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Detector of microwave photon pairs based on a Josephson photomultiplier

E. V. Stolyarov1,* and R. A. Baskov2,3,†

  • 1Quantum Optics and Quantum Information Group, Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, vul. Metrolohichna 14-b, Kyiv 03143, Ukraine
  • 2Department of Physics and Applied Physics, Yale University, P.O. Box 208120, New Haven, Connecticut 06520-8120, USA
  • 3Yale Quantum Institute, 17 Hillhouse Avenue, P.O. Box 208334, New Haven, Connecticut 06520-8263, USA

  • *Contact author: eugene.stolyarov@bitp.kyiv.ua
  • †Contact author: roman.baskov@yale.edu
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Phys. Rev. Research 7, 033263 – Published 17 September, 2025

DOI: https://doi.org/10.1103/6p8x-snzm

Abstract

We propose a viable design of a microwave two-photon threshold detector. In essence, the considered scheme is an extension of the existing single-photon detector—a Josephson photomultiplier (JPM)—an absorbing microwave detector based on a capacitively shunted rf superconducting quantum interference device (SQUID). To implement a two-photon threshold detector, we utilize a dimer of resonators—two lumped-element resonators interacting via an asymmetric dc SQUID, with one of the resonators capacitively coupled to the JPM. By specific tuning of the resonator frequencies and the external flux through the dc SQUID coupler, we engineer a nonperturbative two-photon coupling between the resonators. This coupling results in the coherent conversion of a photon pair from one resonator into a single photon in another resonator, enabling selective response to quantum states with at least two photons. We also consider an extended coupler design that allows on-demand in situ switching of two-photon coupling. In addition, we propose the modified JPM design to improve its performance. Our calculations demonstrate that, for realistic circuit parameters, we can achieve more than 99% fidelity of photon pair detection in less than 50 ns. The considered scheme may serve as a building block for the implementation of efficient photon-number-resolving detectors in circuit QED architecture.

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References (153)

  1. R. H. Hadfield, Single-photon detectors for optical quantum information applications, Nat. Photonics 3, 696 (2009).
  2. M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, Invited review article: Single-photon sources and detectors, Rev. Sci. Instrum. 82, 071101 (2011).
  3. L. You, Superconducting nanowire single-photon detectors for quantum information, Nanophotonics 9, 2673 (2020).
  4. J. Fiurášek, R. García-Patrón, and N. J. Cerf, Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions, Phys. Rev. A 72, 033822 (2005).
  5. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, Generating optical Schrödinger kittens for quantum information processing, Science 312, 83 (2006).
  6. J. Sperling, W. Vogel, and G. S. Agarwal, Quantum state engineering by click counting, Phys. Rev. A 89, 043829 (2014).
  7. T. Sonoyama, W. Asavanant, K. Fukui, M. Endo, J.-I. Yoshikawa, and A. Furusawa, Analysis of optical quantum state preparation using photon detectors in the finite-temporal-resolution regime, Phys. Rev. A 105, 043714 (2022); T. Sonoyama, K. Takahashi, B. Charoensombutamon, S. Takasu, K. Hattori, D. Fukuda, K. Fukui, K. Takase, W. Asavanant, J.-I. Yoshikawa, M. Endo, and A. Furusawa, Non-Gaussian-state generation with time-gated photon detection, Phys. Rev. Res. 5, 033156 (2023).
  8. E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature (London) 409, 46 (2001).
  9. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys. 79, 135 (2007).
  10. M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, Photonic boson sampling in a tunable circuit, Science 339, 794 (2013).
  11. J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, Boson sampling on a photonic chip, Science 339, 798 (2013).
  12. M. Tillmann, B. Dakić, R. Heilmann, S. Nolte, A. Szameit, and P. Walther, Experimental boson sampling, Nat. Photonics 7, 540 (2013).
  13. H. Shibata, T. Honjo, and K. Shimizu, Quantum key distribution over a 72 dB channel loss using ultralow dark count superconducting single-photon detectors, Opt. Lett. 39, 5078 (2014).
  14. A. Koehler-Sidki, J. F. Dynes, M. Lucamarini, G. L. Roberts, A. W. Sharpe, Z. L. Yuan, and A. J. Shields, Best-practice criteria for practical security of self-differencing avalanche photodiode detectors in quantum key distribution, Phys. Rev. Appl. 9, 044027 (2018).
  15. A. E. Lita, D. V. Reddy, V. B. Verma, R. P. Mirin, and S. W. Nam, Development of superconducting single-photon and photon-number resolving detectors for quantum applications, J. Lightwave Technol. 40, 7578 (2022).
  16. Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, Gigahertz quantum key distribution with InGaAs avalanche photodiodes, Appl. Phys. Lett. 92, 201104 (2008).
