基于SFQ电路操控的超导量子比特性能研究

超导量子计算因其操控精度高、拓展性强和制备工艺可兼容传统半导体的先进技术等优点，是目前最有可能实现通用量子计算的方案之一。目前超导量子计算已经发展到需要对上千个比特进行调控的研究阶段，而传统的IQ混频技术操控方案不利于比特数目的进一步增长。本论文介绍的单磁通量子(single flux quantum,SFQ)电路控制超导量子比特的方法为解决多比特操控提供了新思路。本论文从超导量子电路混合系统的基本原理出发，实现了由SFQ电路芯片和超导量子比特芯片构成的多芯片模块(multichip module,MCM)超导量子处理器的设计和制备，并演示了SFQ电路驱动比特的实验。本论文的主要研究内容和结果如下:
(1)完成了用于SFQ控制的超导量子比特芯片的设计及工艺开发。设计并验证了兼容Nb基SFQ芯片和Al基超导量子比特芯片的倒装工艺，该倒装工艺简单稳定，可重复性高。利用该倒装工艺制备的MCM处理器的能量弛豫时间超过50 μs。
(2)表征了我们制备的用于控制超导量子比特的DC/SFQ转换器芯片，其在超导量子比特频率范围内有很宽的正确工作参数区域，可以用于比特的操控。
(3)演示了SFQ脉冲驱动比特的实验。实现了在比特不同次谐频率下驱动比特;完成了SFQ脉冲驱动的拉姆齐干涉实验，其退相位时间超过6 μs。

综上所述，本论文实现了基于SFQ电路的MCM片上集成超导量子比特控制，为实现SFQ电路高保真控制比特奠定了基础。

[1]GROVER L K. Quantum mechanics helps in searching for a needle in a haystack[J]. Physicalreview letters, 1997, 79(2): 325.
[2]SHOR P W. Algorithms for quantum computation: discrete logarithms and factoring[C]//Proceedings 35th annual symposium on foundations of computer science. leee, 1994: 124-134.
[3]ALBASH T, LIDAR D A. Adiabatic quantum computation[J]. Reviews of Modern Physics,2018, 90(1): 015002.
[4]DAS A, CHAKRABARTI B K. Colloquium: Quantum annealing and analog quantum compu-tation[J]. Reviews of Modern Physics, 2008, 80(3): 1061.
[5]MCGEOCH C C. Adiabatic quantum computation and quantum annealing: Theory and practice[M]. Springer Nature, 2022.
[6]LEBFRIED D, BLATT R, MONROE C, et al. Quantum dynamics of single trapped ions[J].Reviews of Modern Physics, 2003, 75(1): 281.
[7]HAFFNER H. Quantum computing with trapped ions[J]. Journal of the Indian Institute ofScience, 2009, 89(3): 317-331.
[8]EBADI S, KEESLING A, CAIN M, et al. Quantum optimization of maximum independent setusing Rydberg atom arrays[J]. Science, 2022, 376(6598): 1209- 1215.
[9] LOSS D, DIVINCENZO D P. Quantum computation with quantum dots[J]. Physical ReviewA, 1998, 57(1): 120.
[10] MORELLO A, PLA JJ, ZWANENBURG F A, et al. Single-shot readout of an electron spin insilicon[J]. Nature, 2010, 467(7316): 687-691.
[11] ARROYO-CAMEJO S, LAZARIEV A, HELL S W, et al. Room temperature high- fidelity holo-nomic single- qubit gate on a solid-state spin[J]. Nature communications, 2014, 5(1): 4870.
[12] GROSS C, BLOCH I. Quantum simulations with ultracold atoms in optical lattices[J]. Science,2017, 357(6355): 995-1001.
[13] NAYAK C, SIMON S H, STERN A, et al. Non-Abelian anyons and topological quantum com-putation[J]. Reviews of Modern Physics, 2008, 80(3): 1083.
[14] REN H, PIENTKA F, HART S, et al. Topological superconductivity in a phase-controlledJosephson junction[J]. Nature, 2019, 569(7754): 93-98.
[15] MOURIK V, ZUO K, FROLOV S M, et al. Signatures of Majorana fermions in hybridsuperconductor-semiconductor nanowire devices[J]. Science, 2012, 336(6084): 1003- 1007.
[16] ARUTE F, ARYA K, BABBUSH R, et al. Quantum supremacy using a programmable super-conducting procesor[J]. Nature, 2019, 5747779): 505-510.
[17] WU Y, BAO W S, CAO S, et al. Strong quantum computational advantage using a supercon-ducting quantum processor[J]. Physical review letters, 2021, 127(18): 180501.
