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arxiv: 2607.01375 · v1 · pith:5BB2ARAHnew · submitted 2026-07-01 · 🪐 quant-ph

Bit flips are erasures in dissipative cat qubits

Filippo Ferrari , Joachim Cohen , Vincenzo Savona , Fabrizio Minganti This is my paper

Pith reviewed 2026-07-03 20:06 UTC · model grok-4.3

classification 🪐 quant-ph
keywords cat qubitsdissipative stabilizationquantum error correctionerasuresphoton burstsautonomous QECquantum trajectories
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The pith

In dissipative cat qubits bit flips produce strong photon bursts that herald logical errors via monitoring.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that bit flips in dissipatively stabilized cat qubits are marked by strong time-localized photon bursts emitted from the stabilizing buffer. These bursts enable photon counting or homodyne detection to identify when logical information is lost. A reader would care because the approach converts silent logical faults into erasures that a decoder can use, which lowers the resources needed for fault tolerance. The work uses quantum trajectories to demonstrate that the autonomous stabilization can continue uninterrupted while the signals are monitored.

Core claim

Using quantum trajectories, bit flips in dissipatively stabilized cat qubits are accompanied by strong time-localized photon bursts from the dissipative buffer. Photon counting and homodyne monitoring therefore herald the loss of logical information without interrupting autonomous stabilization, so that bit flips are erasures. Emitted signals from engineered reservoirs can serve as built-in failure monitors for autonomous QEC.

What carries the argument

Framework based on past quantum states and number-resolved master equations that quantifies detectability of logical failures from the emitted signal.

If this is right

  • Bit flips become erasures that are available to a decoder.
  • Rare logical faults are converted into detectable events that reduce fault-tolerance overhead.
  • Engineered reservoirs supply built-in failure monitors for autonomous quantum error correction.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same monitoring of reservoir signals could detect errors in other autonomous QEC schemes beyond cat qubits.
  • Incorporating this heralding may allow experimental systems to reach lower logical error rates without separate detection hardware.

Load-bearing premise

The photon bursts are sufficiently strong, time-localized, and distinguishable from background noise to allow reliable heralding without degrading the autonomous stabilization.

What would settle it

An experiment in which bit flips occur with no photon burst above background levels or in which monitoring the buffer visibly degrades the stabilization.

Figures

Figures reproduced from arXiv: 2607.01375 by Fabrizio Minganti, Filippo Ferrari, Joachim Cohen, Vincenzo Savona.

Figure 1
Figure 1. Figure 1: FIG. 1. As a function of time and in a quantum trajectory [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Quantum trajectory analysis of a bit flip event as a [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Conditioned buffer emission [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Number-resolved master equation results. (a-c) Ex [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. As a function of [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. For an imperfect photodetector and as a function of [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Homodyne detection of bit flips. As a function of the [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Dissipative repetition code of distance [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Wigner functions of the quantum trajectory [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Expectation value of the logical Pauli operator, [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Bit flips in an autonomously stabilized repetition code. (a) Scaling of the bit-flip error rate Γ [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
read the original abstract

Autonomous quantum error correction (QEC) stabilizes a logical manifold through dissipative events that emit into output channels, which are typically accessible to measurement. These signals are often discarded, and whether they contain useful information about logical failures remains generally unclear. Using quantum trajectories, we show that in dissipatively stabilized cat qubits bit flips are not silent logical errors: each flip is accompanied by a strong, time-localized photon burst from the dissipative buffer. Photon counting and homodyne monitoring can therefore herald the loss of logical information without interrupting the autonomous stabilization: bit flips in dissipative cat qubits are erasures. More broadly, our results show that the emitted signals of engineered reservoirs can act as built-in failure monitors for autonomous QEC, turning rare logical faults into erasures available to a decoder and reducing fault-tolerance overhead. To this end, we develop a general framework, based on past quantum states and number-resolved master equations, to quantify the detectability of such logical failures in autonomous QEC from the emitted signal.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that in dissipatively stabilized cat qubits, bit-flip errors are not silent: each is accompanied by a strong, time-localized photon burst emitted by the dissipative buffer. Using quantum trajectories and a number-resolved master equation, the authors show that photon counting or homodyne monitoring of the output channel can herald these events, converting bit flips into erasures without interrupting autonomous stabilization. A general framework based on past quantum states is introduced to quantify detectability of such logical failures from the emitted signals.

