硅基单原子体系中的电学操控理论研究

硅基磷原子的原子核自旋因其较好的相干时间而被视为固态量子比特的良好信息载体。核自旋的相干控制一般是通过核磁共振实现的，拉比频率较慢，且核自旋难以直接耦合到其他系统，不利于体系的大规模扩展。为核自旋创造电偶极矩以实现快速核电共振的挑战在于如何使核自旋可被电场有效驱动，但又要避免电噪声引起的自旋退相干。本文从理论上出，在超精细相互作用和磁场梯度这两种机制下，通过一个类似拉曼跃迁的过程，可以间接实现快速的电偶极诱导的核电共振。与纯磁学控制的核自旋跃迁相比，该方案中的电子、原子核和电荷的杂化导致了更强的电偶极矩跃迁。分析对体系哈密顿量作数值对角化的结果，可发现在特定的操纵点——电离点时，核自旋比特获得最大电偶极驱动强度(约为 39 MHz)，且核自旋共振频率对电噪声具有一定鲁棒性，从而实现了高保真的量子门操作，核自旋比特在相干时间内可以实现 100 多次的拉比振荡，展现了 Si:P 核自旋量子比特的快速电学控制在硅基量子计算中的应用前景。

[1]  CIRAC J I, ZOLLER P. Quantum computations with cold trapped ions[J]. Physical Review Letters, 1995, 74(20): 4091. 

[2]  BALL P. Semiconductor technology looks up[J]. Nature Materials, 2022, 21(2): 132-132. 

[3]  台湾积体电路制造股份有限公司. 专业集成电路制造服务[EB/OL]. 2022
[2022-04-07]. https://www.tsmc.com/chinese/dedicatedFoundry/technology/logic. 

[4]  ANTHONY S. Beyond Silicon: IBM Unveils World’s First 7nm Chip[J]. Ars Technica, 2015, 9. 

[5]  FEYNMAN R P. Simulating Physics with Computers[J]. International Journal of Theoretical Physics, 1982, 21(6/7). 

[6]  SANDERS B C. Quantum Leap for Quantum Primacy[J]. Physics, 2021, 14: 147. 

[7]  ARUTE F, ARYA K, BABBUSH R, et al. Quantum supremacy using a programmable super- conducting processor[J]. Nature, 2019, 574(7779): 505-510. 

[8]  ZHONG H S, WANG H, DENG Y H, et al. Quantum computational advantage using photons [J]. Science, 2020, 370(6523): 1460-1463. 

[9]  GROVER L K. A fast quantum mechanical algorithm for database search[C]//Proceedings of the twenty-eighth annual ACM symposium on Theory of computing. 1996: 212-219. 

[10]  SHOR P W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer[J]. SIAM review, 1999, 41(2): 303-332. 

[11]  KANDALA A, MEZZACAPO A, TEMME K, et al. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets[J]. Nature, 2017, 549(7671): 242-246. 

[12]  BARENCO A, BENNETT C H, CLEVE R, et al. Elementary gates for quantum computation [J]. Physical Review A, 1995, 52(5): 3457. 

[13]  NIELSEN M A, CHUANG I. Quantum computation and quantum information[M]. American Association of Physics Teachers, 2002. 

[14]  DIVINCENZO D P. Quantum gates and circuits[J]. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1998, 454(1969): 261-276. 

[15]  DIVINCENZO D P. The physical implementation of quantum computation[J]. Fortschritte der Physik: Progress of Physics, 2000, 48(9-11): 771-783. 

[16]  VELDHORST M, EENINK H, YANG C H, et al. Silicon CMOS architecture for a spin-based quantum computer[J]. Nature Communications, 2017, 8(1): 1-8. 

[17]  CAMENZIND L C, GEYER S, FUHRER A, et al. A hole spin qubit in a fin field-effect transistor above 4 kelvin[J]. Nature Electronics, 2022, 5(3): 178-183. 

[18]  ZWERVER A, KRÄHENMANN T, WATSON T, et al. Qubits made by advanced semiconductor manufacturing[J]. Nature Electronics, 2022, 5(3): 184-190.
[19]  LOSS D, DIVINCENZO D P. Quantum computation with quantum dots[J]. Physical Review A, 1998, 57(1): 120. 

[20]  KANE B E. A silicon-based nuclear spin quantum computer[J]. Nature, 1998, 393(6681): 133-137. 