[18] JOSEPHSON B D. Possible new effects in superconductive tunnelling[J]. Physics letters, 1962,1(7): 251-253.
[19]JOSEPHSON B D. The discovery of tunnelling supercurrents[J]. Reviews of Modern Physics,1974, 46(2): 251.
[20]NAKAMURA Y, PASHKIN Y A, TSAI J. Coherent control of macroscopic quantum states ina single-Cooper pair box[J]. nature, 1999, 398(6730): 786-788.
[21]BLAIS A, HUANG R S, WALLRAFF A, et al. Cavity quantum electrodynamics for supercon-ducting electrical circuits: An architecture for quantum computation[J]. Physical Review A,2004, 69(6): 062320.
[22] KOCHJ, TERRI M Y, GAMBETTA J, et al. Charge-insensitive qubit design derived from theCooper pair box[J]. Physical Review A, 2007, 76(4): 042319.
[23]DICARLO L, CHOW J M, GAMBETTA J M, et al. Demonstration of two-qubit algorithmswith a superconducting quantum processor[J]. Nature, 2009, 460(7252): 240-244.
[24]BARENDS R, KELLY J, MEGRANT A, et al. Coherent Josephson qubit suitable for scalablequantum integrated circuits[J]. Physical review letters, 2013, 111(8): 080502.
[25]BARENDS R, KELLY J, MEGRANT A, et al. Superconducting quantum circuits at the surfacecode threshold for fault tolerance[J]. Nature, 2014, 508(7497): 500 503.
[26] NIZ, LI s, DENG X, et al. Beating the break even point with a discrete-variable-encoded logicalqubit[J]. Nature, 2023, 616(7955): 56-60.
[27]SONGC,XUK,LIUW,etal.10-qubit entanglement and parallel logic operations with asuperconducting circuit[J]. Physical review letters, 2017, 119(18): 180511.
[28]GONG M, WANG S, ZHA C, et al. Quantum walks on a programmable two-dimensional 62-qubit superconducting processor[J]. Science, 2021, 372(6545): 948-952.
[29]GAMBETTA J. IBM Quantum System Two: the era of quantum utility is here[EB/OL]. 2033.htps:/www .ibm.com/quantum/blog/quantum roadmap- 2033.
[30]DIAL 0. Eagle' s Quantum Performance Progress[EB/OL]. 2022. htps://research.ibm.com/blog/eagle-quantum-processor-performance.
[31]PRESKILL J. Quantum computing in the NISQ era and beyond[J]. Quantum, 2018, 2: 79.
[32] 0' MALLEY P J, BABBUSH R, KIVLICHAN I D, et al. Scalable quantum simulation ofmolecular energies[J]. Physical Review X, 2016, 6(3): 031007.
[33] ARUTE F, ARYA K, BABBUSH R, et al. Quantum supremacy using a programmable super-conducting processor[J]. Nature, 2019, 574(7779): 505-510.
[34] GONG M, WANG S, ZHA C, et al. Quantum walks on a programmable two dimensional 62-qubit superconducting processor[J]. Science, 2021, 372(6545): 948-952.
[35]WALLRAFF A, SCHUSTER D I, BLAIS A, et al. Approaching unit visibility for control of asuperconducting qubit with dispersive readout[J]. Physical review letters, 2005, 95(6): 060501.
[36] BARDIN J. Beyond-Classical Computing Using Superconducting Quantum Processors[C/OL]//2022 IEEE International Solid-State Circuits Conference (ISSCC): volume 65. 2022: 422-424.DOI: 10.1109/ISSCC42614.2022.9731635.
[37] FOWLER A G, MARIANTONI M, MARTINIS J M, et al. Surface codes: Towards practicallarge-scale quantum computation[J/OL]. Phys. Rev. A, 2012, 86: 032324. htp://ink.aps.org/doi/10.1 103/PhysRevA.86.032324.
[38]DICKEL C, WESDORP J, LANGFORD N, et al. Chip-to-chip entanglement of transmon qubitsusing engineered measurement fields[J]. Physical Review B, 2018, 97(6): 064508.
[39] CAMPAGNE- IBARCQ P, ZALYS-GELLER E, NARLA A, et al. Deterministic Remote Entan-glement of Superconducting Circuits through Microwave Two-Photon Transitions[J/OL]. Phys.Rev. Lett, 2018, 120: 200501. htps://link.aps.org/doi/10.1 103/PhysRevLett. 1 20.200501.
[40] QIUJ, LIU Y, NIU J, et al. Deterministic quantum teleportation between distant superconduct-ing chips[A]. 2023. arXiv: 2302.08756.