  17. B. Cabrera, R. M. Clarke, P. Colling, A. J. Miller, S. Nam, and R. W. Romani, Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors, Appl. Phys. Lett. 73, 735 (1998).
  18. A. E. Lita, A. J. Miller, and S. W. Nam, Counting near-infrared single-photons with 95% efficiency, Opt. Express 16, 3032 (2008).
  19. C. M. Natarajan, M. G. Tanner, and R. H. Hadfield, Superconducting nanowire single-photon detectors: Physics and applications, Supercond. Sci. Technol. 25, 063001 (2012).
  20. E. A. Dauler, M. E. Grein, A. J. Kerman, F. Marsili, S. Miki, S. W. Nam, M. D. Shaw, H. Terai, V. B. Verma, and T. Yamashita, Review of superconducting nanowire single-photon detector system design options and demonstrated performance, Opt. Eng. 53, 081907 (2014).
  21. I. Esmaeil Zadeh, J. Chang, J. W. N. Los, S. Gyger, A. W. Elshaari, S. Steinhauer, S. N. Dorenbos, and V. Zwiller, Superconducting nanowire single-photon detectors: A perspective on evolution, state-of-the-art, future developments, and applications, Appl. Phys. Lett. 118, 190502 (2021).
  22. A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69, 062320 (2004).
  23. X. Gu, A. F. Kockum, A. Miranowicz, Y. X Liu, and F. Nori, Microwave photonics with superconducting quantum circuits, Phys. Rep. 718–719, 1 (2017).
  24. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  25. M. H. Devoret and R. J. Schoelkopf, Superconducting circuits for quantum information: An outlook, Science 339, 1169 (2013).
  26. G. Wendin, Quantum information processing with superconducting circuits: A review, Rep. Prog. Phys. 80, 106001 (2017).
  27. A. Blais, S. M. Girvin, and W. D. Oliver, Quantum information processing and quantum optics with circuit quantum electrodynamics, Nat. Phys. 16, 247 (2020).
  28. E. Jeffrey, D. Sank, J. Y. Mutus, T. C. White, J. Kelly, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, P. J. J. O’Malley, C. Neill, P. Roushan, A. Vainsencher, J. Wenner, A. N. Cleland, and J. M. Martinis, Fast accurate state measurement with superconducting qubits, Phys. Rev. Lett. 112, 190504 (2014).
  29. T. Walter, P. Kurpiers, S. Gasparinetti, P. Magnard, A. Potočnik, Y. Salathé, M. Pechal, M. Mondal, M. Oppliger, C. Eichler, and A. Wallraff, Rapid high-fidelity single-shot dispersive readout of superconducting qubits, Phys. Rev. Appl. 7, 054020 (2017); J. Heinsoo, C. K. Andersen, A. Remm, S. Krinner, T. Walter, Y. Salathé, S. Gasparinetti, J.-C. Besse, A. Potočnik, A. Wallraff, and C. Eichler, Rapid high-fidelity multiplexed readout of superconducting qubits, ibid. 10, 034040 (2018).
  30. Y.-F. Chen, D. Hover, S. Sendelbach, L. Maurer, S. T. Merkel, E. J. Pritchett, F. K. Wilhelm, and R. McDermott, Microwave photon counter based on Josephson junctions, Phys. Rev. Lett. 107, 217401 (2011).
  31. G. Oelsner, C. K. Andersen, M. Rehák, M. Schmelz, S. Anders, M. Grajcar, U. Hübner, K. Mølmer, and E. Il'ichev, Detection of weak microwave fields with an underdamped Josephson junction, Phys. Rev. Appl. 7, 014012 (2017).
  32. A. Opremcak, I. V. Pechenezhskiy, C. Howington, B. G. Christensen, M. A. Beck, E. Leonard, Jr., J. Suttle, C. Wilen, K. N. Nesterov, G. J. Ribeill, T. Thorbeck, F. Schlenker, M. G. Vavilov, B. L. T. Plourde, and R. McDermott, Measurement of a superconducting qubit with a microwave photon counter, Science 361, 1239 (2018).
  33. A. Opremcak, C. H. Liu, C. Wilen, K. Okubo, B. G. Christensen, D. Sank, T. C. White, A. Vainsencher, M. Giustina, A. Megrant, B. Burkett, B. L. T. Plourde, and R. McDermott, High-fidelity measurement of a superconducting qubit using an on-chip microwave photon counter, Phys. Rev. X 11, 011027 (2021).
  34. J. M. Martinis, Superconducting phase qubits, Quantum Inf. Process. 8, 81 (2009).
  35. D. S. Golubev, E. V. Il'ichev, and L. S. Kuzmin, Single-photon detection with a Josephson junction coupled to a resonator, Phys. Rev. Appl. 16, 014025 (2021).
