量子计算的进展及展望ppt课件

1、Quantum information with cold atoms Zheng-Wei Zhou(Zheng-Wei Zhou(周正威周正威Key Lab of Quantum Information , CAS, USTCKey Lab of Quantum Information , CAS, USTCOctober, 2021KITPC Backgrounds on Quantum Computation(QC) Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for

2、QC One-Way QC QS for highly-correlated many body models Quantum Communication Summary and OutlookOutlineBackgrounds on Quantum Computation(QC)Father of QC19811985Elementary Gates for QC 2019A. Barenco (Oxford), C. H. Bennett (IBM), R. Cleve (Calgary), D. P. DiVincenzo (IBM), N. Margolus (MIT), P. Sh

3、or (AT&T), T. Sleator (NYU), J. Smolin (UCLA), H. Weinfurter (Innsbruck) R. FeynmanD. DeutschC. H. BennettQuantum Algorithms19942019Some Methods to Overcome Decoherence1Quantum Error Correcting CodesShor，Steane，Calderbank，Laflamme，Preskill，etc.201920002Decoherence-Free SubspacesDuan, Guo, Zanard

4、i, Whaley，Bacon, Lidar, etc.201920003Dynamical Decoupling methodLolyd，Viola，Duan，Guo, Zanardi，etc. 20192019Standard Model for QCBeyond Standard model (I) Topological Quantum ComputingA. Kitaev (2019)Beyond Standard model (II) One Way Quantum ComputingR. RaussendorfH. Briegel (2000)Beyond Standard mo

5、del (III) Adiabatic Quantum ComputationDorit Aharonov et. al (2019)J. Goldstone et. al (2000)Et.Adiabatic QCStandard QCP. Zoller D. Jaksch, C. Bruder, C.W. Gardiner, J.I. Cirac and P. Zoller (2019)Intermediate targets of QCSimulating highly-correlated many body systemsD. JakschQuantum ComputerStanda

6、rd QC modelQuantum SimulationAdiabatic QCBeyond Classical ComputerTopological QCDecoherence, Scalability, Energy gap, etcOnce Fault-Tolerant QC can be realized Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC QS for highly-correlated many body model

7、sStandard Model for QC1. 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 (2019)2. Initialization of the qubit registerHowever, nonideal conditions will always result in defe

8、cts 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, (2019)3、4. Tools for manipulation: 1- and 2-qubit gates and readout 1-qubit1: Whether global o

9、perations are enough to implement universal quantum computation?2: How to addressing single qubit in this system?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 implemen

10、t universal quantum computation, we should answer the following questions:OR(S. Lloyd, Science 261, 1569 (1993); S. C. Benjamin, PRA 61, 020301R, 2000, PRL 88, 017904, 2019)Some proposals for QC via global operationsCellular-automata MachineQC via translation-invariant operations R. Raussendorf, Phy

11、s. Rev. A 72, 052301 (2019). K. G. H. Vollbrecht et al., Phys. Rev. A 73, 012324 (2019). G. Ivanyos, et al., Phys. Rev. A 72, 022339 (2019).Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2019). In the above proposals, only translationally invariant global operations are required!Redundant qubits (spac

12、e and time overhead)InitializationPhysical implementationShortcomings:Bose Hubbard modelIsing ModelType IType IIPRL 91,090402 (2019)PRL 81, 3108 (2019); 90, 100401(2019); 91,090402 (2019)Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2019).(Effective periodic magnetic field induced by left and right c

13、ircularly polarized light)1D2DAddressing single qubitTwo-qubit operationZ. W. Zhou, et al., Phys. Rev. A 74, 052334 (2019).(Phys. Rev. A 70, 012306 (2019); Phys. Rev. Lett. 93, 220502 (2019)Some proposals for QC via addressing single atomMarked Qubit as Data-busPhys. Rev. A 70, 012306 (2019)single-q

14、ubit rotation via multiqubit addressingJ. Joo, et al., PHYSICAL REVIEW A 74, 042344 (2019)single-qubit rotation via Position-dependent hyperfine splittingsC. Zhang, et al., PHYSICAL REVIEW A 74, 042316 (2019)the progress of experiments Imaging of single atoms in an optical latticeNelson, K. D., Li,

15、X. & Weiss, D. S. Nature Phys. 3, 556560 (2019).effective magnetic field results from the atoms vector light shift：Novel quantum gates via exchange interactionsAnderlini, M. et al. Controlled exchange interaction between pairs of neutral atoms in anoptical lattice. Nature 448, 452456 (2019).Scie

16、nce 319, 295299 (2019).Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295299 (2019).5. Long decoherence timesHow many gate operations could be carried out within a fixed decoherence time?“ For the atoms of

17、 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 osci

18、llation 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 dipoledipole interactions between polar molecules, for example, or Rydberg atoms; in the lat