[41] AT ETH ZURICH P. Longest microwave quantum link[EB/OL]. 2020. htps://ethz.ch/en/news- and- events/eth- news/news/2020/03/longest- microwave- quantum- link.html.
[42] PAUKA S, DAS K, KALRA R, et al. A cryogenic CMOS chip for generating control signalsfor multiple qubits[J]. Nature Electronics, 2021, 4(1): 64-70.
[43] LECOCQ F, QUINLAN F, CICAK K, et al. Control and readout of a superconducting qubitusing a photonic link[J]. Nature, 2021, 591(7851): 575-579.
[44]UNDERWOOD D, GLICKJ A, INOUE K, et al. Using cryogenic CMOS control electronicsto enable a two-qubit cross -resonance gate[J]. PRX Quantum, 2024, 5(1): 010326. ..
[45] CHARBON E, SEBASTIANO F, VLADIMIRESCU A, et al. Cryo-CMOS for quantum com-puting[C]//2016 IEEE International Electron Devices Meeting (IEDM). IEEE, 2016: 13-5.
[46] LIKHAREV K K, MUKHANOV O A, SEMENOV V K. Resistive single fux quantum logicfor the Josephson-junction digital technology[J]. SQUID, 1985, 85: 1103-1108.
[47] ZHOU X, HABIF JL, HERR A M, et al. A tipping pulse scheme for a rf- SQUID qubit[J]. IEEEtransactions on applied superconductivity, 2001, 11(1): 1018-1021..
[48] OHKIT A, WULF M, BOCKO M F. Picosecond on-chip qubit control circuitry[J]. IEEEtransactions on applied superconductivity, 2005, 15(2): 837-840.
[49] CASTELLANO M G, CHIARELLO F, LEONI R, et al. Rapid single- fux quantum control ofthe energy potential in a double SQUID qubit circuit[J]. Superconductor Science and Technol-ogy, 2007, 20(6): 500.
[50] CRANKSHAW DS, HABIF J L, ZHOU X, et al. An RSFQ variable duty cycle oscillator fordriving a superconductive qubit[J]. IEEE transactions on applied superconductivity, 2003, 13(2): 966-969.
[51] YAMANASHI Y, ASANO T, YOSHIKAWA N. On-chip microwave generator for manipulationof superconductive quantum bits[J]. Physica C: Superconductivity and its applications, 2006,445: 967-970.
[52] MIURA S, TAKEUCHI N, YAMANASHI Y, et al. Implementation of SFQ microwave choppersfor controlling quantum bits[J]. Physics Procedia, 2012, 36: 250-255.
[53] MATSUDA G, YAMANASHI Y, YOSHIKAWA N. Design of an SFQ microwave chopperfor controlling quantum bits[J]. IEEE transactions on applied superconductivity, 2007, 17(2):146- 149.
[54] TAKEUCHI N, 0ZAWA D, YAMANASHI Y, et al. On-chip RSFQ microwave pulse gener-ator using a multi-flux -quantum driver for controlling superconducting qubits[J]. Physica C: .Superconductivity and its applications, 2010, 470(20): 1550-1554.
[55]BRUMMER G, RAFIQUE R, OHKI T. Phase and amplitude modulator for microwave pulsegeneration[J]. IEEE transactions on applied superconductivity, 2010, 21(3): 583-586.
[56] MCDERMOTT R, VAVILOV M. Accurate qubit control with single fux quantum pulses[J].Physical Review Applied, 2014, 2(1): 014007.
[57] LEONARD JR E, BECK M A, NEL SON J, et al. Digital coherent control of a superconductingqubit[J]. Physical Review Applied, 2019, 11(1): 014009.
[58] LIEBERMANN P J, WILHELM F K. Optimal qubit control using single-fAux quantum pulses[J]. Physical Review Applied, 2016, 6(2): 024022.
[59] LI K, MCDERMOTT R, VAVILOV M G. Hardware efficient qubit control with single-flux-quantum pulse sequences[J]. Physical Review Applied, 2019, 12(1): 014044.
[60] LIUC H, BALLARD A, OL AYA D, et al. Single fux quantum-based digital control of super-conducting qubits in a multichip module[J]. PRX Quantum, 2023, 4(3): 030310.
[61] WANG Y, GAO W, LIU K, et al. Single- Flux-Quantum-Activated Controlled-Z Gate for Trans-mon Qubits[J]. Physical Review Applied, 2023, 19(4): 044031.
[62] LIU K, WANG Y, JI B, et al. Single-flux-quantum-based qubit control with tunable drivingstrength[J]. Chinese Physics B, 2023, 32(12): 128501.