  36. C. Guarcello, A. S. Piedjou Komnang, C. Barone, A. Rettaroli, C. Gatti, S. Pagano, and G. Filatrella, Josephson-based scheme for the detection of microwave photons, Phys. Rev. Appl. 16, 054015 (2021).
  37. M. Steffen, M. Ansmann, R. McDermott, N. Katz, R. C. Bialczak, E. Lucero, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, State tomography of capacitively shunted phase qubits with high fidelity, Phys. Rev. Lett. 97, 050502 (2006).
  38. L. C. G. Govia, E. J. Pritchett, C. Xu, B. L. T. Plourde, M. G. Vavilov, F. K. Wilhelm, and R. McDermott, High-fidelity qubit measurement with a microwave-photon counter, Phys. Rev. A 90, 062307 (2014).
  39. A. M. Sokolov and E. V. Stolyarov, Single-photon limit of dispersive readout of a qubit with a photodetector, Phys. Rev. A 101, 042306 (2020).
  40. A. Sokolov, Optimal conditions for high-fidelity dispersive readout of a qubit with a photon-number-resolving detector, Phys. Rev. A 93, 032323 (2016).
  41. E. V. Stolyarov, O. V. Kliushnichenko, V. S. Kovtoniuk, and A. A. Semenov, Photon-number resolution with microwave Josephson photomultipliers, Phys. Rev. A 108, 063710 (2023).
  42. A. M. Sokolov and F. K. Wilhelm, Superconducting detector that counts microwave photons up to two, Phys. Rev. Appl. 14, 064063 (2020).
  43. A. Vrajitoarea, Z. Huang, P. Groszkowski, J. Koch, and A. A. Houck, Quantum control of an oscillator using a stimulated Josephson nonlinearity, Nat. Phys. 16, 211 (2020).
  44. S.-P. Wang, A. Mercurio, A. Ridolfo, Y. Wang, M. Chen, T. Li, F. Nori, S. Savasta, and J. Q. You, Strong coupling between a single photon and a photon pair, arXiv:2401.02738 [quant-ph].
  45. M. Ayyash, X. Xu, S. Ashhab, and M. Mariantoni, Driven multiphoton qubit-resonator interactions, Phys. Rev. A 110, 053711 (2024).
  46. E. V. Stolyarov, V. L. Andriichuk, and A. M. Sokolov, Two-photon coupling via Josephson element: Breaking the symmetry with magnetic fields, Phys. Rev. B 111, 214517 (2025).
  47. E. V. Stolyarov, V. L. Andriichuk, and A. M. Sokolov, Two-photon coupling via Josephson element II: Interaction renormalizations and cross-Kerr coupling, arXiv:2507.13427 [quant-ph].
  48. Here, we assume that the buffer resonator is initially in the vacuum state, while the SPD is in its ground state. We also assume an idealized scenario without thermal photons in the system and false clicks of the SPD.
  49. L. Shi, T. Guo, R. Su, T. Chi, Y. Sheng, J. Jiang, C. Cao, J. Wu, X. Tu, G. Sun, J. Chen, and P. Wu, Tantalum microwave resonators with ultra-high intrinsic quality factors, Appl. Phys. Lett. 121, 242601 (2022).
  50. K. D. Crowley et al., Disentangling losses in tantalum superconducting circuits, Phys. Rev. X 13, 041005 (2023).
  51. R. Dhundhwal, H. Duan, L. Brauch, S. Arabi, D. Fuchs, A.-A. Haghighirad, A. Welle, F. Scharwaechter, S. Pal, M. Scheffler, J. Palomo, Z. Leghtas, A. Murani, H. Hahn, J. Aghassi-Hagmann, C. Kübel, W. Wulfhekel, I. M. Pop, and T. Reisinger, High quality superconducting tantalum resonators with beta phase defects arXiv:2502.17247 [quant-ph].
  52. J.-C. Besse, S. Gasparinetti, M. C. Collodo, T. Walter, P. Kurpiers, M. Pechal, C. Eichler, and A. Wallraff, Single-shot quantum nondemolition detection of individual itinerant microwave photons, Phys. Rev. X 8, 021003 (2018).
  53. B. Royer, A. L. Grimsmo, A. Choquette-Poitevin, and A. Blais, Itinerant microwave photon detector, Phys. Rev. Lett. 120, 203602 (2018).
  54. R. Lescanne, S. Deléglise, E. Albertinale, U. Réglade, T. Capelle, E. Ivanov, T. Jacqmin, Z. Leghtas, and E. Flurin, Irreversible qubit-photon coupling for the detection of itinerant microwave photons, Phys. Rev. X 10, 021038 (2020).
  55. P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A quantum engineer's guide to superconducting qubits, Appl. Phys. Rev. 6, 021318 (2019).
  56. G. De Simoni, F. Paolucci, P. Solinas, E. Strambini, and F. Giazotto, Metallic supercurrent field-effect transistor, Nat. Nanotechnol. 13, 802 (2018).
