett. 93, 220502 (2004))

  23. Phys. Rev. A 70, 012306 (2004)

  24. single-qubit rotation via multiqubit addressing J. Joo, et al., PHYSICAL REVIEW A 74, 042344 (2006)

  25. single-qubit rotation via Position-dependent hyperfine splittings C. Zhang, et al., PHYSICAL REVIEW A 74, 042316 (2006)

  26. the progress of experiments Imaging of single atoms in an optical lattice Nelson, K. D., Li, X. & Weiss, D. S. Nature Phys. 3, 556–560 (2007).

  27. effective magnetic field results from the atom‘s vector light shift：

  28. Novel quantum gates via exchange interactions

  29. Anderlini, M. et al. Controlled exchange interaction between pairs of neutral atoms in an optical lattice. Nature 448, 452–456 (2007).

  30. Science 319, 295–299 (2008).

  31. Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008).

  32. 5. Long decoherence times How many gate operations could be carried out within a fixed decoherence time? “ For the atoms of ultracold gases in optical lattices, Feshbach resonances can be used to increase the collisional interactions and thereby speed up gate operations. However, the ‘unitarity limit’ in scattering theory does not allow the collisional interaction energy to be increased beyond the on-site vibrational oscillation frequency, so the lower timescale for a gate operation is typically a few tens of microseconds.” “ Much larger interaction energies, and hence faster gate times, could be achieved by using the electric dipole–dipole interactions between polar molecules, for example, or Rydberg atoms; in the latter case, gate times well below the microsecond range are possible.” I. Bloch, NATURE|Vol 453|19 June 2008|doi:10.1038.

  33. Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC QS for highly-correlated many body models

  34. R. Raussendorf H. Briegel R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188, (2001)

  35. Given a graph , the corresponding graph state is • Given a graph , the corresponding graph state is 1 2 3 Graph states • Graph States Stabilizer code • For Example:

  36. A Controlled Phase Gate D. Jaksch, et. al., Entanglement of atoms via coldcontrolled collisions, Phys. Rev. Lett. 82, 1975 (1999).

  37. Nature 425, 937 (2003)

  38. Nature 425, 937 (2003)

  39. New Journal of Physics 10 (2008) 023005

  40. New Journal of Physics 10 (2008) 023005

  41. Preparation of decoherence-free cluster states with optical superlattices Liang Jiang, et. Al., Phys. Rev. A 79, 022309 (2009)

  42. Logical qubit in decoherence-free subspace Here, Logical qubit: Implementing a C-Phase Gate

  43. Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC QS for highly-correlated many body models

  44. Cold Atoms Trapped in Optical Lattices to Simulate condensed matter physics D. Jaksch, C. Bruder, C.W. Gardiner, J.I. Cirac andP. Zoller (1998)

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