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Engineering high-coherence superconducting qubits


Advances in materials science and engineering have played a central role in the development of classical computers and will undoubtedly be critical in propelling the maturation of quantum information technologies. In approaches to quantum computation based on superconducting circuits, as one goes from bulk materials to functional devices, amorphous films and non-equilibrium excitations — electronic and phononic — are introduced, leading to dissipation and fluctuations that limit the computational power of state-of-the-art qubits and processors. In this Review, the major sources of decoherence in superconducting qubits are identified through an exploration of seminal qubit and resonator experiments. The proposed microscopic mechanisms associated with these imperfections are summarized, and directions for future research are discussed. The trade-offs between simple qubit primitives based on a single Josephson tunnel junction and more complex designs that use additional circuit elements, or new junction modalities, to reduce sensitivity to local noise sources are discussed, particularly in the context of materials optimization strategies for each architecture.

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Fig. 1: Superconducting qubits.
Fig. 2: Qubit types.
Fig. 3: Sources of decoherence.
Fig. 4: TLS defects.
Fig. 5: Experimental evidence for TLS defects.
Fig. 6: Quasiparticles.
Fig. 7: Noise-protected circuits.
Fig. 8: Novel superconducting qubits.


  1. 1.

    Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information 10th anniversary edn (Cambridge Univ. Press, 2010).

  2. 2.

    Hidary, J. D. Quantum Computing: An Applied Approach (Springer, 2019).

  3. 3.

    Bell, J. S. & Aspect, A. Speakable and Unspeakable in Quantum Mechanics. Collected Papers on Quantum Philosophy (Cambridge Univ. Press, 2008).

  4. 4.

    Zurek, W. H. Decoherence and the transition from quantum to classical. Phys. Today 44, 36–44 (1991).

    Article  Google Scholar 

  5. 5.

    Terhal, B. M. Quantum error correction for quantum memories. Rev. Mod. Phys. 87, 307–346 (2015).

    Article  Google Scholar 

  6. 6.

    Arute, F. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019).

    CAS  Article  Google Scholar 

  7. 7.

    Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum information: an outlook. Science 339, 1169–1174 (2013).

    CAS  Article  Google Scholar 

  8. 8.

    Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999).

    CAS  Article  Google Scholar 

  9. 9.

    Tinkham, M. Introduction to Superconductivity 2nd edn (Dover, 2004).

  10. 10.

    Martinis, J. M., Devoret, M. H. & Clarke, J. Energy-level quantization in the zero-voltage state of a current-biased Josephson junction. Phys. Rev. Lett. 55, 1543–1546 (1985).

    CAS  Article  Google Scholar 

  11. 11.

    Martinis, J. M., Devoret, M. H. & Clarke, J. Quantum Josephson junction circuits and the dawn of artificial atoms. Nat. Phys. 16, 234–237 (2020).

    CAS  Article  Google Scholar 

  12. 12.

    Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).

    Article  CAS  Google Scholar 

  13. 13.

    You, J. Q., Hu, X., Ashhab, S. & Nori, F. Low-decoherence flux qubit. Phys. Rev. B 75, 140515 (2007).

    Article  CAS  Google Scholar 

  14. 14.

    Duzer, T. V. Principles of Superconductive Devices and Circuits 2nd edn (Prentice Hall, 1998).

  15. 15.

    Golubov, A. A., Kupriyanov, M. Y. & Il’ichev, E. The current-phase relation in Josephson junctions. Rev. Mod. Phys. 76, 411–469 (2004).

    CAS  Article  Google Scholar 

  16. 16.

    Makhlin, Y., Schön, G. & Shnirman, A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys. 73, 357–400 (2001).

    Article  Google Scholar 

  17. 17.

    Wendin, G. & Shumeiko, V. S. Quantum bits with Josephson junctions (review article). Low Temp. Phys. 33, 724–744 (2007).

    CAS  Article  Google Scholar 

  18. 18.

    Kjaergaard, M. et al. Superconducting qubits: current state of play. Annu. Rev. Condens. Matter Phys. 11, 369–395 (2020).

    Article  Google Scholar 

  19. 19.

    Krantz, P. et al. A quantum engineers guide to superconducting qubits. Appl. Phys. Rev. 6, 021318 (2019).

    Article  CAS  Google Scholar 

  20. 20.

    Wendin, G. Quantum information processing with superconducting circuits: a review. Rep. Prog. Phys. 80, 106001 (2017).

    CAS  Article  Google Scholar 

  21. 21.

    Kockum, A. F. & Nori, F. in Fundamentals and Frontiers of the Josephson Effect (ed. Tafuri, F.) 703–741 (Springer, 2019).

  22. 22.

    Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Appl. Phys. Lett. 107, 162601 (2015).

    Article  CAS  Google Scholar 

  23. 23.

    Córcoles, A. D. et al. Protecting superconducting qubits from radiation. Appl. Phys. Lett. 99, 181906 (2011).

    Article  CAS  Google Scholar 

  24. 24.