  57. L. Casparis, N. J. Pearson, A. Kringhøj, T. W. Larsen, F. Kuemmeth, J. Nygård, P. Krogstrup, K. D. Petersson, and C. M. Marcus, Voltage-controlled superconducting quantum bus, Phys. Rev. B 99, 085434 (2019).
  58. T. W. Larsen, K. D. Petersson, F. Kuemmeth, T. S. Jespersen, P. Krogstrup, J. Nygård, and C. M. Marcus, Semiconductor-nanowire-based superconducting qubit, Phys. Rev. Lett. 115, 127001 (2015); G. de Lange, B. van Heck, A. Bruno, D. J. van Woerkom, A. Geresdi, S. R. Plissard, E. P. A. M. Bakkers, A. R. Akhmerov, and L. DiCarlo, Realization of microwave quantum circuits using hybrid superconducting-semiconducting nanowire Josephson elements, ibid. 115, 127002 (2015).
  59. W. M. Strickland, B. H. Elfeky, J. O. Yuan, W. F. Schiela, P. Yu, D. Langone, M. G. Vavilov, V. E. Manucharyan, and J. Shabani, Superconducting resonators with voltage-controlled frequency and nonlinearity, Phys. Rev. Appl. 19, 034021 (2023).
  60. J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76, 042319 (2007).
  61. Z. Wang, M. Pechal, E. A. Wollack, P. Arrangoiz-Arriola, M. Gao, N. R. Lee, and A. H. Safavi-Naeini, Quantum dynamics of a few-photon parametric oscillator, Phys. Rev. X 9, 021049 (2019); R. Dassonneville, T. Ramos, V. Milchakov, L. Planat, E. Dumur, F. Foroughi, J. Puertas, S. Leger, K. Bharadwaj, J. Delaforce, C. Naud, W. Hasch-Guichard, J. J. García-Ripoll, N. Roch, and O. Buisson, Fast high-fidelity quantum nondemolition qubit readout via a nonperturbative cross-Kerr coupling, ibid. 10, 011045 (2020).
  62. R. Barends, J. Kelly, A. Megrant, D. Sank, E. Jeffrey, Y. Chen, Y. Yin, B. Chiaro, J. Mutus, C. Neill, P. O’Malley, P. Roushan, J. Wenner, T. C. White, A. N. Cleland, and J. M. Martinis, Coherent Josephson qubit suitable for scalable quantum integrated circuits, Phys. Rev. Lett. 111, 080502 (2013).
  63. L. Casparis, M. R. Connolly, M. Kjaergaard, N. J. Pearson, A. Kringhøj, T. W. Larsen, F. Kuemmeth, T. Wang, C. Thomas, S. Gronin, G. C. Gardner, M. J. Manfra, C. M. Marcus, and K. D. Petersson, Superconducting gatemon qubit based on a proximitized two-dimensional electron gas, Nat. Nanotechnol. 13, 915 (2018).
  64. H. Riechert, S. Annabi, A. Peugeot, H. Duprez, M. Hantute, K. Watanabe, T. Taniguchi, E. Arrighi, J. Griesmar, J.-D. Pillet, and L. Bretheau, The carbon nanotube gatemon qubit, Nat. Commun. 16, 7197 (2025).
  65. R. Dassonneville, R. Assouly, T. Peronnin, P. Rouchon, and B. Huard, Number-resolved photocounter for propagating microwave mode, Phys. Rev. Appl. 14, 044022 (2020).
  66. L. Balembois, J. Travesedo, L. Pallegoix, A. May, E. Billaud, M. Villiers, D. Estève, D. Vion, P. Bertet, and E. Flurin, Cyclically operated microwave single-photon counter with sensitivity of 10−22W/Hz, Phys. Rev. Appl. 21, 014043 (2024).
  67. H. Sun, F. Wu, H.-S. Ku, X. Ma, J. Qin, Z. Song, T. Wang, G. Zhang, J. Zhou, Y. Shi, H.-H. Zhao, and C. Deng, Characterization of loss mechanisms in a fluxonium qubit, Phys. Rev. Appl. 20, 034016 (2023).
  68. J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491 (1966).
  69. S. Bravyi, D. P. DiVincenzo, and D. Loss, Schrieffer–Wolff transformation for quantum many-body systems, Ann. Phys. 326, 2793 (2011).
  70. G. Zhu, D. G. Ferguson, V. E. Manucharyan, and J. Koch, Circuit QED with fluxonium qubits: Theory of the dispersive regime, Phys. Rev. B 87, 024510 (2013).
  71. T. Hillmann and F. Quijandría, Designing Kerr interactions for quantum information processing via counterrotating terms of asymmetric Josephson-junction loops, Phys. Rev. Appl. 17, 064018 (2022).