Significance. If the central claim holds with quantitative support, the result offers a concrete mechanism to extract logical-error information from the engineered reservoir output already present in autonomous QEC, potentially lowering fault-tolerance overhead by turning rare bit flips into detectable erasures. The development of the past-quantum-state plus number-resolved-master-equation framework is a methodological contribution that could be applied to other dissipative encodings.

major comments (2)
  1. [Abstract and framework section (past quantum states + number-resolved ME)] The central claim that each bit flip produces a 'strong, time-localized photon burst' distinguishable from the continuous dissipative output rests on the quantum-trajectory and number-resolved-master-equation analysis, yet the manuscript supplies no numerical values for burst contrast (integrated photon number above background), temporal width relative to the stabilization timescale, or false-positive rate once finite detector efficiency, dark counts, and cavity loss are included.
  2. [Quantum-trajectory simulations] The heralding argument assumes that monitoring the output channel does not degrade the autonomous stabilization; however, the quantitative trade-off between detection probability and the back-action or added loss on the cat manifold is not reported, leaving the 'without interrupting the autonomous stabilization' statement unverified.
minor comments (2)
  1. Notation for the dissipative buffer operators and the logical bit-flip operator should be introduced with explicit definitions before the first use of the number-resolved master equation.
  2. Figure captions for the trajectory plots should state the specific parameter values (drive strength, two-photon dissipation rate, etc.) used in the simulations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and will incorporate revisions where appropriate to strengthen the quantitative support for our claims.

read point-by-point responses

  1. Referee: [Abstract and framework section (past quantum states + number-resolved ME)] The central claim that each bit flip produces a 'strong, time-localized photon burst' distinguishable from the continuous dissipative output rests on the quantum-trajectory and number-resolved-master-equation analysis, yet the manuscript supplies no numerical values for burst contrast (integrated photon number above background), temporal width relative to the stabilization timescale, or false-positive rate once finite detector efficiency, dark counts, and cavity loss are included.

    Authors: We agree that explicit numerical quantification of burst contrast, temporal width, and false-positive rates (including realistic detector imperfections) would strengthen the central claim. The past-quantum-state and number-resolved master-equation framework introduced in the manuscript is precisely designed to enable such calculations from the emitted signal. In the revised version we will add these metrics, computed for representative parameter regimes of the dissipative cat qubit, together with estimates under finite efficiency and dark counts. revision: yes

  2. Referee: [Quantum-trajectory simulations] The heralding argument assumes that monitoring the output channel does not degrade the autonomous stabilization; however, the quantitative trade-off between detection probability and the back-action or added loss on the cat manifold is not reported, leaving the 'without interrupting the autonomous stabilization' statement unverified.

    Authors: Monitoring is performed on the output field of the dissipative buffer that is already required for autonomous stabilization; therefore no additional loss channel is introduced. Nevertheless, we acknowledge that a quantitative characterization of any residual trade-off between heralding fidelity and stabilization fidelity is desirable. In the revision we will report detection probability versus monitoring strength (or integration time) and explicitly verify that the cat-manifold stabilization remains intact under the considered continuous monitoring. revision: yes

Circularity Check

0 steps flagged

No circularity: standard open-system methods applied to cat-qubit dynamics

full rationale

The derivation applies quantum trajectories and number-resolved master equations (standard tools) to the dissipatively stabilized cat-qubit model to show that bit flips produce time-localized photon bursts. No step reduces by construction to a fitted input, self-defined quantity, or load-bearing self-citation; the emitted-signal detectability follows directly from the Lindblad dynamics and trajectory unraveling without reparameterization or renaming of known results. The framework is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on standard quantum-optics tools; no free parameters, ad-hoc axioms, or invented entities are indicated in the abstract.

axioms (1)
  • standard math Standard quantum mechanics and open-system master equations govern the dissipative cat-qubit dynamics.
    The number-resolved master equations and quantum-trajectory approach presuppose the validity of the Lindblad formalism for the engineered reservoir.