    Gambetta, J. M. et al. Investigating surface loss effects in superconducting transmon qubits. IEEE Trans. Appl. Superconductivity 27, 1–5 (2017).

    Article  Google Scholar 

  25. 25.

    Douçot, B. & Ioffe, L. B. Physical implementation of protected qubits. Rep. Prog. Phys. 75, 072001 (2012).

    Article  Google Scholar 

  26. 26.

    Esteve, D., Devoret, M. H. & Martinis, J. M. Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Phys. Rev. B 34, 158–163 (1986).

    CAS  Article  Google Scholar 

  27. 27.

    Oliver, W. D. & Welander, P. B. Materials in superconducting quantum bits. MRS Bull. 38, 816–825 (2013).

    CAS  Article  Google Scholar 

  28. 28.

    Müller, C., Cole, J. H. & Lisenfeld, J. Towards understanding two-level-systems in amorphous solids: insights from quantum circuits. Rep. Prog. Phys. 82, 124501 (2019).

    Article  CAS  Google Scholar 

  29. 29.

    Arutyunov, K. Y. et al. Relaxation of nonequilibrium quasiparticles in mesoscopic size superconductors. J. Phys. Condens. Matter 30, 343001 (2018).

    Article  Google Scholar 

  30. 30.

    Glazman, L. I. & Catelani, G. Bogoliubov quasiparticles in superconducting qubits. SciPost Phys. Lect. Notes (2021).

  31. 31.

    Devoret, M., Huard, B., Schoelkopf, R. & Cugliandolo, L. F. (eds) Quantum Machines: Measurement and Control of Engineered Quantum Systems Vol. 96 (Oxford Univ. Press, 2014).

  32. 32.

    Gokhale, P. et al. Extending the frontier of quantum computers with qutrits. IEEE Micro 40, 64–72 (2020).

    Article  Google Scholar 

  33. 33.

    Morvan, A. et al. Qutrit randomized benchmarking. Phys. Rev. Lett. 126, 210504 (2021).

    CAS  Article  Google Scholar 

  34. 34.

    Kreikebaum, J. M., O’Brien, K. P., Morvan, A. & Siddiqi, I. Improving wafer-scale Josephson junction resistance variation in superconducting quantum coherent circuits. Supercond. Sci. Technol. 33, 06LT02 (2020).

    Article  Google Scholar 

  35. 35.

    Martinis, J. M., Nam, S., Aumentado, J. & Urbina, C. Rabi oscillations in a large Josephson-junction qubit. Phys. Rev. Lett. 89, 117901 (2002).

    Article  CAS  Google Scholar 

  36. 36.

    Steffen, M. et al. State tomography of capacitively shunted phase qubits with high fidelity. Phys. Rev. Lett. 97, 050502 (2006).

    Article  CAS  Google Scholar 

  37. 37.

    Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Phys. Rev. Lett. 107, 240501 (2011).

    Article  CAS  Google Scholar 

  38. 38.

    Mooij, J. E. et al. Josephson persistent-current qubit. Science 285, 1036–1039 (1999).

    CAS  Article  Google Scholar 

  39. 39.

    Manucharyan, V. E., Koch, J., Glazman, L. I. & Devoret, M. H. Fluxonium: single Cooper-pair circuit free of charge offsets. Science 326, 113–116 (2009).

    CAS  Article  Google Scholar 

  40. 40.

    Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014).

    CAS  Article  Google Scholar 

  41. 41.

    Nguyen, L. B. et al. High-coherence fluxonium qubit. Phys. Rev. X 9, 041041 (2019).

    CAS  Google Scholar 

  42. 42.

    Earnest, N. et al. Realization of a Λ system with metastable states of a capacitively shunted fluxonium. Phys. Rev. Lett. 120, 150504 (2018).

    CAS  Article  Google Scholar 

  43. 43.

    Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).

    CAS  Article  Google Scholar 

  44. 44.

    Göppl, M. et al. Coplanar waveguide resonators for circuit quantum electrodynamics. J. Appl. Phys. 104, 113904 (2008).

    Article  CAS  Google Scholar 

  45. 45.

    Blais, A., Huang, R.-S., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004).

    Article  CAS  Google Scholar 

  46. 46.

    Mirrahimi, M. et al. Dynamically protected cat-qubits: a new paradigm for universal quantum computation. N. J. Phys. 16, 045014 (2014).

    Article  Google Scholar 

  47. 47.

    Rosenberg, D. et al. 3D integrated superconducting qubits. npj Quantum Inf. 3, 42 (2017).

    Article  Google Scholar 

  48. 48.

    Brecht, T. et al. Demonstration of superconducting micromachined cavities. Appl. Phys. Lett. 107, 192603 (2015).

    Article  CAS  Google Scholar 

  49. 49.

    Minev, Z. K. et al. Planar multilayer circuit quantum electrodynamics. Phys. Rev. Appl. 5, 044021 (2016).

    Article  CAS  Google Scholar 

  50. 50.

    O’Connell, A. D. et al. Microwave dielectric loss at single photon energies and millikelvin temperatures. Appl. Phys. Lett. 92, 112903 (2008).