  72. J. Griesmar, A mesoscopic spectrometer based on the Josephson effect, Ph.D. thesis, Université Paris Sciences et Lettres, 2018.
  73. L. Peyruchat, Topological phenomena in Josephson tunnel junction circuits, Ph.D. thesis, Université Paris Sciences et Lettres, 2022.
  74. L. Peyruchat, R. H. Rodriguez, J.-L. Smirr, R. Leone, and Ç. Ö. Girit, Spectral signatures of nontrivial topology in a superconducting circuit, Phys. Rev. X 14, 041041 (2024).
  75. L. Di Palma, A. Miano, P. Mastrovito, D. Massarotti, M. Arzeo, G. Pepe, F. Tafuri, and O. Mukhanov, Discriminating the phase of a coherent tone with a flux-switchable superconducting circuit, Phys. Rev. Appl. 19, 064025 (2023).
  76. M. Tinkham, Introduction to Superconductivity, 2nd ed. (Dover Publications, Mineola, NY, 2004).
  77. J. T. Peltonen, P. C. J. J. Coumou, Z. H. Peng, T. M. Klapwijk, J. S. Tsai, and O. V. Astafiev, Hybrid rf squid qubit based on high kinetic inductance, Sci. Rep. 8, 10033 (2018).
  78. D. Niepce, J. Burnett, and J. Bylander, High kinetic inductance NbN nanowire superinductors, Phys. Rev. Appl. 11, 044014 (2019).
  79. V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Fluxonium: Single Cooper-pair circuit free of charge offsets, Science 326, 113 (2009).
  80. L. B. Nguyen, Y.-H. Lin, A. Somoroff, R. Mencia, N. Grabon, and V. E. Manucharyan, High-coherence fluxonium qubit, Phys. Rev. X 9, 041041 (2019).
  81. F. Bao et al., Fluxonium: An alternative qubit platform for high-fidelity operations, Phys. Rev. Lett. 129, 010502 (2022).
  82. V. I. Shnyrkov, W. Yangcao, A. A. Soroka, O. G. Turutanov, and V. Y. Lyakhno, Frequency-tuned microwave photon counter based on a superconductive quantum interferometer, Low Temp. Phys. 44, 213 (2018).
  83. Y. Krupko, V. D. Nguyen, T. Weißl, E. Dumur, J. Puertas, R. Dassonneville, C. Naud, F. W. J. Hekking, D. M. Basko, O. Buisson, N. Roch, and W. Hasch-Guichard, Kerr nonlinearity in a superconducting Josephson metamaterial, Phys. Rev. B 98, 094516 (2018).
  84. J. Puertas Martínez, S. Léger, N. Gheeraert, R. Dassonneville, L. Planat, F. Foroughi, Y. Krupko, O. Buisson, C. Naud, W. Hasch-Guichard, S. Florens, I. Snyman, and N. Roch, A tunable Josephson platform to explore many-body quantum optics in circuit-qed, npj Quantum Inf. 5, 19 (2019).
  85. L. J. Splitthoff, A. Bargerbos, L. Grünhaupt, M. Pita-Vidal, J. J. Wesdorp, Y. Liu, A. Kou, C. K. Andersen, and B. van Heck, Gate-tunable kinetic inductance in proximitized nanowires, Phys. Rev. Appl. 18, 024074 (2022); L. J. Splitthoff, J. J. Wesdorp, M. Pita-Vidal, A. Bargerbos, Y. Liu, and C. K. Andersen, Gate-tunable kinetic inductance parametric amplifier, ibid. 21, 014052 (2024).
  86. The SQUID Handbook: Fundamentals and Technology of SQUIDs and SQUID Systems, edited by J. Clarke and A. I. Braginski (Wiley-VCH, Weinheim, 2004), Vol. I.
  87. C. Guarcello, R. Citro, O. Durante, F. S. Bergeret, A. Iorio, C. Sanz-Fernández, E. Strambini, F. Giazotto, and A. Braggio, rf-SQUID measurements of anomalous Josephson effect, Phys. Rev. Res. 2, 023165 (2020).
  88. C. Guarcello, P. Solinas, M. Di Ventra, and F. Giazotto, Hysteretic superconducting heat-flux quantum modulator, Phys. Rev. Appl. 7, 044021 (2017).
  89. M. Wegner, C. Enss, and S. Kempf, Analytical model of the readout power and SQUID hysteresis parameter dependence of the resonator characteristics of microwave SQUID multiplexers, Supercond. Sci. Technol. 35, 075011 (2022).
  90. J. Lisenfeld, Experiments on superconducting Josephson phase quantum bits, Ph.D. thesis, Universität Erlangen-Nürnberg, 2007.
  91. D. A. Bennett, L. Longobardi, V. Patel, W. Chen, D. V. Averin, and J. E. Lukens, Decoherence in rf SQUID qubits, Quantum Inf. Process. 8, 217 (2009).
