非绝热和乐量子计算新进展
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摘要
量子计算是基于量子力学规律调控量子信息单元进行计算的一种新型计算模型.众所周知,对噪声不敏感的高保真度量子逻辑门是实现大规模量子计算的关键.几何量子计算是利用几何相位来实现量子逻辑门操作的量子计算策略,其特点是利用几何相位的整体性质避免某些局域噪声对量子操作的影响,从而实现高保真度的量子逻辑门.因此,基于几何相位的量子操控是量子信息处理领域中非常重要的研究课题.该文以基于非阿贝尔几何相位的和乐量子计算为例,介绍非绝热和乐量子计算方案的新进展.
Quantum computation,processing quantum information based on the laws of quantum mechanics,is a new computation model.As it is well known,high-fidelity quantum gates,which are insensitive to noise,is the key to realizing large-scale quantum computation.Geometric quantum computation utilizes geometric phases, which are insensitive to certain local noises due to the global properties,and thus lead to high-fidelity quantum logic gate.Therefore,quantum manipulation based on geometric phases is an important research topic in quantum information processing.In this review,taking the holonomic quantum computation,based on non-Abelian geometric phases,as a typical example,we summarized the recent progress on its nonadiabatic implementation.
Quantum computation,processing quantum information based on the laws of quantum mechanics,is a new computation model.As it is well known,high-fidelity quantum gates,which are insensitive to noise,is the key to realizing large-scale quantum computation.Geometric quantum computation utilizes geometric phases, which are insensitive to certain local noises due to the global properties,and thus lead to high-fidelity quantum logic gate.Therefore,quantum manipulation based on geometric phases is an important research topic in quantum information processing.In this review,taking the holonomic quantum computation,based on non-Abelian geometric phases,as a typical example,we summarized the recent progress on its nonadiabatic implementation.
引文
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[21]XUE Z Y,GU F L,HONG Z P,et al.Nonadiabatic holonomic quantum computation with dressed-state qubits[J].Phys Rev Appl,2017,7:054022.
[22]HONG Z P,LIU B J,CAI J Q,et al.Implementing universal nonadiabatic holonomic quantum gates with transmons[J].Phys Rev A,2018,97:022332.
[23]FALCI G,FAZIO R,PALMA G M,et al.Detection of geometric phases in superconducting nanocircuits[J].Nature(London),2002,407:355-358.
[24]LEIBFRIED D,DEMARCO B,MEYER V,et al.Experimental demonstration of a robust,high-fidelity geometric two ion-qubit phase gate[J].Nature(London),2003,422:412-415.
[25]DU J,ZOU P,WANG Z D.Experimental implementation of high-fidelity unconventional geometric quantum gates using an NMR interferometer[J].Phys Rev A,2006,74:020302.
[26]LEEK P J,FINK J M,BLAIS A,et al.Observation of Berry’s phase in a solid state qubit[J].Science,2007,318:1889-1892.
[27]MTTNEN M,VARTIANINEN J J,PEKOLA J P.Experimental determination of the Berry phase in a superconducting charge pump[J].Phys Rev Lett,2008,100:177201.
[28]PECHAL M,BERGER S,ABDUMALIKOV A A,et al.Geometric phase and nonadiabatic effects in an electronic harmonic oscillator[J].Phys Rev Lett,2012,108:170401.
[29]ABDUMALIKOV A A,FINK J M,JULIUSSON K,et al.Experimental realization of non-Abelian nonadiabatic geometric gates[J].Nature(London),2013,496:482-485.
[30]FENG G,XU G F,LONG G G.Experimental realization of nonadiabatic holonomic quantum computation[J].Phys Rev Lett,2013,110:190501.
[31]ZU C,WANG W B,HE L,et al.Experimental realization of universal geometric quantum gates with solidstate spins[J].Nature(London),2014,514:72-75.
[32]CAMEJO S A,LAZARIEV A,HELL S W,et al.Room temperature high-fidelityholonomic single-qubit gate on a solid-state spin[J].Nat Commun,2014,5:4870.
[33]TALE C G,HEREMANS F J,ZHOU B B,et al.Optical manipulation of the Berry phase in a solid-state spin qubit[J].Nat Photonics,2016,10:184-189.