[63] MCDERMOTT R, VAVILOV M, PLOURDE B, et al. Quantum- classical interface based onsingle fux quantum digital logic[J]. Quantum science and technology, 2018, 3(2): 024004.
[64] LONDON F, LONDON H. The electromagnetic equations of the supraconductor[J]. Proceed-ings of the Royal Society of London. Series A-Mathematical and Physical Sciences, 1935, 149(866): 71-88.
[65] BARDEEN J, COOPER L N, SCHRIEFFER J R. Theory of superconductivity[J]. Physicalreview, 1957, 108(5): 1175.
[66]DOLL R, NABAUER M. Experimental proof of magnetic flux quantization in a superconduct-ing ring[]. Physical Review Letters, 1961, 7(2): 51.
[67] LANGFORD N K. Circuit qed-lecture notes[A]. 2013.
[68]GRIFFITHS D J, SCHROETER D. Instructor's Solutions Manual: Introduction to QuantumMechanics[M]. Pearson education, 2005.
[69] STEWART W. Current-voltage characteristics of Josephson junctions[J]. Applied physics let-ters, 1968, 12(8): 277-280.
[70] KAUTZ R L. Noise, chaos, and the Josephson voltage standard[J]. Reports on Progress inPhysics, 1996, 59(8): 935.
[71] DEVORET M H, et al. Quantum fuctuations in electrical circuits[J]. Les Houches, SessionLXIII, 1995, 7(8): 133-135.
[72] DEVORET M H, HUARD B, SCHOELKOPF R, et al. Quantum machines: measurement andcontrol of engineered quantum systems: volume 96[M]. Oxford University Press, USA, 2014.
[73] DEVORET M H, SCHOELKOPF R J. Superconducting circuits for quantum information: anoutlook[J]. Science, 2013, 339(6124): 1169-1174.
[74] GRIFFITHS D J, SCHROETER D F. Introduction to quantum mechanics[M]. Cambridgeuniversity press, 2018.
[75] SIMONS R N. Coplanar waveguide circuits, components, and systems[M]. John Wiley & Sons,2004.
[76] POZAR D M. Microwave engineering[M]. John wiley & sons, 2011.
[77] SYSTEMS C D. AWR RF 1 Microwave Design[EB/OL]. 2024. htps://www .cadence com/en_US/home/tools/system- analysis/rf- microwave-design.html.
[78]A quantum engineer's guide to superconducting qubits[]. Applied physics reviews, 2019, 6(2).
[79] NIELSEN M A, CHUANG I L. Quantum computation and quantum information[M]. Cam-bridge university press, 2010.
[80]Sonnet Software[EB/OL]. htps://www.sonnetsoftware.com/.
[81] Ansys HFSS I 3D High Frequency Simulation Software[EB/OL]. htps://ww .ansys.com/products/electronics/ ansys-hfss.
[82] COMSOL Multiphysics[Z].
[83] SAKURAI J J, NAPOLITANO J. Modern quantum mechanics[M]. Cambridge UniversityPress, 2020.
[84]YU Y, HAN S, CHU X, et al. Coherent temporal oscillations of macroscopic quantum states ina Josephson junction[J]. Science, 2002, 296(5569): 889-892.
[85] NAKAMURA Y, PASHKIN Y A, TSAIJ S. Rabi oscillations in a Josephson-junction chargetwo-level system[J]. Physical Review Letters, 2001, 87(24): 246601.
[86]SCULLY M O, ZUBAIRY M S. Quantum optics[M]. Cambridge university press, 1997.
[87] SCHUSTER D, HOUCK A A, SCHREIER J, et al. Resolving photon number states in a super-conducting circuit[J]. Nature, 2007, 445(7127): 515-518.
[88] OLIVER W D, WELANDER P B. Materials in superconducting quantum bits[J]. MRS bulletin,2013, 38(10): 816-825.
[89]MCDERMOTT R. Materials origins of decoherence in superconducting qubits[J]. IEEE Trans-actions on Applied Superconductivity, 2009, 19(1): 2-13.
[90]SIDDIQI I. Engineering high-coherence superconducting qubits[J]. Nature Reviews Materials,2021, 6(10): 875-891.
[91] DOLAN G. Ofset masks for lift-off photoprocessing[J]. Applied Physics Letters, 1977, 31(5):337-339.
[92] LECOCQ F, POP I M, PENG Z, et al. Junction fabrication by shadow evaporation without asuspended bridge[J]. Nanotechnology, 201 1, 22(31): 315302.