  92. V. I. Shnyrkov, A. P. Shapovalov, V. Y. Lyakhno, A. O. Dumik, A. A. Kalenyuk, and P. Febvre, An RF SQUID readout for a flux qubit-based microwave single photon counter, Supercond. Sci. Technol. 36, 035005 (2023).
  93. C. Howington, A. Opremcak, R. McDermott, A. Kirichenko, O. A. Mukhanov, and B. L. T. Plourde, Interfacing superconducting qubits with cryogenic logic: Readout, IEEE Trans. Appl. Supercond. 29, 1700305 (2019).
  94. C. J. Howington, Digital readout and control of a superconducting qubit, Ph.D. thesis, Syracuse University, 2019.
  95. D. V. Averin, K. Rabenstein, and V. K. Semenov, Rapid ballistic readout for flux qubits, Phys. Rev. B 73, 094504 (2006).
  96. A. Fedorov, A. Shnirman, G. Schön, and A. Kidiyarova-Shevchenko, Reading out the state of a flux qubit by Josephson transmission line solitons, Phys. Rev. B 75, 224504 (2007).
  97. C. Guarcello, Lévy noise effects on Josephson junctions, Chaos Solitons Fractals 153, 111531 (2021).
  98. R. Grimaudo, D. Valenti, B. Spagnolo, G. Filatrella, and C. Guarcello, Josephson-junction-based axion detection through resonant activation, Phys. Rev. D 105, 033007 (2022).
  99. K. Serniak, M. Hays, G. de Lange, S. Diamond, S. Shankar, L. D. Burkhart, L. Frunzio, M. Houzet, and M. H. Devoret, Hot nonequilibrium quasiparticles in transmon qubits, Phys. Rev. Lett. 121, 157701 (2018).
  100. R. Barends, J. Wenner, M. Lenander, Y. Chen, R. C. Bialczak, J. Kelly, E. Lucero, P. O’Malley, M. Mariantoni, D. Sank, H. Wang, T. C. White, Y. Yin, J. Zhao, A. N. Cleland, J. M. Martinis, and J. J. A. Baselmans, Minimizing quasiparticle generation from stray infrared light in superconducting quantum circuits, Appl. Phys. Lett. 99, 113507 (2011).
  101. A. P. Vepsäläinen, A. H. Karamlou, J. L. Orrell, A. S. Dogra, B. Loer, F. Vasconcelos, D. K. Kim, A. J. Melville, B. M. Niedzielski, J. L. Yoder, S. Gustavsson, J. A. Formaggio, B. A. VanDevender, and W. D. Oliver, Impact of ionizing radiation on superconducting qubit coherence, Nature (London) 584, 551 (2020).
  102. R. W. Simmonds, K. M. Lang, D. A. Hite, S. Nam, D. P. Pappas, and J. M. Martinis, Decoherence in Josephson phase qubits from junction resonators, Phys. Rev. Lett. 93, 077003 (2004).
  103. M. Cattaneo and G. S. Paraoanu, Engineering dissipation with resistive elements in circuit quantum electrodynamics, Adv. Quantum Technol. 4, 2100054 (2021); S. A. Lemziakov, B. Karimi, S. Nakamura, D. S. Lvov, R. Upadhyay, C. D. Satrya, Z.-Y. Chen, D. Subero, Y.-C. Chang, L. B. Wang, and J. P. Pekola, Applications of superconductor–normal metal interfaces, J. Low Temp. Phys. 217, 54 (2024).
  104. M. D. Reed, B. R. Johnson, A. A. Houck, L. DiCarlo, J. M. Chow, D. I. Schuster, L. Frunzio, and R. J. Schoelkopf, Fast reset and suppressing spontaneous emission of a superconducting qubit, Appl. Phys. Lett. 96, 203110 (2010).
  105. This problem is addressed in detail in Ref.  [106].
  106. O. A. Ilinskaya, A. I. Ryzhov, and S. N. Shevchenko, Flux qubit based detector of microwave photons, Phys. Rev. B 110, 155414 (2024).
  107. Hereinafter, we assume that the number of thermal excitations in the system is negligible. Indeed, for the typical working temperatures Ts≈10−30mK and operational frequencies ωs/2π≈5−10GHz of the circuit QED setups, the number of thermal excitations in the system is nth<10−2.
  108. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, New York, 2002).
  109. D. Manzano, A short introduction to the Lindblad master equation, AIP Adv. 10, 025106 (2020).
  110. J. Q. You, X. Hu, S. Ashhab, and F. Nori, Low-decoherence flux qubit, Phys. Rev. B 75, 140515 (2007).
  111. P. J. Jones, J. Salmilehto, and M. Möttönen, Highly controllable qubit-bath coupling based on a sequence of resonators, J. Low Temp. Phys. 173, 152 (2013).