[34]LI H,YANG L,LONG G G.Experimental realization of single-shot nonadiabatic holonomic gates in nuclear spins[J].Sci China Phys Mech Astron,2017,60:080311.
[35]SEKIGUCHI Y,NIIKURA N,KUROIWA R,et al.Optical holonomic single quantum gates with a geometric spin under a zero field[J].Nat Photonics,2017,11:309-314.
[36]ZHOU B B,JERGER P C,SHKOLNIKOV V O,et al.Holonomic quantum control by coherent optical excitation in diamond[J].Phys Rev Lett,2017,119:140503.
[37]EGGER D J,GANZHORN M,SALIS G,et al.Entanglement generation in superconducting qubits using holonomic operations[EB/OL].(2018-04-13)[2018-11-24].https://arxiv.org/abs/1804.04900.
[38]XU Y,CAI W,MA Y,et al.Single-loop realization of arbitrary nonadiabatic holonomic single-qubit quantum gates in a superconducting circuit[J].Phys Rev Lett,2018,121:110501.
[39]YAN T,LIU B J,XU K,et al.Experimental realization of non-adiabatic shortcut to non-Abelian geometric gates[EB/OL].(2018-04-22)[2018-11-24].https://arxiv.org/abs/1804.08142.
[40]LIU B J,SONG X K,XUE Z Y,et al.Plug-and-play approach to non-adiabatic geometric quantum computation[EB/OL].(2018-06-20)[2018-11-24].https://arxiv.org/abs/1806.07904.
[41]ZEY T S,PECHAL M,BERGER S,et al.Microwave-induced amplitude-and phase-tunable qubit-resonator coupling in circuit quantum electrodynamics[J].Phys Rev A,2015,91:043846.
[42]STEPHENSA M.Fault-tolerant thresholds for quantum error correction with the surface code[J].Phys Rev A,2014,89:022321.
[43]ZHANG J,DEVITT S J,YOU J Q,et al.Holonomic surface codes for fault-tolerant quantum computation[J].Phys Rev A,2018,97:022335.
[44]ZHENG S B,YANG C P,NORI F.Comparison of the sensitivity to systematic errors between nonadiabatic non-Abelian geometric gates and their dynamical counterparts[J].Phys Rev A,2016,93:032313.
[45]DUAN L M,GUO G C.Preserving coherence in quantum computation by pairing quantum bits[J].Phys Rev Lett,1997,79:1953.
[46]ZANARDI P,RASETTI M.Noiseless quantum codes[J].Phys Rev Lett,1997,79:3306.
[47]LIDAR D A,CHUANG I L,WHALEY K B.Decoherence-free subspaces for quantum computation[J].Phys Rev Lett,2009,81:2594.
[48]XU G F,ZHANG J,TONG D M,et al.Nonadiabatic holonomic quantum computation in decoherence-free subspaces[J].Phys Rev Lett,2012,109:170501.
[49]XUE Z Y,ZHOU J,WANG Z D.Universal holonomic quantum gates in decoherence-free subspace on superconducting circuits[J].Phys Rev A,2015,92:022320.
[50]XUE Z Y,ZHOU J,CHU Y M,et al.Nonadiabatic holonomic quantum computation with all-resonant control[J].Phys Rev A,2016,94:022331.
[51]ZHAO P Z,XU G F,DING Q M,et al.Single-shot realization of nonadiabatic holonomic quantum gates in decoherence-free subspaces[J].Phys Rev A,2017,95:062310.
[2]BERRY M V.Quantal phase factors accompanying adiabatic changes[J].Proc R Soc Lond A,1984,392:45-57.
[3]WILCZEK F,ZEE A.Appearance of Gauge structure in simple dynamical systems[J].Phys Rev Lett,1984,52:2111.
[4]PACHOS J,ZANARDI P,RASETTI M.Non-Abelian Berry connections for quantum computation[J].Phys Rev A,1999,61:010305.
[5]DUAN L M,CIRAC J I,ZOLLER P.Geometric manipulation of trapped ions for quantum computation[J].Science,2001,292:1695-1697.