    Article  CAS  Google Scholar 

  51. 51.

    Kaiser, C. et al. Measurement of dielectric losses in amorphous thin films at gigahertz frequencies using superconducting resonators. Supercond. Sci. Technol. 23, 075008 (2010).

    Article  CAS  Google Scholar 

  52. 52.

    Sarabi, B., Ramanayaka, A. N., Burin, A. L., Wellstood, F. C. & Osborn, K. D. Projected dipole moments of individual two-level defects extracted using circuit quantum electrodynamics. Phys. Rev. Lett. 116, 167002 (2016).

    CAS  Article  Google Scholar 

  53. 53.

    Pappas, D. P., Vissers, M. R., Wisbey, D. S., Kline, J. S. & Gao, J. Two level system loss in superconducting microwave resonators. IEEE Trans. Appl. Supercond. 21, 871–874 (2011).

    CAS  Article  Google Scholar 

  54. 54.

    Faoro, L. & Ioffe, L. B. Internal loss of superconducting resonators induced by interacting two-level systems. Phys. Rev. Lett. 109, 157005 (2012).

    Article  CAS  Google Scholar 

  55. 55.

    Faoro, L. & Ioffe, L. B. Interacting tunneling model for two-level systems in amorphous materials and its predictions for their dephasing and noise in superconducting microresonators. Phys. Rev. B 91, 014201 (2015).

    Article  CAS  Google Scholar 

  56. 56.

    Barends, R. et al. Minimizing quasiparticle generation from stray infrared light in superconducting quantum circuits. Appl. Phys. Lett. 99, 113507 (2011).

    Article  CAS  Google Scholar 

  57. 57.

    Vepsäläinen, A. P. et al. Impact of ionizing radiation on superconducting qubit coherence. Nature 584, 551–556 (2020).

    Article  CAS  Google Scholar 

  58. 58.

    Cohen-Tannoudji, C., Dupont-Roc, J. & Grynberg, G. Atom–Photon Interactions: Basic Processes and Applications (Wiley, 1992).

  59. 59.

    Anderson, P. W., Halperin, B. I. & Varma, C. M. Anomalous low-temperature thermal properties of glasses and spin glasses. Phil. Mag. 25, 1–9 (1972).

    CAS  Article  Google Scholar 

  60. 60.

    Phillips, W. A. Two-level states in glasses. Rep. Prog. Phys. 50, 1657–1708 (1987).

    CAS  Article  Google Scholar 

  61. 61.

    Phillips, W. A. Tunneling states in amorphous solids. J. Low Temp. Phys. 7, 351–360 (1972).

    CAS  Article  Google Scholar 

  62. 62.

    Dekker, H. Quantum mechanical barrier problems: III. Dissipative tunnelling at finite temperatures for the weakly biased oscillator. Phys. A 146, 396–403 (1987).

    Article  Google Scholar 

  63. 63.

    Halataei, S. M. H. & Leggett, A. J. Tunnel splitting in asymmetric double well potentials: an improved WKB calculation (Univ. Illinois, 2017).

  64. 64.

    Ku, L.-C. & Yu, C. C. Decoherence of a Josephson qubit due to coupling to two-level systems. Phys. Rev. B 72, 024526 (2005).

    Article  CAS  Google Scholar 

  65. 65.

    Steffen, M., Sandberg, M. & Srinivasan, S. Recent research trends for high coherence quantum circuits. Supercond. Sci. Technol. 30, 030301 (2017).

    Article  CAS  Google Scholar 

  66. 66.

    Burnett, J. J. et al. Decoherence benchmarking of superconducting qubits. npj Quantum Inf. 5, 54 (2019).

    Article  Google Scholar 

  67. 67.

    Shnirman, A., Schön, G., Martin, I. & Makhlin, Y. Low- and high-frequency noise from coherent two-level systems. Phys. Rev. Lett. 94, 127002 (2005).

    Article  CAS  Google Scholar 

  68. 68.

    Simmonds, R. W. et al. Decoherence in Josephson phase qubits from junction resonators. Phys. Rev. Lett. 93, 077003 (2004).

    CAS  Article  Google Scholar 

  69. 69.

    Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric loss. Phys. Rev. Lett. 95, 210503 (2005).

    Article  CAS  Google Scholar 

  70. 70.

    Simmonds, R. W. et al. Coherent interactions between phase qubits, cavities, and TLS defects. Quantum Inf. Process. 8, 117–131 (2009).

    CAS  Article  Google Scholar 

  71. 71.

    Gunnarsson, D. et al. Dielectric losses in multi-layer Josephson junction qubits. Supercond. Sci. Technol. 26, 085010 (2013).

    CAS  Article  Google Scholar 

  72. 72.

    Palomaki, T. A. et al. Multilevel spectroscopy of two-level systems coupled to a dc SQUID phase qubit. Phys. Rev. B 81, 144503 (2010).

    Article  CAS  Google Scholar 

  73. 73.