  112. L. C. G. Govia, E. J. Pritchett, S. T. Merkel, D. Pineau, and F. K. Wilhelm, Theory of Josephson photomultipliers: Optimal working conditions and back action, Phys. Rev. A 86, 032311 (2012).
  113. M. Schöndorf, L. C. G. Govia, M. G. Vavilov, R. McDermott, and F. K. Wilhelm, Optimizing microwave photodetection: Input–output theory, Quantum Sci. Technol. 3, 024009 (2018).
  114. G. Ithier, E. Collin, P. Joyez, P. J. Meeson, D. Vion, D. Esteve, F. Chiarello, A. Shnirman, Y. Makhlin, J. Schriefl, and G. Schön, Decoherence in a superconducting quantum bit circuit, Phys. Rev. B 72, 134519 (2005).
  115. F. Yoshihara, K. Harrabi, A. O. Niskanen, Y. Nakamura, and J. S. Tsai, Decoherence of flux qubits due to 1/f flux noise, Phys. Rev. Lett. 97, 167001 (2006).
  116. R. C. Bialczak, R. McDermott, M. Ansmann, M. Hofheinz, N. Katz, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, A. N. Cleland, and J. M. Martinis, 1/f flux noise in Josephson phase qubits, Phys. Rev. Lett. 99, 187006 (2007).
  117. N. Didier, E. A. Sete, J. Combes, and M. P. da Silva, ac flux sweet spots in parametrically modulated superconducting qubits, Phys. Rev. Appl. 12, 054015 (2019).
  118. A. Di Paolo, T. E. Baker, A. Foley, D. Senechal, and A. Blais, Efficient modeling of superconducting quantum circuits with tensor networks, npj Quantum Inf. 7, 11 (2021).
  119. P. Groszkowski, A. Seif, J. Koch, and A. A. Clerk, Simple master equations for describing driven systems subject to classical non-Markovian noise, Quantum 7, 972 (2023).
  120. J. M. Martinis, S. Nam, J. Aumentado, K. M. Lang, and C. Urbina, Decoherence of a superconducting qubit due to bias noise, Phys. Rev. B 67, 094510 (2003).
  121. P. J. J. O’Malley et al., Qubit metrology of ultralow phase noise using randomized benchmarking, Phys. Rev. Appl. 3, 044009 (2015).
  122. S. M. Anton, C. Müller, J. S. Birenbaum, S. R. O’Kelley, A. D. Fefferman, D. S. Golubev, G. C. Hilton, H.-M. Cho, K. D. Irwin, F. C. Wellstood, G. Schön, A. Shnirman, and J. Clarke, Pure dephasing in flux qubits due to flux noise with spectral density scaling as 1/fα, Phys. Rev. B 85, 224505 (2012).
  123. E. A. Sete, M. J. Reagor, N. Didier, and C. T. Rigetti, Charge- and flux-insensitive tunable superconducting qubit, Phys. Rev. Appl. 8, 024004 (2017).
  124. S. Danilin, N. Nugent, and M. Weides, Quantum sensing with tunable superconducting qubits: Optimization and speed-up, New J. Phys. 26, 103029 (2024).
  125. R. H. Koch, D. P. DiVincenzo, and J. Clarke, Model for 1/f flux noise in SQUIDs and qubits, Phys. Rev. Lett. 98, 267003 (2007).
  126. M. D. Hutchings, J. B. Hertzberg, Y. Liu, N. T. Bronn, G. A. Keefe, M. Brink, J. M. Chow, and B. L. T. Plourde, Tunable superconducting qubits with flux-independent coherence, Phys. Rev. Appl. 8, 044003 (2017).
  127. A. Kou, W. C. Smith, U. Vool, R. T. Brierley, H. Meier, L. Frunzio, S. M. Girvin, L. I. Glazman, and M. H. Devoret, Fluxonium-based artificial molecule with a tunable magnetic moment, Phys. Rev. X 7, 031037 (2017).
  128. S. Hazra, W. Dai, T. Connolly, P. D. Kurilovich, Z. Wang, L. Frunzio, and M. H. Devoret, Benchmarking the readout of a superconducting qubit for repeated measurements, Phys. Rev. Lett. 134, 100601 (2025).
  129. S. Krämer, D. Plankensteiner, L. Ostermann, and H. Ritsch, QuantumOptics.jl: A Julia framework for simulating open quantum systems, Comput. Phys. Commun. 227, 109 (2018).
  130. J. Bezanson, A. Edelman, S. Karpinski, and V. B. Shah, Julia: A fresh approach to numerical computing, SIAM Rev. 59, 65 (2017).
  131. A. P. M. Place et al., New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds, Nat. Commun. 12, 1779 (2021).
  132. C. Wang et al., Towards practical quantum computers: Transmon qubit with a lifetime approaching 0.5 milliseconds, npj Quantum Inf. 8, 3 (2022).
