Journal of Quantum Optics, Volume. 29, Issue 2, 20401(2023)
Designing the Non-adiabatic Geometric Quantum Gates
[1] [1] SHOR P W. Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer[J]. Siam Review, 1999, 41(2):303-332. DOI: 10.1137/S0097539795293172.
[2] [2] GROVER L K. Quantum Mechanics Helps in Searching for a Needle in a Haystack[J]. Physical Review Letters, 1997. 79(2):2-14. DOI: 10.1103/PhysRevLett.79.325.
[3] [3] PRESKILL J. Quantum Computing in the NISQ era and beyond[J]. Quantum, 2018, 2:79-98. DOI: 10.22331/q-2018-08-06-79.
[4] [4] YAN T X, LIU B J, SONG C, et al. Experimental Realization of Nonadiabatic Shortcut to Non-Abelian Geometric Gates[J]. Physical Review Letters, 2019, 122(8):080501. DOI: 10.1103/PhysRevLett.122.080501.
[5] [5] KANG Y H, SHI Z C, HUANG B H, et al. Flexible scheme for the implementation of nonadiabatic geometric quantum computation[J]. Physical Review A, 2020, 101(3):049902. DOI: 10.1103/PhysRevA.101.032322.
[6] [6] LIU B J, WANG Y S, YUNG M H. Super-robust nonadiabatic geometric quantum control[J]. Physical Review Research, 2021, 3(3):L032066. DOI: 10.1103/PHYSREVRESEARCH.3.L032066.
[7] [7] BERRY M V. Quantal Phase Factors Accompanying Adiabatic Changes[J]. Proceedings of the Royal Society, 1984, 392(1802):45-57. DOI: 10.1098/rspa.1984.0023.
[8] [8] DUAN L M, CIRAC J I, ZOLLER P. Geometric Manipulation of Trapped Ions for Quantum Computation[J]. Science, 2001, 292(5522):1695-1697. DOI: 10.1126/science.1058835.
[9] [9] WILCZEK F, ZEE A. Appearance of Gauge Structure in Simple Dynamical Systems[J]. Physical Review Letters, 1984, 52(24):2111-2114. DOI: 10.1103/PhysRevLett.52.2111.
[10] [10] ANANDAN J. Non-adiabatic Non-abelian Geometric Phase[J]. Physics Letters A, 1988, 133(4-5):171-175. DOI: 10.1016/0375-9601(88)91010-9.
[11] [11] WANG X B, MATSUMOTO K. Nonadiabatic Conditional Geometric Phase Shift with NMR[J]. Physical Review Letters, 2002, 87(9):097901. DOI: 10.1103/PhysRevLett.87.097901.
[12] [12] ZHU S L, WANG Z D. Implementation of Universal Quantum Gates Based on Nonadiabatic Geometric Phases[J]. Physical Review Letters, 2002, 89(9):097902. DOI: 10.1103/physrevlett.89.097902.
[13] [13] SJQVIST E, TONG D M, HESSMO B, et al. Non-adiabatic Holonomic Quantum Computation[J]. New Journal of Physics, 2012, 14(17):103035. DOI: 10.1088/1367-2630/14/10/103035.
[14] [14] ZHANG J, KYAW T H, FILIPP S, et al. Geometric and Holonomic Quantum Computation[J]. 2021, ArXiv.2110.03602. DOI: 10.48550/arXiv.2110.03602.
[15] [15] ZHANG Z, ZHAO P Z, WANG T, et al. Single-shot Realization of Nonadiabatic Holonomic Gates with a Superconducting Xmon Qutrit[J]. New Journal of Physics, 2019, 21(7):073024. DOI: 10.1088/1367-2630/AB2E26.
[16] [16] CHEN T, SHEN P, XUE Z Y. Robust and Fast Holonomic Quantum Gates with Encoding on Superconducting Circuits[J]. Physical Review Applied, 2020, 14(3):034038. DOI: 10.1103/PhysRevApplied.14.034038.
[17] [17] XU K, NING W, HUANG X J, et al. Demonstration of a Non-Abelian Geometric Controlled-NOT Gate in a Superconducting Circuit[J]. Optica, 2021, 8(7):972-976. DOI:10.1364/OPTICA.416264.
[18] [18] SONG C, ZHENG S B, ZHANG P, et al. Continuous-variable Geometric Phase and its Manipulation for Quantum Computation in a Superconducting Circuit[J]. Nature Communications, 2017, 8(1):1-7. DOI: 10.1038/s41467-017-01156-5.
[19] [19] WANG T, ZHANG Z, XIANG L, et al. The Experimental Realization of high-fidelity ‘Shortcut-to-Adiabaticity’ Quantum Gates in a Superconducting Xmon Qubit[J]. New Journal of Physics, 2018, 20(6):065003. DOI: 10.1088/1367-2630/aac9e7.
[20] [20] XU Y, CAI W, MA Y, et al. Single-Loop Realization of Arbitrary Nonadiabatic Holonomic Single-Qubit Quantum Gates in a Superconducting Circuit[J]. Physical Review Letters, 2018, 121(11):110501. DOI: 10.1103/PhysRevLett.121.110501.
