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Amplifying microwave pulses with a single qubit engine fueled by quantum measurements

R. Dassonneville1,*, C. Elouard2,†, R. Cazali1, R. Assouly1, A. Bienfait1, A. Auffèves3,4, and B. Huard1,‡

  • *Present address: Aix Marseille Université, Université de Toulon, CNRS, IM2NP, Marseille, France.
  • †Present address: Université de Lorraine, CNRS, LPCT, F-54000 Nancy, France.
  • ‡Contact author: benjamin.huard@ens-lyon.fr
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Phys. Rev. Research 8, 013228 – Published 2 March, 2026

DOI: https://doi.org/10.1103/rygc-bc3c

Abstract

Recent progress in manipulating individual quantum systems enables the exploration of engines exploiting nonclassical resources. One of the most appealing is the energy provided by the inherent backaction of quantum measurements. While a handful of experiments have investigated the inner dynamics of engines fueled by measurement backaction, powering a task by such an engine is missing. Here, we demonstrate the amplification of microwave signals by an engine fueled by repeated quantum measurements of a superconducting transmon qubit. Using feedback, the engine acts as a quantum Maxwell demon operating without a hot thermal source. Measuring the gain of this amplification constitutes a direct probing of the work output of the engine, in contrast to inferring the work by measuring the qubit state along its evolution. Observing a good agreement between both work estimation methods, our experiment validates the accuracy of the indirect method. We characterize the long-term stability of the engine as well as its robustness to transmon decoherence, loss, and drifts. Our experiment exemplifies the use of energy brought by quantum measurement backaction.

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References (88)

  1. N. M. Myers, O. Abah, and S. Deffner, Quantum thermodynamic devices: From theoretical proposals to experimental reality, AVS Quantum Sci. 4, 027101 (2022).
  2. L. M. Cangemi, C. Bhadra, and A. Levy, Quantum engines and refrigerators, Phys. Rep. 1087, 1 (2024).
  3. C. Elouard, D. A. Herrera-Martí, M. Clusel, and A. Auffèves, The role of quantum measurement in stochastic thermodynamics, npj Quantum Inf. 3, 9 (2017).
  4. S. Rogers and A. N. Jordan, Postselection and quantum energetics, Phys. Rev. A 106, 052214 (2022).
  5. M. H. Mohammady, Classicality of the heat produced by quantum measurements, Phys. Rev. A 104, 062202 (2021).
  6. A. Solfanelli, L. Buffoni, A. Cuccoli, and M. Campisi, Maximal energy extraction via quantum measurement, J. Stat. Mech. (2019) 094003.
  7. A. Auffèves, A short story of quantum and information thermodynamics, SciPost Phys. Lect. Notes 27 (2021).
  8. A. N. Jordan, C. Elouard, and A. Auffèves, Quantum measurement engines and their relevance for quantum interpretations, Quantum Stud.: Math. Found. 7, 203 (2020).
  9. K. Brandner, M. Bauer, M. T. Schmid, and U. Seifert, Coherence-enhanced efficiency of feedback-driven quantum engines, New J. Phys. 17, 065006 (2015).
  10. C. Elouard, D. Herrera-Martí, B. Huard, and A. Auffèves, Extracting work from quantum measurement in Maxwell's demon engines, Phys. Rev. Lett. 118, 260603 (2017).
  11. C. Elouard and A. N. Jordan, Efficient quantum measurement engines, Phys. Rev. Lett. 120, 260601 (2018).
  12. Y. Wang, S. Xia, J. Chen, J. Chen, and S. Su, Conditional control of measurement-driven machines, Phys. Lett. A 493, 129243 (2024).
  13. L. Bresque, D. Das, and É. Roldán, Run-and-tumble exact work statistics in a lazy quantum measurement engine: Stochastic information processing, Phys. Rev. Lett. 134, 200402 (2025).
  14. J. Yi, P. Talkner, and Y. W. Kim, Single-temperature quantum engine without feedback control, Phys. Rev. E 96, 022108 (2017).