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discussion (0)

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Reference graph

Works this paper leans on

72 extracted references · 2 canonical work pages · 2 internal anchors

  1. [1]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information: 10th Anniversary Edition, 1st ed. (Cambridge University Press, 2012)

    2012

  2. [2]

    An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation

    D. Gottesman, An introduction to quantum error cor- rection and fault-tolerant quantum computation (2009), arXiv:0904.2557 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  3. [3]

    Knill and R

    E. Knill and R. Laflamme, Theory of quantum error- correcting codes, Phys. Rev. A55, 900 (1997)

    1997

  4. [4]

    Knill, R

    E. Knill, R. Laflamme, and L. Viola, Theory of Quantum 6 Error Correction for General Noise, Phys. Rev. Lett.84, 2525 (2000)

    2000

  5. [5]

    Puttermanet al., Hardware-efficient quantum error correction via concatenated bosonic qubits, Nature638, 927 (2025)

    H. Puttermanet al., Hardware-efficient quantum error correction via concatenated bosonic qubits, Nature638, 927 (2025)

    2025

  6. [6]

    Dennis, A

    E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topo- logical quantum memory, J. Math. Phys.43, 4452 (2002)

    2002

  7. [7]

    A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A86, 032324 (2012)

    2012

  8. [8]

    Krinner, N

    S. Krinner, N. Lacroix, A. Remm, A. Di Paolo, E. Genois, C. Leroux, C. Hellings, S. Lazar, F. Swiadek, J. Her- rmann, G. J. Norris, C. K. Andersen, M. M¨ uller, A. Blais, C. Eichler, and A. Wallraff, Realizing repeated quantum error correction in a distance-three surface code, Nature 605, 669 (2022)

    2022

  9. [9]

    Google Quantum AI, Suppressing quantum errors by scaling a surface code logical qubit, Nature614, 676 (2023)

    2023

  10. [10]

    Google Quantum AI and Collaborators, Quantum error correction below the surface code threshold, Nature638, 920 (2025)

    2025

  11. [11]

    J. F. Poyatos, J. I. Cirac, and P. Zoller, Quantum Reser- voir Engineering with Laser Cooled Trapped Ions, Phys. Rev. Lett.77, 4728 (1996)

    1996

  12. [12]

    Verstraete, M

    F. Verstraete, M. M. Wolf, and J. Ignacio Cirac, Quan- tum computation and quantum-state engineering driven by dissipation, Nat. Phys.5, 633 (2009)

    2009

  13. [13]

    Pastawski, L

    F. Pastawski, L. Clemente, and J. I. Cirac, Quantum memories based on engineered dissipation, Phys. Rev. A 83, 012304 (2011)

    2011

  14. [14]

    Cohen and M

    J. Cohen and M. Mirrahimi, Dissipation-induced contin- uous quantum error correction for superconducting cir- cuits, Phys. Rev. A90, 062344 (2014)

    2014

  15. [15]

    Kapit, Hardware-Efficient and Fully Autonomous Quantum Error Correction in Superconducting Circuits, Phys

    E. Kapit, Hardware-Efficient and Fully Autonomous Quantum Error Correction in Superconducting Circuits, Phys. Rev. Lett.116, 150501 (2016)

    2016

  16. [16]

    Reiter, A

    F. Reiter, A. S. Sørensen, P. Zoller, and C. A. Muschik, Dissipative quantum error correction and application to quantum sensing with trapped ions, Nat. Commun.8, 1822 (2017)

    2017

  17. [17]

    J.-M. Lihm, K. Noh, and U. R. Fischer, Implementation- independent sufficient condition of the Knill-Laflamme type for the autonomous protection of logical qudits by strong engineered dissipation, Phys. Rev. A98, 012317 (2018)

    2018

  18. [18]

    P. M. Harrington, E. J. Mueller, and K. W. Murch, Engi- neered dissipation for quantum information science, Nat. Rev. Phys.4, 660 (2022)

    2022

  19. [19]

    Y. Lin, J. P. Gaebler, F. Reiter, T. R. Tan, R. Bowler, A. S. Sørensen, D. Leibfried, and D. J. Wineland, Dissi- pative production of a maximally entangled steady state of two quantum bits, Nature504, 415 (2013)