    Barends, R. et al. Coherent Josephson qubit suitable for scalable quantum integrated circuits. Phys. Rev. Lett. 111, 080502 (2013).

    CAS  Article  Google Scholar 

  74. 74.

    Paladino, E., Galperin, Y. M., Falci, G. & Altshuler, B. L. 1/f noise: implications for solid-state quantum information. Rev. Mod. Phys. 86, 361–418 (2014).

    Article  Google Scholar 

  75. 75.

    Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Phys. Rev. B 92, 035442 (2015).

    Article  CAS  Google Scholar 

  76. 76.

    Schlör, S. et al. Correlating decoherence in transmon qubits: low frequency noise by single fluctuators. Phys. Rev. Lett. 123, 190502 (2019).

    Article  Google Scholar 

  77. 77.

    Klimov, P. V. et al. Fluctuations of energy-relaxation times in superconducting qubits. Phys. Rev. Lett. 121, 090502 (2018).

    CAS  Article  Google Scholar 

  78. 78.

    Grabovskij, G. J., Peichl, T., Lisenfeld, J., Weiss, G. & Ustinov, A. V. Strain tuning of individual atomic tunneling systems detected by a superconducting qubit. Science 338, 232–234 (2012).

    CAS  Article  Google Scholar 

  79. 79.

    Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Inf. 5, 105 (2019).

    Article  Google Scholar 

  80. 80.

    Lisenfeld, J. et al. Observation of directly interacting coherent two-level systems in an amorphous material. Nat. Commun. 6, 6182 (2015).

    CAS  Article  Google Scholar 

  81. 81.

    Zmuidzinas, J. Superconducting microresonators: physics and applications. Annu. Rev. Condens. Matter Phys. 3, 169–214 (2012).

    CAS  Article  Google Scholar 

  82. 82.

    McRae, C. R. H. et al. Materials loss measurements using superconducting microwave resonators. Rev. Sci. Instrum. 91, 91101 (2020).

    CAS  Article  Google Scholar 

  83. 83.

    Day, P. K., LeDuc, H. G., Mazin, B. A., Vayonakis, A. & Zmuidzinas, J. A broadband superconducting detector suitable for use in large arrays. Nature 425, 817–821 (2003).

    CAS  Article  Google Scholar 

  84. 84.

    Gao, J. The Physics of Superconducting Microwave Resonators. Thesis, Calif. Inst. Technol. (2008).

  85. 85.

    Burnett, J., Bengtsson, A., Niepce, D. & Bylander, J. Noise and loss of superconducting aluminium resonators at single photon energies. J. Phys. Conf. Ser. 969, 012131 (2018).

    Article  CAS  Google Scholar 

  86. 86.

    Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Appl. Phys. Lett. 95, 233508 (2009).

    Article  CAS  Google Scholar 

  87. 87.

    Khalil, M. S. et al. Landau–Zener population control and dipole measurement of a two-level-system bath. Phys. Rev. B 90, 100201 (2014).

    Article  CAS  Google Scholar 

  88. 88.

    Paik, H. & Osborn, K. D. Reducing quantum-regime dielectric loss of silicon nitride for superconducting quantum circuits. Appl. Phys. Lett. 96, 072505 (2010).

    Article  CAS  Google Scholar 

  89. 89.

    Altoé, M. V. P. et al. Localization and reduction of superconducting quantum coherent circuit losses. Preprint at arXiv (2020).

  90. 90.

    Verjauw, J. et al. Investigation of microwave loss induced by oxide regrowth in high-Q niobium resonators. Phys. Rev. Appl. 16, 014018 (2021).

    CAS  Article  Google Scholar 

  91. 91.

    Noroozian, O. et al. Two-level system noise reduction for microwave kinetic inductance detectors. AIP Conf. Proc. 1185, 148–151 (2009).

    Article  Google Scholar 

  92. 92.

    Gao, J. et al. Power dependence of phase noise in microwave kinetic inductance detectors. Proc. SPIE 6275, 64–71 (2006).

  93. 93.

    de Graaf, S. E. et al. Two-level systems in superconducting quantum devices due to trapped quasiparticles. Sci. Adv. 6, eabc5055 (2020).

    Article  CAS  Google Scholar 

  94. 94.

    Place, A. P. M. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nat. Commun. 12, 1779 (2020).

    Article  CAS  Google Scholar 

  95. 95.

    Romanenko, A. et al. Three-dimensional superconducting resonators at T < 20 mK with photon lifetimes up to τ = 2 s. Phys. Rev. Appl. 13, 034032 (2020).

    CAS  Article  Google Scholar 

  96. 96.

    de Visser, P. J. et al. Number fluctuations of sparse quasiparticles in a superconductor. Phys. Rev. Lett. 106, 167004 (2011).

    Article  CAS  Google Scholar 

  97. 97.

    Martinis, J. M. Saving superconducting quantum processors from decay and correlated errors generated by gamma and cosmic rays. npj Quantum Inf. 7, 90 (2021).

    Article  Google Scholar 

  98. 98.