  15. X. Ding, J. Yi, Y. W. Kim, and P. Talkner, Measurement-driven single temperature engine, Phys. Rev. E 98, 042122 (2018).
  16. S. Su, Z. Lin, and J. Chen, Thermal divergences of quantum measurement engine, J. Appl. Phys. 133, 124401 (2023).
  17. S. K. Manikandan, C. Elouard, K. W. Murch, A. Auffèves, and A. N. Jordan, Efficiently fueling a quantum engine with incompatible measurements, Phys. Rev. E 105, 044137 (2022).
  18. T. Opatrný, A. Misra, and G. Kurizki, Work generation from thermal noise by quantum phase-sensitive observation, Phys. Rev. Lett. 127, 040602 (2021).
  19. G. Manzano and R. Zambrini, Quantum thermodynamics under continuous monitoring: A general framework, AVS Quantum Sci. 4, 025302 (2022).
  20. L. P. Bettmann, M. J. Kewming, and J. Goold, Thermodynamics of a continuously monitored double-quantum-dot heat engine in the repeated interactions framework, Phys. Rev. E 107, 044102 (2023).
  21. N. Behzadi, Quantum engine based on general measurements, J. Phys. A: Math. Theor. 54, 015304 (2021).
  22. T. Purves and A. J. Short, Channels, measurements, and postselection in quantum thermodynamics, Phys. Rev. E 104, 014111 (2021).
  23. L. Buffoni, A. Solfanelli, P. Verrucchi, A. Cuccoli, and M. Campisi, Quantum measurement cooling, Phys. Rev. Lett. 122, 070603 (2019).
  24. L. Bresque, P. A. Camati, S. Rogers, K. Murch, A. N. Jordan, and A. Auffèves, Two-qubit engine fueled by entanglement and local measurements, Phys. Rev. Lett. 126, 120605 (2021).
  25. M. F. Anka, T. R. de Oliveira, and D. Jonathan, Measurement-based quantum heat engine in a multilevel system, Phys. Rev. E 104, 054128 (2021).
  26. J.-S. Yan and J. Jing, Charging by quantum measurement, Phys. Rev. Appl. 19, 064069 (2023).
  27. K. Wang, R. Xia, L. Bresque, and P. Xue, Experimental demonstration of a quantum engine driven by entanglement and local measurements, Phys. Rev. Res. 4, L032042 (2022).
  28. N.-N. Wang, H. Cao, C. Zhang, X.-Y. Xu, B.-H. Liu, Y.-F. Huang, C.-F. Li, and G.-C. Guo, Experimental demonstration of quantum cooling engine powered by entangled measurement, arXiv:2302.09948.
  29. V. F. Lisboa, P. R. Dieguez, J. R. Guimarães, J. F. G. Santos, and R. M. Serra, Experimental investigation of a quantum heat engine powered by generalized measurements, Phys. Rev. A 106, 022436 (2022).
  30. P. R. Dieguez, V. F. Lisboa, and R. M. Serra, Thermal devices powered by generalized measurements with indefinite causal order, Phys. Rev. A 107, 012423 (2023).
  31. N. Cottet, S. Jezouin, L. Bretheau, P. Campagne-Ibarcq, Q. Ficheux, J. Anders, A. Auffèves, R. Azouit, P. Rouchon, and B. Huard, Observing a quantum Maxwell demon at work, Proc. Natl. Acad. Sci. USA 114, 7561 (2017).
  32. M. Naghiloo, J. J. Alonso, A. Romito, E. Lutz, and K. W. Murch, Information gain and loss for a quantum Maxwell's demon, Phys. Rev. Lett. 121, 030604 (2018).
  33. Y. Masuyama, K. Funo, Y. Murashita, A. Noguchi, S. Kono, Y. Tabuchi, R. Yamazaki, M. Ueda, and Y. Nakamura, Information-to-work conversion by Maxwell's demon in a superconducting circuit quantum electrodynamical system, Nat. Commun. 9, 1291 (2018).
  34. M. Naghiloo, D. Tan, P. M. Harrington, J. J. Alonso, E. Lutz, A. Romito, and K. W. Murch, Heat and work along individual trajectories of a quantum bit, Phys. Rev. Lett. 124, 110604 (2020).