[21] [21] AI M Z, LI S, HE R, et al. Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates with Two Dark Paths in a Trapped Ion[J]. Fundamental Research, 2022, 2(5):661-666. DOI: 10.1016/j.fmre.2021.11.031.
[22] [22] NAOKI I, TAKAAKI N, TOUTA T, et al. Universal Holonomic Single Quantum Gates over a Geometric Spin with Phase-modulated Polarized Light[J]. Optics Letters, 2018, 43(10):2380-2383. DOI: 10.1364/OL.43.002380.
[23] [23] SEKIGUCHI Y, NIIKURA N, KUROIWA R, et al. Optical Holonomic Single Quantum Gates with a Geometric Spin under a Zero Field[J]. Nature Photonics, 2017, 11(5):309-314. DOI: 10.1038/nphoton.2017.40.
[24] [24] YAN Y, SHI C Y, KINOS A. et al. Experimental Implementation of Precisely Tailored Light-matter Interaction via Inverse Engineering[J]. npj Quantum Information, 2021, 7:138. DOI: 10.1038/s41534-021-00473-4.
[25] [25] KINOS A, RIPPE L, KROLL S, et al. Designing Gate Operations for Single-ion Quantum Computing in Rare-earth-ion-doped Crystals[J]. Physical Review A, 2021, 104(5):052624. DOI: 10.1103/PhysRevA.104.052624.
[26] [26] KINOS A, HUNGER D, KOLESOV R, et al. Roadmap for Rare-earth Quantum Computing[J]. 2021, arXiv:2103.15743. DOI: 10.48550/arXiv.2103.15743.
[27] [27] AHARONOV Y, ANANDAN J. Phase Change during a Cyclic Quantum Evolution[J]. Physical Review Letters, 1987, 58(16):1593-1596. DOI: 10.1103/PhysRevLett.58.1593.
[28] [28] LIU B J, SONG X K, XUE Z Y, et al. Plug-and-Play Approach to Nonadiabatic Geometric Quantum Gates[J]. Physical Review Letters, 2019, 123(8):100501. DOI: 10.1103/PhysRevLett.123.100501.
[29] [29] LIANG Y, SHEN P, CHEN T, XUE Z Y. Composite Short-path Nonadiabatic Holonomic Quantum Gates[J]. Physical Review Applied, 2022, 17(3):034015. DOI: 10.1103/PhysRevApplied.17.034015.
[30] [30] VITANOV N V, RANGELOV A A, SHORE B W, et al. Stimulated Raman Adiabatic Passage in Physics, Chemistry, and Beyond[J]. Reviews of Modern Physics, 2017, 89(1):015006. DOI: 10.1103/RevModPhys.89.015006.
[31] [31] TANG G, YANG X Y, YAN Y., LU J. Fast Evolution of Single Qubit Gate in Non-Adiabatic Geometric Quantum Computing[J]. Physics Letters A, 2022, 499:128349. DOI: 10.1016/j.physleta.2022.128349.
[32] [32] JI L N, LIANG Y, SHEN P, XUE Z Y. Nonadiabatic Holonomic Quantum Computation via Path Optimization[J]. Physical Review Applied, 2022, 18(4):044034. DOI: 10.1103/PhysRevApplied.18.044034.
[33] [33] LIU B J, XUE Z Y, YUNG M H. Brachistochrone Non-Adiabatic Holonomic Quantum Control[J]. 2021, arXiv:2001.05182. DOI: 10.48550/arXiv.2001.05182.
[34] [34] ZHOU J, LI S, XUE Z Y, et al. Nonadiabatic Geometric Quantum Gates that are Insensitive to Qubit-frequency Drifts[J]. Physical Review A, 2021, 103(3):032609. DOI: 10.1103/PhysRevA.103.032609.
[35] [35] Li S, Chen T, Xue Z Y. Fast Holonomic Quantum Computation on Superconducting Circuits with Optimal Control[J]. Advanced Quantum Technologies, 2020, 3(3):2000001. DOI: 10.1002/qute.202000001.
[36] [36] LI S, XUE Z Y. Dynamically Corrected Nonadiabatic Holonomic Quantum Gates[J]. Physical Review Applied, 2021, 16(4):044005. DOI: 10.1103/PhysRevApplied.16.044005.
[37] [37] YAN Y, LI Y C, CHEN X, et al. Inverse Engineering of Shortcut Pulses for High Fidelity Initialization on Qubits Closely Spaced in Frequency[J]. Optics Express, 2019, 27(6):8267-8282. DOI: 10.1364/OE.27.008267.
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YANG Xiao-yong, YAN Ying, LU Jie. Designing the Non-adiabatic Geometric Quantum Gates[J]. Journal of Quantum Optics, 2023, 29(2): 20401
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Received: Jun. 29, 2022
Accepted: --
Published Online: Mar. 15, 2024
The Author Email: YAN Ying (yingyan@suda.edu.cn)