[93]POTTS A, ROUTLEY P, PARKER G J, et al. Novel fabrication methods for submicrometerJosephson junction qubits[J]. Journal of Materials Science: Materials in Electronics, 2001, 12:289-293.
[94] COSTACHE M V, BRIDOUX G, NEUMANN I, et al. Lateral metallic devices made by amultiangle shadow evaporation technique[J]. Journal of Vacuum Science & Technology B,2012, 30(4).
[95]MARTINIS J M, COOPER K B, MCDERMOTT R, et al. Decoherence in Josephson Qubitsfrom Dielectric Loss[J/OL]. Phys. Rev. Lett, 2005, 95: 210503. htp://ink .aps.org/doi/10.1103/PhysRevLtt95.210503.
[96]WOODS W, CALUSINE G, MELVILLE A, et al. Determining Interface Dielectric Losses inSuperconducting Coplanar Waveguide Resonators[J/OL]. Phys. Rev. Appl., 2019, 12: 014012.htp://ink .aps.org/doi/10.1103/PhysRevApplied.12.014012.
[97]PAPPAS D P, VISSERS M R, WISBEY D S, et al. Two Level System Loss in SuperconductingMicrowave Resonators[J/OL]. IEEE Transactions on Applied Superconductivity, 2011, 21(3):871-874. DOI: 10.1109/TASC.2010.2097578.
[98] ROSENBERG D, KIM D, DAS R, et al.3D integrated superconducting qubits[J]. npj quantuminformation, 2017, 3(1): 42.
[99]MARTINIS J M, ANSMANN M, AUMENTADO J. Energy decay in superconductingJosephson-junction qubits from nonequilibrium quasiparticle excitations[J]. Physical reviewletters, 2009, 103(9): 097002.
[100] CATELANI G, KOCH J, FRUNZIO L, et al. Quasiparticle Relaxation of SuperconductingQubits in the Presence of Flux[J/OL]. Phys. Rev. Lett, 2011, 106: 077002. htps://in// .aps.org/doi/10.1 103/PhysRevLett.106.077002.
[101] RISTE D, BULTINK C, TIGGELMAN M J, et al. Millisecond charge- parity fuctuations andinduced decoherence in a superconducting transmon qubit[J]. Nature communications, 2013, 4(1): 1913.
[102] GIAZOTTO F, HEIKKILA T T, LUUKANEN A, et al. Opportunities for mesoscopics in ther-mometry and refrigeration: Physics and applications[J]. Reviews of Modern Physics, 2006, 78(1): 217.
[103] KOSEN S, LI H X, ROMMEL M, et al. Building blocks of a fip- chip integrated superconduct-ing quantum processor[J]. Quantum Science and Technology, 2022, 7(3): 035018.
[104] RUANO-LOPEZJ, AGUIRREGABIRIA M, TIJERO M, et al. A new SU-8 process to integrateburied waveguides and sealed microchannels for a Lab-on-a-Chip[J]. Sensors and Actuators B:Chemical, 2006, 114(1): 542-551.
[105] ZINE-EL-ABIDINE I, OKONIEWSKI M. A low-temperature SU-8 based wafer level hermeticpackaging for MEMS devices[J]. IEEE transactions on Advanced Packaging, 2009, 32(2): 448-452.
[106] LAKER A, COUTU R A. Using cross-linked SU-8 to fip-chip bond, assemble, and packageMEMS devices[]. IEEE Transactions on Components, Packaging and Manufacturing Technol-ogy, 2015, 5(3): 301-306.
[107] REED M, DICARLO L, JOHNSON B, et al. High- fidelity readout in circuit quantum electro-dynamics using the Jaynes-Cummings nonlinearity[J]. Physical review letters, 2010, 105(17):173601.
[108] BISHOP L S, GINOSSAR E, GIRVIN S. Response of the strongly driven jaynes-cummingsoscillator[J]. Physical review letters, 2010, 105(10): 100505.
[109] MEGRANT A, NEILL C, BARENDS R, et al. Planar superconducting resonators with internalquality factors above one million[J]. Applied Physics Letters, 2012, 100(11).
[110] REDFIELD A G. On the theory of relaxation processes[J]. IBM Journal of Research andDevelopment, 1957, 1(1): 19-31.
[111] ITHIER G, COLLIN E, JOYEZ P, et al. Decoherence in a superconducting quantum bit circuit[J]. Physical Review B, 2005, 72(13): 134519.
[112] SHAPIRO S. Josephson currents in superconducting tunneling: The effect of microwaves andother observations[J]. Physical Review Letters, 1963, 11(2): 80.