  35. X. Song, M. Naghiloo, and K. Murch, Quantum process inference for a single-qubit Maxwell demon, Phys. Rev. A 104, 022211 (2021).
  36. J. P. Pekola and B. Karimi, Colloquium: Quantum heat transport in condensed matter systems, Rev. Mod. Phys. 93, 041001 (2021).
  37. J. Stevens, D. Szombati, M. Maffei, C. Elouard, R. Assouly, N. Cottet, R. Dassonneville, Q. Ficheux, S. Zeppetzauer, A. Bienfait, A. N. Jordan, A. Auffèves, and B. Huard, Energetics of a single qubit gate, Phys. Rev. Lett. 129, 110601 (2022).
  38. X. Linpeng, L. Bresque, M. Maffei, A. N. Jordan, A. Auffèves, and K. W. Murch, Energetic cost of measurements using quantum, coherent, and thermal light, Phys. Rev. Lett. 128, 220506 (2022).
  39. M. Spiecker, P. Paluch, N. Gosling, N. Drucker, S. Matityahu, D. Gusenkova, S. Günzler, D. Rieger, I. Takmakov, F. Valenti, P. Winkel, R. Gebauer, O. Sander, G. Catelani, A. Shnirman, A. V. Ustinov, W. Wernsdorfer, Y. Cohen, and I. M. Pop, Two-level system hyperpolarization using a quantum Szilard engine, Nat. Phys. 19, 1320 (2023).
  40. E. Gümüş, D. Majidi, D. Nikolić, P. Raif, B. Karimi, J. T. Peltonen, E. Scheer, J. P. Pekola, H. Courtois, W. Belzig, and C. B. Winkelmann, Calorimetry of a phase slip in a Josephson junction, Nat. Phys. 19, 196 (2023).
  41. S. Erdamar, M. Abbasi, B. Ha, W. Chen, J. Muldoon, Y. Joglekar, and K. W. Murch, Constraining work fluctuations of non-Hermitian dynamics across the exceptional point of a superconducting qubit, Phys. Rev. Res. 6, L022013 (2024).
  42. X. Linpeng, N. Piccione, M. Maffei, L. Bresque, S. P. Prasad, A. N. Jordan, A. Auffèves, and K. W. Murch, Quantum energetics of a noncommuting measurement, Phys. Rev. Res. 6, 033045 (2024).
  43. C. W. Gardiner and M. J. Collett, Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation, Phys. Rev. A 31, 3761 (1985).
  44. U. Vool and M. Devoret, Introduction to quantum electromagnetic circuits, Int. J. Circuit Theory Appl. 45, 897 (2017).
  45. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Cham, 1995).
  46. C. Gardiner and P. Zoller, Quantum Noise (Springer, Berlin 2004).
  47. N. Cottet, Energy and information in fluorescence with superconducting circuits, Ph.D thesis, ENS Paris, 2018.
  48. J. Monsel, M. Fellous-Asiani, B. Huard, and A. Auffèves, The energetic cost of work extraction, Phys. Rev. Lett. 124, 130601 (2020).
  49. S. P. Prasad, M. Maffei, P. A. Camati, C. Elouard, and A. Auffèves, Thermodynamics of autonomous optical Bloch equations, arXiv:2404.09648.
  50. I. Maillette de Buy Wenniger, S. E. Thomas, M. Maffei, S. C. Wein, M. Pont, N. Belabas, S. Prasad, A. Harouri, A. Lemaître, I. Sagnes, N. Somaschi, A. Auffèves, and P. Senellart, Experimental analysis of energy transfers between a quantum emitter and light fields, Phys. Rev. Lett. 131, 260401 (2023).
  51. K. Jacobs, Second law of thermodynamics and quantum feedback control: Maxwell's demon with weak measurements, Phys. Rev. A 80, 012322 (2009).
  52. Y. Guryanova, N. Friis, and M. Huber, Ideal projective measurements have infinite resource costs, Quantum 4, 222 (2020).
  53. C. L. Latune and C. Elouard, A thermodynamically consistent approach to the energy costs of quantum measurements, Quantum 9, 1614 (2025).