[21]  ELZERMAN J, HANSON R, WILLEMS VAN BEVEREN L, et al. Semiconductor few- electron quantum dots as spin qubits[M]//Quantum Computing in Solid State Systems. Springer, 2006: 298-305. 

[22]  HANSON R, KOUWENHOVEN L P, PETTA J R, et al. Spins in few-electron quantum dots [J]. Reviews of Modern Physics, 2007, 79(4): 1217. 

[23]  NOWACK K C, KOPPENS F, NAZAROV Y V, et al. Coherent control of a single electron spin with electric fields[J]. Science, 2007, 318(5855): 1430-1433. 

[24]  CAO G, LI H O, TU T, et al. Ultrafast universal quantum control of a quantum-dot charge qubit using Landau–Zener–Stückelberg interference[J]. Nature Communications, 2013, 4(1): 1-7. 

[25]  KIM J S, TYRYSHKIN A M, LYON S A. Annealing shallow Si/SiO2 interface traps in electron-beam irradiated high-mobility metal-oxide-silicon transistors[J]. Applied Physics Letters, 2017, 110(12): 123505. 

[26]  WANG K, LI H O, LUO G, et al. Improving mobility of silicon metal-oxide–semiconductor devices for quantum dots by high vacuum activation annealing[J]. Europhysics Letters, 2020, 130(2): 27001. 

[27]  ZWANENBURG F A, DZURAK A S, MORELLO A, et al. Silicon quantum electronics[J]. Reviews of Modern Physics, 2013, 85(3): 961. 

[28]  WITZEL W M, CARROLL M S, MORELLO A, et al. Electron spin decoherence in isotope- enriched silicon[J]. Physical Review Letters, 2010, 105(18): 187602. 

[29]  TYRYSHKIN A M, TOJO S, MORTON J J, et al. Electron spin coherence exceeding seconds in high-purity silicon[J]. Nature Materials, 2012, 11(2): 143-147. 

[30]  KASTNER M A. The single-electron transistor[J]. Reviews of Modern Physics, 1992, 64(3): 849. 

[31]  ZAJAC D M, SIGILLITO A J, RUSS M, et al. Resonantly driven CNOT gate for electron spins [J]. Science, 2018, 359(6374): 439-442. 

[32]  KOPPENS F H, BUIZERT C, TIELROOIJ K J, et al. Driven coherent oscillations of a single electron spin in a quantum dot[J]. Nature, 2006, 442(7104): 766-771. 

[33]  WATSON T F, WEBER B, HSUEH Y L, et al. Atomically engineered electron spin lifetimes of 30 s in silicon[J]. Science Advances, 2017, 3(3): e1602811. 

[34]  PLA J J, TAN K Y, DEHOLLAIN J P, et al. A single-atom electron spin qubit in silicon[J]. Nature, 2012, 489(7417): 541-545. 

[35]  HE Y, GORMAN S, KEITH D, et al. A two-qubit gate between phosphorus donor electrons in silicon[J]. Nature, 2019, 571(7765): 371-375. 

[36]  KRANZ L, GORMAN S K, THORGRIMSSON B, et al. Exploiting a Single-Crystal Environment to Minimize the Charge Noise on Qubits in Silicon[J]. Advanced Materials, 2020, 32(40): 2003361. 

[37]  TAKEDA K, NOIRI A, NAKAJIMA T, et al. Quantum tomography of an entangled three-qubit state in silicon[J]. Nature Nanotechnology, 2021, 16(9): 965-969. 

[38]  HENDRICKX N W, LAWRIE W I, RUSS M, et al. A four-qubit germanium quantum processor [J]. Nature, 2021, 591(7851): 580-585. 

[39]  PHILIPS S G, MĄDZIK M T, AMITONOV S V, et al. Universal control of a six-qubit quantum processor in silicon[EB/OL]. 2022. https://arxiv.com/abs/2202.09252. 

[40]  XUE X, RUSS M, SAMKHARADZE N, et al. Quantum logic with spin qubits crossing the surface code threshold[J]. Nature, 2022, 601(7893): 343-347. 

[41]  NOIRI A, TAKEDA K, NAKAJIMA T, et al. Fast universal quantum gate above the fault- tolerance threshold in silicon[J]. Nature, 2022, 601(7893): 338-342. 

[42]  FUECHSLE M, MIWA J A, MAHAPATRA S, et al. A single-atom transistor[J]. Nature Nanotechnology, 2012, 7(4): 242-246. 