    Mattis, D. C. & Bardeen, J. Theory of the anomalous skin effect in normal and superconducting metals. Phys. Rev. 111, 412–417 (1958).

    Article  Google Scholar 

  99. 99.

    Annett, J. F. & Kruchinin, S. (eds) New Trends in Superconductivity (Kluwer, 2002).

  100. 100.

    Martinis, J. M., Ansmann, M. & Aumentado, J. Energy decay in superconducting Josephson-junction qubits from nonequilibrium quasiparticle excitations. Phys. Rev. Lett. 103, 097002 (2009).

    Article  CAS  Google Scholar 

  101. 101.

    Catelani, G. & Basko, D. Non-equilibrium quasiparticles in superconducting circuits: photons vs. phonons. SciPost Phys. 6, 013 (2019).

    Article  Google Scholar 

  102. 102.

    Lenander, M. et al. Measurement of energy decay in superconducting qubits from nonequilibrium quasiparticles. Phys. Rev. B 84, 024501 (2011).

    Article  CAS  Google Scholar 

  103. 103.

    Catelani, G., Nigg, S. E., Girvin, S. M., Schoelkopf, R. J. & Glazman, L. I. Decoherence of superconducting qubits caused by quasiparticle tunneling. Phys. Rev. B 86, 184514 (2012).

    Article  CAS  Google Scholar 

  104. 104.

    Catelani, G., Schoelkopf, R. J., Devoret, M. H. & Glazman, L. I. Relaxation and frequency shifts induced by quasiparticles in superconducting qubits. Phys. Rev. B 84, 064517 (2011).

    Article  CAS  Google Scholar 

  105. 105.

    Catelani, G. et al. Quasiparticle relaxation of superconducting qubits in the presence of flux. Phys. Rev. Lett. 106, 077002 (2011).

    CAS  Article  Google Scholar 

  106. 106.

    Naaman, O. & Aumentado, J. Time-domain measurements of quasiparticle tunneling rates in a single-Cooper-pair transistor. Phys. Rev. B 73, 172504 (2006).

    Article  CAS  Google Scholar 

  107. 107.

    Shaw, M. D., Lutchyn, R. M., Delsing, P. & Echternach, P. M. Kinetics of nonequilibrium quasiparticle tunneling in superconducting charge qubits. Phys. Rev. B 78, 024503 (2008).

    Article  CAS  Google Scholar 

  108. 108.

    Ristè, D. et al. Millisecond charge-parity fluctuations and induced decoherence in a superconducting transmon qubit. Nat. Commun. 4, 1913 (2013).

    Article  CAS  Google Scholar 

  109. 109.

    Sun, L. et al. Measurements of quasiparticle tunneling dynamics in a band-gap-engineered transmon qubit. Phys. Rev. Lett. 108, 230509 (2012).

    CAS  Article  Google Scholar 

  110. 110.

    Serniak, K. et al. Hot nonequilibrium quasiparticles in transmon qubits. Phys. Rev. Lett. 121, 157701 (2018).

    CAS  Article  Google Scholar 

  111. 111.

    Houzet, M., Serniak, K., Catelani, G., Devoret, M. H. & Glazman, L. I. Photon-assisted charge-parity jumps in a superconducting qubit. Phys. Rev. Lett. 123, 107704 (2019).

    CAS  Article  Google Scholar 

  112. 112.

    Wenner, J. et al. Excitation of superconducting qubits from hot nonequilibrium quasiparticles. Phys. Rev. Lett. 110, 150502 (2013).

    CAS  Article  Google Scholar 

  113. 113.

    Vool, U. et al. Non-poissonian quantum jumps of a fluxonium qubit due to quasiparticle excitations. Phys. Rev. Lett. 113, 247001 (2014).

    CAS  Article  Google Scholar 

  114. 114.

    Grünhaupt, L. et al. Loss mechanisms and quasiparticle dynamics in superconducting microwave resonators made of thin-film granular aluminum. Phys. Rev. Lett. 121, 117001 (2018).

    Article  Google Scholar 

  115. 115.

    Goetz, J. et al. Loss mechanisms in superconducting thin film microwave resonators. J. Appl. Phys. 119, 015304 (2016).

    Article  CAS  Google Scholar 

  116. 116.

    de Visser, P. J. et al. Evidence of a nonequilibrium distribution of quasiparticles in the microwave response of a superconducting aluminum resonator. Phys. Rev. Lett. 112, 047004 (2014).

    Article  CAS  Google Scholar 

  117. 117.

    Kreikebaum, J. M., Dove, A., Livingston, W., Kim, E. & Siddiqi, I. Optimization of infrared and magnetic shielding of superconducting TiN and Al coplanar microwave resonators. Supercond. Sci. Technol. 29, 104002 (2016).

    Article  CAS  Google Scholar 

  118. 118.

    Cardani, L. et al. Reducing the impact of radioactivity on quantum circuits in a deep-underground facility. Nat. Commun. 12, 2733 (2021).

    CAS  Article  Google Scholar 

  119. 119.