[6]ZHANG P,WANG Z D,SUN J D,et al.Holonomic quantum computation using RF superconducting quantum interference devices coupled through a microwave cavity[J].Phys Rev A,2005,71:042301.
[7]WU L A,ZANARDI P,LIDAR D A.Holonomic quantum computation in decoherence-free subspaces[J].Phys Rev Lett,2005,95:130501.
[8]YIN Z Q,LI F L,PENG P.Implementation of holonomic quantum computation through engineering and manipulating the environment[J].Phys Rev A,2007,76:062311.
[9]KAMLEITNER I,SOLINAS P,MULLER C,et al.Geometric quantum gates with superconducting qubits[J].Phys Rev B,2011,83:214518.
[10]ALBERT V V,SHU C,KRASTANOV S,et al.Holonomic quantum control with continuous variable systems[J].Phys Rev Lett,2016,116:140502.
[11]WANG X B,KEI J M.Nonadiabatic conditional geometric phase shift with NMR[J].Phys Rev Lett,2001,87:097901.
[12]ZHU S L,WANG Z D.Implementation of universal quantum gates based on nonadiabatic geometric phases[J].Phys Rev Lett,2002,89:097902.
[13]ZHU S L,WANG Z D.Unconventional geometric quantum computation[J].Phys Rev A,2003,67:022319.
[14]ZHAO P Z,CUI X D,XU G F,et al.Rydberg-atom-based scheme ofnonadiabatic geometric quantum computation[J].Phys Rev A,2017,96:052316.
[15]CHEN T,XUE Z Y.Nonadiabatic geometric quantum computation with parametrically tunable coupling[J].Phys Rev Appl,2018,10:054051.
[16]SJQVIST E,TONG D M,ANDERSSON L M,et al.Non-adiabatic holonomic quantum computation[J].New J Phys,2012,14:103035.
[17]ZHANG J,KWEK L C,SJQVIST E,et al.Quantum computation in noiseless subsystems with fast nonAbelian holonomies[J].Phys Rev A,2014,89:042302.
[18]XU G F,LIU C L,ZHAO P Z,et al.Nonadiabatic holonomic gates realized by a single-shot implementation[J].Phys Rev A,2015,92:052302.
[19]HERTERICH E,SJQVIST E.Single-loop multiple-pulse nonadiabatic holonomic quantum gates[J].Phys Rev A,2016,94:052310.
[20]XU G F,ZHAO P Z,XING T H,et al.Composite nonadiabatic holonomic quantum computation[J].Phys Rev A,2017,95:032311.
[21]XUE Z Y,GU F L,HONG Z P,et al.Nonadiabatic holonomic quantum computation with dressed-state qubits[J].Phys Rev Appl,2017,7:054022.
[22]HONG Z P,LIU B J,CAI J Q,et al.Implementing universal nonadiabatic holonomic quantum gates with transmons[J].Phys Rev A,2018,97:022332.
[23]FALCI G,FAZIO R,PALMA G M,et al.Detection of geometric phases in superconducting nanocircuits[J].Nature(London),2002,407:355-358.
[24]LEIBFRIED D,DEMARCO B,MEYER V,et al.Experimental demonstration of a robust,high-fidelity geometric two ion-qubit phase gate[J].Nature(London),2003,422:412-415.
[25]DU J,ZOU P,WANG Z D.Experimental implementation of high-fidelity unconventional geometric quantum gates using an NMR interferometer[J].Phys Rev A,2006,74:020302.
[26]LEEK P J,FINK J M,BLAIS A,et al.Observation of Berry’s phase in a solid state qubit[J].Science,2007,318:1889-1892.
[27]MTTNEN M,VARTIANINEN J J,PEKOLA J P.Experimental determination of the Berry phase in a superconducting charge pump[J].Phys Rev Lett,2008,100:177201.
[28]PECHAL M,BERGER S,ABDUMALIKOV A A,et al.Geometric phase and nonadiabatic effects in an electronic harmonic oscillator[J].Phys Rev Lett,2012,108:170401.
[29]ABDUMALIKOV A A,FINK J M,JULIUSSON K,et al.Experimental realization of non-Abelian nonadiabatic geometric gates[J].Nature(London),2013,496:482-485.