[43]  MĄDZIK M T, ASAAD S, YOUSSRY A, et al. Precision tomography of a three-qubit donor quantum processor in silicon[J]. Nature, 2022, 601(7893): 348-353. 

[44]  BURKARD G, LADD T D, NICHOL J M, et al. Semiconductor Spin Qubits[EB/OL]. 2021. https://arxiv.com/abs/2112.08863. 

[45]  ELZERMAN J, HANSON R, WILLEMS VAN BEVEREN L, et al. Single-shot read-out of an individual electron spin in a quantum dot[J]. Nature, 2004, 430(6998): 431-435. 

[46]  REILLY D, MARCUS C, HANSON M, et al. Fast single-charge sensing with a rf quantum point contact[J]. Applied Physics Letters, 2007, 91(16): 162101. 

[47]  GOLOVACH V N, BORHANI M, LOSS D. Electric-dipole-induced spin resonance in quantum dots[J]. Physical Review B, 2006, 74(16): 165319. 

[48]  LEVY J. Universal quantum computation with spin-1/2 pairs and Heisenberg exchange[J]. Physical Review Letters, 2002, 89(14): 147902. 

[49]  PETTA J R, JOHNSON A C, TAYLOR J M, et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots[J]. Science, 2005, 309(5744): 2180-2184. 

[50]  BLUHM H, FOLETTI S, NEDER I, et al. Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 𝜇s[J]. Nature Physics, 2011, 7(2): 109-113. 

[51]  MAUNE B M, BORSELLI M G, HUANG B, et al. Coherent singlet-triplet oscillations in a silicon-based double quantum dot[J]. Nature, 2012, 481(7381): 344-347. 

[52]  NICHOL J M, ORONA L A, HARVEY S P, et al. High-fidelity entangling gate for double- quantum-dot spin qubits[J]. NPJ Quantum Information, 2017, 3(1): 1-5. 

[53]  BØTTCHER C, HARVEY S, FALLAHI S, et al. Parametric longitudinal coupling between a high-impedance superconducting resonator and a semiconductor quantum dot singlet-triplet spin qubit[EB/OL]. 2021. https://arxiv.com/abs/2107.10269. 

[54]  DIVINCENZO D P, BACON D, KEMPE J, et al. Universal quantum computation with the exchange interaction[J]. Nature, 2000, 408(6810): 339-342. 

[55]  MEDFORD J, BEIL J, TAYLOR J, et al. Self-consistent measurement and state tomography of an exchange-only spin qubit[J]. Nature Nanotechnology, 2013, 8(9): 654-659. 

[56]  ENG K, LADD T D, SMITH A, et al. Isotopically enhanced triple-quantum-dot qubit[J]. Sci- ence Advances, 2015, 1(4): e1500214. 

[57]  TAYLOR J M, SRINIVASA V, MEDFORD J. Electrically protected resonant exchange qubits in triple quantum dots[J]. Physical Review Letters, 2013, 111(5): 050502. 

[58]  RUSS M, BURKARD G. Asymmetric resonant exchange qubit under the influence of electrical noise[J]. Physical Review B, 2015, 91(23): 235411. 

[59]  SHIM Y P, TAHAN C. Charge-noise-insensitive gate operations for always-on, exchange-only qubits[J]. Physical Review B, 2016, 93(12): 121410. 

[60]  PAKKIAM P, TIMOFEEV A, HOUSE M, et al. Single-shot single-gate rf spin readout in silicon [J]. Physical Review X, 2018, 8(4): 041032. 

[61]  MUHONEN J T, DEHOLLAIN J P, LAUCHT A, et al. Storing quantum information for 30 seconds in a nanoelectronic device[J]. Nature Nanotechnology, 2014, 9(12): 986-991. 

[62]  KOILLER B, HU X, SARMA S D. Exchange in silicon-based quantum computer architecture [J]. Physical Review Letters, 2001, 88(2): 027903. 

[63]  MORELLO A, PLA J J, ZWANENBURG F A, et al. Single-shot readout of an electron spin in silicon[J]. Nature, 2010, 467(7316): 687-691. 

[64]  WEBER B, MAHAPATRA S, RYU H, et al. Ohm’s law survives to the atomic scale[J]. Science, 2012, 335(6064): 64-67. 

[65]  PLA J J, TAN K Y, DEHOLLAIN J P, et al. High-fidelity readout and control of a nuclear spin qubit in silicon[J]. Nature, 2013, 496(7445): 334-338. 

[66]  MUHONEN J, LAUCHT A, SIMMONS S, et al. Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking[J]. Journal of Physics: Condensed Matter, 2015, 27(15): 154205. 