    Swenson, L. J. et al. High-speed phonon imaging using frequency-multiplexed kinetic inductance detectors. Appl. Phys. Lett. 96, 263511 (2010).

    Article  CAS  Google Scholar 

  120. 120.

    Wilen, C. D. et al. Correlated charge noise and relaxation errors in superconducting qubits. Nature 594, 369–373 (2021).

    CAS  Article  Google Scholar 

  121. 121.

    McEwen, M. et al. Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits. Preprint at arXiv (2021).

  122. 122.

    Taupin, M., Khaymovich, I. M., Meschke, M., Mel’nikov, A. S. & Pekola, J. P. Tunable quasiparticle trapping in Meissner and vortex states of mesoscopic superconductors. Nat. Commun. 7, 10977 (2016).

    CAS  Article  Google Scholar 

  123. 123.

    Wang, C. et al. Measurement and control of quasiparticle dynamics in a superconducting qubit. Nat. Commun. 5, 5836 (2014).

    CAS  Article  Google Scholar 

  124. 124.

    Levenson-Falk, E. M., Kos, F., Vijay, R., Glazman, L. & Siddiqi, I. Single-quasiparticle trapping in aluminum nanobridge Josephson junctions. Phys. Rev. Lett. 112, 047002 (2014).

    CAS  Article  Google Scholar 

  125. 125.

    Riwar, R.-P. et al. Normal-metal quasiparticle traps for superconducting qubits. Phys. Rev. B 94, 104516 (2016).

    Article  CAS  Google Scholar 

  126. 126.

    Aumentado, J., Keller, M. W., Martinis, J. M. & Devoret, M. H. Nonequilibrium quasiparticles and 2e periodicity in single-Cooper-pair transistors. Phys. Rev. Lett. 92, 066802 (2004).

    CAS  Article  Google Scholar 

  127. 127.

    Riwar, R.-P. & Catelani, G. Efficient quasiparticle traps with low dissipation through gap engineering. Phys. Rev. B 100, 144514 (2019).

    CAS  Article  Google Scholar 

  128. 128.

    Gustavsson, S. et al. Suppressing relaxation in superconducting qubits by quasiparticle pumping. Science 354, 1573–1577 (2016).

    CAS  Article  Google Scholar 

  129. 129.

    Marín-Suárez, M., Peltonen, J. T. & Pekola, J. P. Active quasiparticle suppression in a non-equilibrium superconductor. Nano Lett. 20, 5065–5071 (2020).

    Article  CAS  Google Scholar 

  130. 130.

    Henriques, F. et al. Phonon traps reduce the quasiparticle density in superconducting circuits. Appl. Phys. Lett. 115, 212601 (2019).

    Article  CAS  Google Scholar 

  131. 131.

    Rostem, K., de Visser, P. J. & Wollack, E. J. Enhanced quasiparticle lifetime in a superconductor by selective blocking of recombination phonons with a phononic crystal. Phys. Rev. B 98, 014522 (2018).

    CAS  Article  Google Scholar 

  132. 132.

    Paladino, E., Galperin, Y., Falci, G. & Altshuler, B. 1/f noise: implications for solid-state quantum information. Rev. Mod. Phys. 86, 361–418 (2014).

    Article  Google Scholar 

  133. 133.

    Shnirman, A., Schön, G., Martin, I. & Makhlin, Y. in Electron Correlation in New Materials and Nanosystems Vol. 241 (eds Scharnberg, K. & Kruchinin, S.) 343–356 (Springer, 2007).

  134. 134.

    Christensen, B. G. et al. Anomalous charge noise in superconducting qubits. Phys. Rev. B 100, 140503 (2019).

    CAS  Article  Google Scholar 

  135. 135.

    Kumar, P. et al. Origin and reduction of 1/f magnetic flux noise in superconducting devices. Phys. Rev. Appl. 6, 041001 (2016).

    Article  Google Scholar 

  136. 136.

    Anton, S. M. et al. Pure dephasing in flux qubits due to flux noise with spectral density scaling as 1/fα. Phys. Rev. B 85, 224505 (2012).

    Article  CAS  Google Scholar 

  137. 137.

    Van Harlingen, D. J., Plourde, B. L. T., Robertson, T. L., Reichardt, P. A. & Clarke, J. in Decoherence in Flux Qubits due to 1/f Noise in Josephson Junctions (eds Leggett, A. J., Ruggiero, B. & Silvestrini P.) 171–184 (Springer, 2004).

  138. 138.

    Constantin, M. & Yu, C. C. Microscopic model of critical current noise in Josephson junctions. Phys. Rev. Lett. 99, 207001 (2007).

    Article  CAS  Google Scholar 

  139. 139.

    Schreier, J. A. et al. Suppressing charge noise decoherence in superconducting charge qubits. Phys. Rev. B 77, 180502(R) (2008).

    Article  CAS  Google Scholar 

  140. 140.