[30]FENG G,XU G F,LONG G G.Experimental realization of nonadiabatic holonomic quantum computation[J].Phys Rev Lett,2013,110:190501.
[31]ZU C,WANG W B,HE L,et al.Experimental realization of universal geometric quantum gates with solidstate spins[J].Nature(London),2014,514:72-75.
[32]CAMEJO S A,LAZARIEV A,HELL S W,et al.Room temperature high-fidelityholonomic single-qubit gate on a solid-state spin[J].Nat Commun,2014,5:4870.
[33]TALE C G,HEREMANS F J,ZHOU B B,et al.Optical manipulation of the Berry phase in a solid-state spin qubit[J].Nat Photonics,2016,10:184-189.
[34]LI H,YANG L,LONG G G.Experimental realization of single-shot nonadiabatic holonomic gates in nuclear spins[J].Sci China Phys Mech Astron,2017,60:080311.
[35]SEKIGUCHI Y,NIIKURA N,KUROIWA R,et al.Optical holonomic single quantum gates with a geometric spin under a zero field[J].Nat Photonics,2017,11:309-314.
[36]ZHOU B B,JERGER P C,SHKOLNIKOV V O,et al.Holonomic quantum control by coherent optical excitation in diamond[J].Phys Rev Lett,2017,119:140503.
[37]EGGER D J,GANZHORN M,SALIS G,et al.Entanglement generation in superconducting qubits using holonomic operations[EB/OL].(2018-04-13)[2018-11-24].https://arxiv.org/abs/1804.04900.
[38]XU Y,CAI W,MA Y,et al.Single-loop realization of arbitrary nonadiabatic holonomic single-qubit quantum gates in a superconducting circuit[J].Phys Rev Lett,2018,121:110501.
[39]YAN T,LIU B J,XU K,et al.Experimental realization of non-adiabatic shortcut to non-Abelian geometric gates[EB/OL].(2018-04-22)[2018-11-24].https://arxiv.org/abs/1804.08142.
[40]LIU B J,SONG X K,XUE Z Y,et al.Plug-and-play approach to non-adiabatic geometric quantum computation[EB/OL].(2018-06-20)[2018-11-24].https://arxiv.org/abs/1806.07904.
[41]ZEY T S,PECHAL M,BERGER S,et al.Microwave-induced amplitude-and phase-tunable qubit-resonator coupling in circuit quantum electrodynamics[J].Phys Rev A,2015,91:043846.
[42]STEPHENSA M.Fault-tolerant thresholds for quantum error correction with the surface code[J].Phys Rev A,2014,89:022321.
[43]ZHANG J,DEVITT S J,YOU J Q,et al.Holonomic surface codes for fault-tolerant quantum computation[J].Phys Rev A,2018,97:022335.
[44]ZHENG S B,YANG C P,NORI F.Comparison of the sensitivity to systematic errors between nonadiabatic non-Abelian geometric gates and their dynamical counterparts[J].Phys Rev A,2016,93:032313.
[45]DUAN L M,GUO G C.Preserving coherence in quantum computation by pairing quantum bits[J].Phys Rev Lett,1997,79:1953.
[46]ZANARDI P,RASETTI M.Noiseless quantum codes[J].Phys Rev Lett,1997,79:3306.
[47]LIDAR D A,CHUANG I L,WHALEY K B.Decoherence-free subspaces for quantum computation[J].Phys Rev Lett,2009,81:2594.
[48]XU G F,ZHANG J,TONG D M,et al.Nonadiabatic holonomic quantum computation in decoherence-free subspaces[J].Phys Rev Lett,2012,109:170501.
[49]XUE Z Y,ZHOU J,WANG Z D.Universal holonomic quantum gates in decoherence-free subspace on superconducting circuits[J].Phys Rev A,2015,92:022320.
[50]XUE Z Y,ZHOU J,CHU Y M,et al.Nonadiabatic holonomic quantum computation with all-resonant control[J].Phys Rev A,2016,94:022331.
[51]ZHAO P Z,XU G F,DING Q M,et al.Single-shot realization of nonadiabatic holonomic quantum gates in decoherence-free subspaces[J].Phys Rev A,2017,95:062310.