[67]  NADJ-PERGE S, FROLOV S, BAKKERS E, et al. Spin–orbit qubit in a semiconductor nanowire[J]. Nature, 2010, 468(7327): 1084-1087. 

[68]  PIORO-LADRIERE M, TOKURA Y, OBATA T, et al. Micromagnets for coherent control of spin-charge qubit in lateral quantum dots[J]. Applied Physics Letters, 2007, 90(2): 024105. 

[69]  TOKURA Y, VAN DER WIEL W G, OBATA T, et al. Coherent single electron spin control in a slanting Zeeman field[J]. Physical Review Letters, 2006, 96(4): 047202. 

[70]  YONEDA J, TAKEDA K, OTSUKA T, et al. A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%[J]. Nature Nanotechnology, 2018, 13(2): 102- 106. 

[71]  BENITO M, CROOT X, ADELSBERGER C, et al. Electric-field control and noise protection of the flopping-mode spin qubit[J]. Physical Review B, 2019, 100(12): 125430. 

[72]  CROOT X, MI X, PUTZ S, et al. Flopping-mode electric dipole spin resonance[J]. Physical Review Research, 2020, 2(1): 012006. 

[73]  MILLS A, GUINN C, GULLANS M, et al. Two-qubit silicon quantum processor with operation fidelity exceeding 99%[J/OL]. Science Advances, 2022, 8(14): eabn5130. https://www.scienc e.org/doi/abs/10.1126/sciadv.abn5130. 

[74]  TOSI G, MOHIYADDIN F A, SCHMITT V, et al. Silicon quantum processor with robust long- distance qubit couplings[J]. Nature Communications, 2017, 8(1): 1-11. 

[75]  KRAUTH F, GORMAN S, HE Y, et al. Flopping-mode electric dipole spin resonance in phosphorus donor qubits in silicon[EB/OL]. 2021. https://arxiv.com/abs/2105.02906. 

[76]  ASAAD S, MOURIK V, JOECKER B, et al. Coherent electrical control of a single high-spin nucleus in silicon[J]. Nature, 2020, 579(7798): 205-209. 

[77]  RUSS M, BURKARD G. Three-electron spin qubits[J]. Journal of Physics: Condensed Matter, 2017, 29(39): 393001. 

[78]  SALFI J, MOL J A, CULCER D, et al. Charge-insensitive single-atom spin-orbit qubit in silicon [J]. Physical Review Letters, 2016, 116(24): 246801. 

[79]  TOSI G, MOHIYADDIN F A, TENBERG S, et al. Robust electric dipole transition at microwave frequencies for nuclear spin qubits in silicon[J]. Physical Review B, 2018, 98(7): 075313. 

[80]  WINKLER R. Spin-orbit coupling effects in two-dimensional electron and hole systems: volume 191[M]. Springer, 2003. 

[81]  ITOH K M, WATANABE H. Isotope engineering of silicon and diamond for quantum computing and sensing applications[J]. MRS Communications, 2014, 4(4): 143-157. 

[82]  RAHMAN R, PARK S H, BOYKIN T B, et al. Gate-induced g-factor control and dimensional transition for donors in multivalley semiconductors[J]. Physical Review B, 2009, 80(15): 155301. 

[83]  SAVYTSKYY R, BOTZEM T, DE FUENTES I F, et al. An electrically-driven single-atom flip- flop’qubit[EB/OL]. 2022. https://arxiv.com/abs/2202.04438. 

[84]  HILL C D, PERETZ E, HILE S J, et al. A surface code quantum computer in silicon[J]. Science Advances, 2015, 1(9): e1500707. 

[85]  O’GORMAN J, NICKERSON N H, ROSS P, et al. A silicon-based surface code quantum computer[J]. NPJ Quantum Information, 2016, 2(1): 1-14. 

[86]  KOBAYASHI T, SALFI J, CHUA C, et al. Engineering long spin coherence times of spin–orbit qubits in silicon[J]. Nature Materials, 2021, 20(1): 38-42. 

[87]  SCAPPUCCI G, KLOEFFEL C, ZWANENBURG F A, et al. The germanium quantum information route[J]. Nature Reviews Materials, 2021, 6(10): 926-943. 

[88]  SALFI J, MOL J A, CULCER D, et al. Charge-insensitive single-atom spin-orbit qubit in silicon [J]. Physical Review Letters, 2016, 116(24): 246801.