  54. P. Y. Wen, A. F. Kockum, H. Ian, J. C. Chen, F. Nori, and I.-C. Hoi, Reflective amplification without population inversion from a strongly driven superconducting qubit, Phys. Rev. Lett. 120, 063603 (2018).
  55. E. Wiegand, P.-Y. Wen, P. Delsing, I.-C. Hoi, and A. F. Kockum, Ultimate quantum limit for amplification: A single atom in front of a mirror, New J. Phys. 23, 043048 (2021).
  56. F. Aziz, K.-T. Lin, P.-Y. Wen, Samina, Y.-C. Lin, E. Weigand, C.-P. Lee, Y.-T. Cheng, Y. Lu, C.-Y. Chen, C.-H. Chien, K.-M. Hsieh, Y.-H. Huang, H.-T. Huang, H. Ian, J.-C. Chen, Y.-H. Lin, A. F. Kockum, G.-D. Lin, and I.-C. Hoi, Nearly quantum-limited microwave amplification via interfering degenerate stimulated emission in a single artificial atom, npj Quantum Inf. 11, 45 (2025).
  57. C. Macklin, K. O'Brien, D. Hover, M. E. Schwartz, V. Bolkhovsky, X. Zhang, W. D. Oliver, and I. Siddiqi, A near–quantum-limited Josephson traveling-wave parametric amplifier, Science 350, 307 (2015).
  58. C. Müller, J. H. Cole, and J. Lisenfeld, Towards understanding two-level-systems in amorphous solids: Insights from quantum circuits, Rep. Prog. Phys. 82, 124501 (2019).
  59. S. Deffner, J. P. Paz, and W. H. Zurek, Quantum work and the thermodynamic cost of quantum measurements, Phys. Rev. E 94, 010103(R) (2016).
  60. L. Mancino, M. Sbroscia, E. Roccia, I. Gianani, F. Somma, P. Mataloni, M. Paternostro, and M. Barbieri, The entropic cost of quantum generalized measurements, npj Quantum Inf. 4, 20 (2018).
  61. N. Piccione, M. Maffei, A. N. Jordan, K. W. Murch, and A. Auffèves, Exploring the accuracy of interferometric quantum measurements under conservation laws, Phys. Rev. Lett. 133, 240202 (2024).
  62. M. H. Mohammady and T. Miyadera, Quantum measurements constrained by the third law of thermodynamics, Phys. Rev. A 107, 022406 (2023).
  63. A. Vepsäläinen, R. Winik, A. H. Karamlou, J. Braumüller, A. D. Paolo, Y. Sung, B. Kannan, M. Kjaergaard, D. K. Kim, A. J. Melville, B. M. Niedzielski, J. L. Yoder, S. Gustavsson, and W. D. Oliver, Improving qubit coherence using closed-loop feedback, Nat. Commun. 13, 1932 (2022).
  64. C. Elouard and M. H. Mohammady, Work, heat and entropy production along quantum trajectories, in Thermodynamics in the Quantum Regime (Springer, Cham, Switzerland, 2019), pp. 363–393.
  65. K. Prech and P. P. Potts, Quantum fluctuation theorem for arbitrary measurement and feedback schemes, Phys. Rev. Lett. 133, 140401 (2024).
  66. Y. Hasegawa, Quantum thermodynamic uncertainty relation for continuous measurement, Phys. Rev. Lett. 125, 050601 (2020).
  67. D. Reiche, J.-T. Hsiang, and B.-L. Hu, Quantum thermodynamic uncertainty relations, generalized current fluctuations and nonequilibrium fluctuation–dissipation inequalities, Entropy 24, 1016 (2022).
  68. A. Maity and A. Ghoshal, Violation of the thermodynamic uncertainty relation in quantum collisional models, Phys. Rev. A 112, 022203 (2025).
  69. S. V. Moreira, M. Radaelli, A. Candeloro, F. C. Binder, and M. T. Mitchison, Precision bounds for multiple currents in open quantum systems, Phys. Rev. E 111, 064107 (2025).