    Murch, K. W., Weber, S. J., Levenson-Falk, E. M., Vijay, R. & Siddiqi, I. 1/f noise of Josephson-junction-embedded microwave resonators at single photon energies and millikelvin temperatures. Appl. Phys. Lett. 100, 142601 (2012).

    Article  CAS  Google Scholar 

  141. 141.

    Dutta, P. & Horn, P. M. Low-frequency fluctuations in solids: 1/f noise. Rev. Mod. Phys. 53, 497–516 (1981).

    CAS  Article  Google Scholar 

  142. 142.

    Atalaya, J., Clarke, J., Schön, G. & Shnirman, A. Flux 1/fα noise in two-dimensional Heisenberg spin glasses: effects of weak anisotropic interactions. Phys. Rev. B 90, 014206 (2014).

    CAS  Article  Google Scholar 

  143. 143.

    Choi, S., Lee, D.-H., Louie, S. G. & Clarke, J. Localization of metal-induced gap states at the metal–insulator interface: origin of flux noise in SQUIDs and superconducting qubits. Phys. Rev. Lett. 103, 197001 (2009).

    Article  CAS  Google Scholar 

  144. 144.

    Voss, R. F. & Clarke, J. ‘1/f noise’ in music and speech. Nature 258, 317–318 (1975).

    Article  Google Scholar 

  145. 145.

    Vion, D. Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002).

    CAS  Article  Google Scholar 

  146. 146.

    Deng, X.-H., Hu, Y. & Tian, L. Protecting superconducting qubits with a universal quantum degeneracy point. Supercond. Sci. Technol. 26, 114002 (2013).

    Article  CAS  Google Scholar 

  147. 147.

    Kitaev, A. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).

    CAS  Article  Google Scholar 

  148. 148.

    Lahtinen, V. & Pachos, J. A short introduction to topological quantum computation. SciPost Phys. 3, 021 (2017).

    Article  Google Scholar 

  149. 149.

    Brooks, P., Kitaev, A. & Preskill, J. Protected gates for superconducting qubits. Phys. Rev. A 87, 052306 (2013).

    Article  CAS  Google Scholar 

  150. 150.

    Gyenis, A. et al. Experimental realization of an intrinsically error-protected superconducting qubit. PRX Quantum 2, 10339 (2019).

    Article  Google Scholar 

  151. 151.

    Dempster, J. M., Fu, B., Ferguson, D. G., Schuster, D. I. & Koch, J. Understanding degenerate ground states of a protected quantum circuit in the presence of disorder. Phys. Rev. B 90, 094518 (2014).

    Article  CAS  Google Scholar 

  152. 152.

    Groszkowski, P. et al. Coherence properties of the 0–π qubit. N. J. Phys. 20, 043053 (2018).

    Article  CAS  Google Scholar 

  153. 153.

    Kitaev, A. Protected qubit based on a superconducting current mirror. Preprint at arXiv (2006).

  154. 154.

    Peruzzo, M., Trioni, A., Hassani, F., Zemlicka, M. & Fink, J. M. Surpassing the resistance quantum with a geometric superinductor. Phys. Rev. Appl. 14, 044055 (2020).

    CAS  Article  Google Scholar 

  155. 155.

    Zhang, W. Applications of Superinductors in Superconducting Quantum Circuits. Thesis, Rutgers Univ. (2019).

  156. 156.

    Masluk, N. A., Pop, I. M., Kamal, A., Minev, Z. K. & Devoret, M. H. Microwave characterization of Josephson junction arrays: implementing a low loss superinductance. Phys. Rev. Lett. 109, 137002 (2012).

    Article  CAS  Google Scholar 

  157. 157.

    Niepce, D., Burnett, J. & Bylander, J. High kinetic inductance NbN nanowire superinductors. Phys. Rev. Appl. 11, 044014 (2019).

    CAS  Article  Google Scholar 

  158. 158.

    Kamenov, P. et al. Granular aluminum meandered superinductors for quantum circuits. Phys. Rev. Appl. 13, 054051 (2020).

    CAS  Article  Google Scholar 

  159. 159.

    Wang, J. I.-J. & Oliver, W. D. An aluminium superinductor. Nat. Mater. 18, 775–776 (2019).

    CAS  Article  Google Scholar 

  160. 160.

    Grünhaupt, L. et al. Granular aluminium as a superconducting material for high-impedance quantum circuits. Nat. Mater. 18, 816–819 (2019).

    Article  CAS  Google Scholar 

  161. 161.

    Gladchenko, S. et al. Superconducting nanocircuits for topologically protected qubits. Nat. Phys. 5, 48–53 (2009).

    CAS  Article  Google Scholar 

  162. 162.

    Douçot, B., Feigel’man, M. V. & Ioffe, L. B. Topological order in the insulating Josephson junction array. Phys. Rev. Lett. 90, 107003 (2003).

    Article  CAS  Google Scholar 

  163. 163.

    Bell, M. T., Paramanandam, J., Ioffe, L. B. & Gershenson, M. E. Protected Josephson rhombus chains. Phys. Rev. Lett. 112, 167001 (2014).

    Article  CAS  Google Scholar 

  164. 164.