19、ter case, gate times well below the microsecond range are possible.I. Bloch, NATURE|Vol 453|19 June 2019|doi:10.1038.Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard model for QC One-Way QC QS for highly-correlated many body modelsR. RaussendorfH. Briegel R. Raussendorf an

20、d H. J. Briegel, Phys. Rev. Lett. 86, 5188, (2019)Graph states Graph StatesStabilizer code For Example:13212X Z123Z X Z23X Z( 000001010011100101110111 )L Given a graph , the corresponding graph state is Given a graph , the corresponding graph state is A Controlled Phase GateD. Jaksch, et. al., Entan

21、glement of atoms via cold controlled collisions, Phys. Rev. Lett. 82, 1975 (2019).Nature 425, 937 (2019)Nature 425, 937 (2019)New Journal of Physics 10 (2019) 023005New Journal of Physics 10 (2019) 023005Preparation of decoherence-free cluster states with optical superlattices)2(cos)(cos)()2(cos)(co

22、s)()()(22212221kyVkyVxVkxVkxVxVyVxVVyyyxxxyxLiang Jiang, et. Al., Phys. Rev. A 79, 022309 (2021)Logical qubit in decoherence-free subspace1,23,42,34,1HVSSSS,12i jijijS 021123VVHHere,Logical qubit:Implementing a C-Phase GateQuantum Computation(QC) and Quantum Simulation(QS) with Cold atoms Standard m

23、odel for QC One-Way QC QS for highly-correlated many body modelsCold Atoms Trapped in Optical Lattices to Simulate condensed matter physicsD. Jaksch, C. Bruder, C.W. Gardiner, J.I. Cirac and P. Zoller (2019)Advantages as one of promising candidates of quantum simulationsNeutral atoms couple only wea

24、kly to the environment, allowing long storage and coherence times.So far, cold atoms trapped in optical lattices is the only system in which a large number of particles can be initialized simultaneously.Highly controllabilityControl of interaction strength with magnetic field (Feshbach Resonance)Var

25、ious geometry of optical latticesControllable tunneling ratesBosons, Fermions, or mixtureBose-Hubbard ModelEffective highly-correlated many body modelsTwo-component Bose-Hubbard ModelFeshbach resonance - magnitudeOptical lattice - diversityExperiments: Ketterle, Esslinger etc. Weakly interacting fer

26、mions in an optical lattice - single-band Hubbard model (Hofstetter et al, PRL 2019)iiiiijjiiweakaaaauaatH, Strongly (resonantly) interacting fermions in optical lattice - Boson-fermion Hubbard model ?iiiiiiionweakstrongbbaabgHHStoof, Holland, Zhou, etc., 2019Inadequate!Fermions in an Optical Lattic

27、e Multi-band populations (T.-L. Ho, cond-mat/0507253; 0507255, PRL 2019) iiiiiiionweakstrongbbaabgHHWhy is it inadequate? bgonEgBand gapOn-site coupling ratetgoff Off-site collision couplings (L.-M. Duan, PRL 95, 243202,2019) Off-site coupling rateTunneling rateOff-site couplingtoffgirpqriiqippqraab

28、g;Different bandsStrong interaction effects Starting point: the field HamiltonianKeep all the bandsKeep the off-site couplingsL.-M. Duan, PRL 95, 243202,2019 Limiting case2: molecule limit Limiting case 1: atom limitQuantum simulation with polar moleculesA. Micheli, G. K. Brennen and P. Zoller, A to

29、olbox for lattice-spinmodels with polar molecules, Nature Physics, 2, 341 (2019) Time-of-flight imaging expansion ttrr densitymktrrt/0condensateDiagonal correlation in momentum space kk Detection of ultracold atomsOne can also utilize density-density correlations in the image of an expanding gas clo

30、ud to probe complex many-body states.Nature Physics, 4, 50 (2019)Nature Physics, 4, 50 (2019)Quantum SimulationQuantum ComputerLimits from classical worldStarting pointQuantum Communication Why long-distance quantum communication is so difficult? Transmission loss/fidelity of entanglementdecreasing

31、exponentially with the length of the connecting channel Solution: Quantum repeater combining entanglement swapping and purification H. Briegel et al., Phys. Rev. Lett. 81, 5932 (2019)Atomic-ensemble-based quantum memory is used to transfer the photonic states to the excitation in atomic internal sta

32、tes so that it can be stored, and after the storage of a programmable time, it should be possible to read out the excitation to photons without change of its quantum state.M.D. Lukin et al., Phys. Rev. Lett. 84, 4232 (2000); M. Fleischhauer and M.D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).Atomic-ensemble-based quantum memoryPhysical implementation of Quantum Repeater: A Scheme based on atomic ensembles, the DLCZ scheme L.-M. Duan et al., Nature 414, 413 (2019)The phase stability proble