  70. A. Eddins, J. M. Kreikebaum, D. M. Toyli, E. M. Levenson-Falk, A. Dove, W. P. Livingston, B. A. Levitan, L. C. G. Govia, A. A. Clerk, and I. Siddiqi, High-efficiency measurement of an artificial atom embedded in a parametric amplifier, Phys. Rev. X 9, 011004 (2019).
  71. R. Dassonneville, R. Assouly, T. Peronnin, P. Rouchon, and B. Huard, Number-resolved photocounter for propagating microwave mode, Phys. Rev. Appl. 14, 044022 (2020).
  72. 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).
  73. 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).
  74. A. Gunyhó, K. Kohvakka, Q.-M. Chen, J.-P. Girard, R. Kokkoniemi, W. Liu, and M. Möttönen, Zeptojoule calorimetry, arXiv:2412.14079.
  75. M. Xia, C. Zhou, C. Liu, P. Patel, X. Cao, P. Lu, B. Mesits, M. Mucci, D. Gorski, D. Pekker, and M. Hatridge, Fast superconducting qubit control with sub-harmonic drives, Nat. Commun. 17, 1024 (2026).
  76. O. Abah, R. Puebla, A. Kiely, G. D. Chiara, M. Paternostro, and S. Campbell, Energetic cost of quantum control protocols, New J. Phys. 21, 103048 (2019).
  77. J. Gea-Banacloche, Minimum energy requirements for quantum computation, Phys. Rev. Lett. 89, 217901 (2002).
  78. J. Ikonen, J. Salmilehto, and M. Möttönen, Energy-efficient quantum computing, npj Quantum Inf. 3, 17 (2017).
  79. S. Silva Pratapsi, P. H. Huber, P. Barthel, S. Bose, C. Wunderlich, and Y. Omar, Classical half-adder using trapped-ion quantum bits: Toward energy-efficient computation, Appl. Phys. Lett. 123, 154003 (2023).
  80. F. Góis, M. Pezzutto, and Y. Omar, Towards energetic quantum advantage in trapped-ion quantum computation, arXiv:2404.11572.
  81. M. Fellous-Asiani, J. H. Chai, Y. Thonnart, H. K. Ng, R. S. Whitney, and A. Auffèves, Optimizing resource efficiencies for scalable full-stack quantum computers, PRX Quantum 4, 040319 (2023).
  82. A. N. Jordan and I. A. Siddiqi, Quantum Measurement: Theory and Practice (Cambridge University Press, 2024).
  83. M. Boselli, J. Grebel, A. Peugeot, R. Dassonneville, B. Huard, and A. Bienfait, Observation and mitigation of microwave echoes from dielectric defects in Josephson traveling wave amplifiers, Phys. Rev. Appl. 24, 034040 (2025).
  84. D. Sank et al., Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation, Phys. Rev. Lett. 117, 190503 (2016).
  85. R. Lescanne, L. Verney, Q. Ficheux, M. H. Devoret, B. Huard, M. Mirrahimi, and Z. Leghtas, Escape of a driven quantum Josephson circuit into unconfined states, Phys. Rev. Appl. 11, 014030 (2019).
  86. R. Shillito, A. Petrescu, J. Cohen, J. Beall, M. Hauru, M. Ganahl, A. G. M. Lewis, G. Vidal, and A. Blais, Dynamics of transmon ionization, Phys. Rev. Appl. 18, 034031 (2022).
  87. C. Lledó, R. Dassonneville, A. Moulinas, J. Cohen, R. Shillito, A. Bienfait, B. Huard, and A. Blais, Cloaking a qubit in a cavity, Nat. Commun. 14, 6313 (2023).
  88. P. Campagne-Ibarcq, E. Flurin, N. Roch, D. Darson, P. Morfin, M. Mirrahimi, M. H. Devoret, F. Mallet, and B. Huard, Persistent control of a superconducting qubit by stroboscopic measurement feedback, Phys. Rev. X 3, 021008 (2013).

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Phys. Rev. Research 8, 013228– Published 2 March, 2026
  • Received 6 February 2025
  • Accepted 2 February 2026
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