    Smith, W. C., Kou, A., Xiao, X., Vool, U. & Devoret, M. H. Superconducting circuit protected by two-Cooper-pair tunneling. npj Quantum Inf. 6, 8 (2020).

    Article  Google Scholar 

  165. 165.

    Kalashnikov, K. et al. Bifluxon: fluxon-parity-protected superconducting qubit. PRX Quantum 1, 010307 (2020).

    Article  Google Scholar 

  166. 166.

    Weides, M. Barriers in Josephson Junctions: An Overview Vol. 1 (Oxford Univ. Press, 2017).

  167. 167.

    Fritz, S., Schneider, R., Radtke, L., Weides, M. & Gerthsen, D. TEM investigations of Al/AlOx/Al Josephson junctions. in European Microscopy Congress 2016: Proceedings (Wiley, 2016).

  168. 168.

    Weides, M. P. et al. Coherence in a transmon qubit with epitaxial tunnel junctions. Appl. Phys. Lett. 99, 262502 (2011).

    Article  CAS  Google Scholar 

  169. 169.

    Kline, J. S. et al. Sub-micrometer epitaxial Josephson junctions for quantum circuits. Supercond. Sci. Technol. 25, 025005 (2011).

    Article  CAS  Google Scholar 

  170. 170.

    Nakamura, Y. et al. Superconducting qubits consisting of epitaxially grown NbN/AlN/NbN Josephson junctions. Appl. Phys. Lett. 99, 212502 (2011).

    Article  CAS  Google Scholar 

  171. 171.

    Liu, Y. et al. Van der Waals heterostructures and devices. Nat. Rev. Mater. 1, 16042 (2016).

    CAS  Article  Google Scholar 

  172. 172.

    Girit, C. et al. Tunable graphene dc superconducting quantum interference device. Nano Lett. 9, 198–199 (2009).

    CAS  Article  Google Scholar 

  173. 173.

    Wang, J. I.-J. et al. Coherent control of a hybrid superconducting circuit made with graphene-based van der Waals heterostructures. Nat. Nanotechnol. 14, 120–125 (2019).

    CAS  Article  Google Scholar 

  174. 174.

    Xiao, Y., Liu, J. & Fu, L. Moiré is more: access to new properties of two-dimensional layered materials. Matter 3, 1142–1161 (2020).

    Article  Google Scholar 

  175. 175.

    Lee, K.-H. et al. Two-dimensional material tunnel barrier for Josephson junctions and superconducting qubits. Nano Lett. 19, 8287–8293 (2019).

    CAS  Article  Google Scholar 

  176. 176.

    Chiu, K.-L. et al. Flux tunable superconducting quantum circuit based on Weyl semimetal MoTe2. Nano Lett. 20, 8469–8475 (2020).

    CAS  Article  Google Scholar 

  177. 177.

    Yabuki, N. et al. Supercurrent in van der Waals Josephson junction. Nat. Commun. 7, 10616 (2016).

    CAS  Article  Google Scholar 

  178. 178.

    Vijay, R., Sau, J. D., Cohen, M. L. & Siddiqi, I. Optimizing anharmonicity in nanoscale weak link Josephson junction oscillators. Phys. Rev. Lett. 103, 087003 (2009).

    CAS  Article  Google Scholar 

  179. 179.

    Astafiev, O. V. et al. Coherent quantum phase slip. Nature 484, 355–358 (2012).

    CAS  Article  Google Scholar 

  180. 180.

    Mooij, J. E. & Harmans, C. J. P. M. Phase-slip flux qubits. N. J. Phys. 7, 219–219 (2005).

    Article  CAS  Google Scholar 

  181. 181.

    Li, Z.-Z., Li, T.-F., Lam, C.-H. & You, J. Q. Collective quantum phase slips in multiple nanowire junctions. Phys. Rev. A 99, 012309 (2019).

    CAS  Article  Google Scholar 

  182. 182.

    Kenawy, A., Magnus, W., Milošević, M. V. & Sorée, B. Electronically tunable quantum phase slips in voltage-biased superconducting rings as a base for phase-slip flux qubits. Supercond. Sci. Technol. 33, 125002 (2020).

    Article  Google Scholar 

  183. 183.

    Winkel, P. et al. Implementation of a transmon qubit using superconducting granular aluminum. Phys. Rev. X 10, 031032 (2020).

    CAS  Google Scholar 

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This work was supported by the Office of Advanced Scientific Computing Research, Testbed Program, Office of Science of the US Department of Energy under contract no. DE-AC02-05CH11231. G. Catelani, J. Clarke, M. Devoret, L. Faoro, L. Glazman, L. Ioffe, A. Jordan, C. Müller, W. Oliver and J. Preskill provided critical comments on the manuscript. L. Nguyen provided the numerical data used in Fig. 2. J. M. Kreikebaum provided the chip photograph used in Fig. 3.

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Siddiqi, I. Engineering high-coherence superconducting qubits. Nat Rev Mater 6, 875–891 (2021).

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