  133. Z. Wang, C. C. Yu, and R. Wu, Why superconducting Ta qubits have fewer tunneling two-level systems at the vacuum-oxide interface than Nb qubits, Phys. Rev. Appl. 23, 024017 (2025).
  134. M. Bal et al., Systematic improvements in transmon qubit coherence enabled by niobium surface encapsulation, npj Quantum Inf. 10, 43 (2024).
  135. R. Kokkoniemi, J.-P. Girard, D. Hazra, A. Laitinen, J. Govenius, R. E. Lake, I. Sallinen, V. Vesterinen, M. Partanen, J. Y. Tan, K. W. Chan, K. Y. Tan, P. Hakonen, and M. Möttönen, Bolometer operating at the threshold for circuit quantum electrodynamics, Nature (London) 586, 47 (2020).
  136. A. M. Gunyhó, S. Kundu, J. Ma, W. Liu, S. Niemelä, G. Catto, V. Vadimov, V. Vesterinen, P. Singh, Q. Chen, and M. Möttönen, Single-shot readout of a superconducting qubit using a thermal detector, Nat. Electron. 7, 288 (2024).
  137. J. P. Pekola and B. Karimi, Ultrasensitive calorimetric detection of single photons from qubit decay, Phys. Rev. X 12, 011026 (2022).
  138. K. Petrovnin, J. Wang, M. Perelshtein, P. Hakonen, and G. S. Paraoanu, Microwave photon detection at parametric criticality, PRX Quantum 5, 020342 (2024).
  139. J. Sperling, W. Vogel, and G. S. Agarwal, True photocounting statistics of multiple on-off detectors, Phys. Rev. A 85, 023820 (2012).
  140. V. S. Kovtoniuk, E. V. Stolyarov, O. V. Kliushnichenko, and A. A. Semenov, Tight inequalities for nonclassicality of measurement statistics, Phys. Rev. A 109, 053710 (2024).
  141. A. Vanselow, B. Beauseigneur, L. Lattier, M. Villiers, A. Denis, P. Morfin, Z. Leghtas, and P. Campagne-Ibarcq, Dissipating quartets of excitations in a superconducting circuit, arXiv:2501.05960 [quant-ph].
  142. S. O. Mundhada, A. Grimm, S. Touzard, U. Vool, S. Shankar, M. H. Devoret, and M. Mirrahimi, Generating higher-order quantum dissipation from lower-order parametric processes, Quantum Sci. Technol. 2, 024005 (2017); S. Mundhada, A. Grimm, J. Venkatraman, Z. Minev, S. Touzard, N. Frattini, V. Sivak, K. Sliwa, P. Reinhold, S. Shankar, M. Mirrahimi, and M. Devoret, Experimental implementation of a Raman-assisted eight-wave mixing process, Phys. Rev. Appl. 12, 054051 (2019).
  143. M. H. Devoret, Quantum fluctuations in electrical circuits, in Proceedings of Les Houches Summer School, Session LXIII, 1995, edited by S. Reynard, E. Giacobino, and J. Zinn-Justin (Elsevier, Amsterdam, 1997), pp. 351–386.
  144. U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl. 45, 897 (2017).
  145. S. Rasmussen, K. Christensen, S. Pedersen, L. Kristensen, T. Bækkegaard, N. Loft, and N. Zinner, Superconducting circuit companion—An introduction with worked examples, PRX Quantum 2, 040204 (2021).
  146. H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, MA, 1980).
  147. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, New York, 1965), Vol. II.
  148. A. Parra-Rodriguez, E. Rico, E. Solano, and I. L. Egusquiza, Quantum networks in divergence-free circuit QED, Quantum Sci. Technol. 3, 024012 (2018).
  149. T. Shitara, M. Bamba, F. Yoshihara, T. Fuse, S. Ashhab, K. Semba, and K. Koshino, Nonclassicality of open circuit QED systems in the deep-strong coupling regime, New J. Phys. 23, 103009 (2021).
  150. S.-Q. Zhang and Z.-D. Chen, Anticoherence in cavity QED systems: Influence from the associated baths beyond a Born approximation, Phys. Rev. A 93, 033849 (2016).
  151. C. A. Brasil, F. F. Fanchini, and R. de Jesus Napolitano, A simple derivation of the Lindblad equation, Rev. Bras. Ensino Fís. 35, 01 (2013).
  152. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82, 1155 (2010).
  153. G. McCauley, B. Cruikshank, D. I. Bondar, and K. Jacobs, Accurate Lindblad-form master equation for weakly damped quantum systems across all regimes, npj Quantum Inf. 6, 74 (2020).

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Phys. Rev. Research 7, 033263– Published 17 September, 2025
  • Received 22 April 2025
  • Accepted 28 August 2025
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