    2013

  20. [20]

    S. D. Cole, S. D. Erickson, G. Zarantonello, K. P. Horn, P.-Y. Hou, J. J. Wu, D. H. Slichter, F. Reiter, C. P. Koch, and D. Leibfried, Resource-efficient dissipative entangle- ment of two trapped-ion qubits, Phys. Rev. Lett.128, 080502 (2022)

    2022

  21. [21]

    Shankar, M

    S. Shankar, M. Hatridge, Z. Leghtas, K. M. Sliwa, A. Narla, U. Vool, S. M. Girvin, L. Frunzio, M. Mir- rahimi, and M. H. Devoret, Autonomously stabilized en- tanglement between two superconducting quantum bits, Nature504, 419 (2013)

    2013

  22. [22]

    J. M. Gertler, B. Baker, J. Li, S. Shirol, J. Koch, and C. Wang, Protecting a bosonic qubit with autonomous quantum error correction, Nature590, 243 (2021)

    2021

  23. [23]

    Z. Li, T. Roy, D. Rodr´ ıguez P´ erez, K.-H. Lee, E. Kapit, and D. I. Schuster, Autonomous stabilization with pro- grammable stabilized state, Nat. Commun.15, 6978 (2024)

    2024

  24. [24]

    Mirrahimi, Z

    M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, Dynamically protected cat-qubits: a new paradigm for universal quan- tum computation, New J. Phys.16, 045014 (2014)

    2014

  25. [25]

    Leghtas, S

    Z. Leghtas, S. Touzard, I. M. Pop, A. Kou, B. Vlas- takis, A. Petrenko, K. M. Sliwa, A. Narla, S. Shankar, M. J. Hatridge, M. Reagor, L. Frunzio, R. J. Schoelkopf, M. Mirrahimi, and M. H. Devoret, Confining the state of light to a quantum manifold by engineered two-photon loss, Science347, 853 (2015)

    2015

  26. [26]

    Lescanne, M

    R. Lescanne, M. Villiers, T. Peronnin, A. Sarlette, M. Delbecq, B. Huard, T. Kontos, M. Mirrahimi, and Z. Leghtas, Exponential suppression of bit-flips in a qubit encoded in an oscillator, Nat. Phys.16, 509 (2020)

    2020

  27. [27]

    Grimm, N

    A. Grimm, N. E. Frattini, S. Puri, S. O. Mundhada, S. Touzard, M. Mirrahimi, S. M. Girvin, S. Shankar, and M. H. Devoret, Stabilization and operation of a Kerr-cat qubit, Nature584, 205 (2020)

    2020

  28. [28]

    R´ eglade, A

    U. R´ eglade, A. Bocquet, R. Gautier, J. Cohen, A. Marquet, E. Albertinale, N. Pankratova, M. Hall´ en, F. Rautschke, L.-A. Sellem, P. Rouchon, A. Sarlette, M. Mirrahimi, P. Campagne-Ibarcq, R. Lescanne, S. Je- zouin, and Z. Leghtas, Quantum control of a cat qubit with bit-flip times exceeding ten seconds, Nature629, 778 (2024)

    2024

  29. [29]

    J. P. Bonilla Ataides, D. K. Tuckett, S. D. Bartlett, S. T. Flammia, and B. J. Brown, The XZZX surface code, Nat. Commun.12, 2172 (2021)

    2021

  30. [30]

    Guillaud and M

    J. Guillaud and M. Mirrahimi, Repetition Cat Qubits for Fault-Tolerant Quantum Computation, Phys. Rev. X9, 041053 (2019)

    2019

  31. [31]

    Grassl, T

    M. Grassl, T. Beth, and T. Pellizzari, Codes for the quan- tum erasure channel, Phys. Rev. A56, 33 (1997)

    1997

  32. [32]

    Y. Wu, S. Kolkowitz, S. Puri, and J. D. Thompson, Era- sure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays, Nat. Commun.13, 4657 (2022)

    2022

  33. [33]

    J. D. Teoh, P. Winkel, H. K. Babla, B. J. Chapman, J. Claes, S. J. De Graaf, J. W. O. Garmon, W. D. Kalfus, Y. Lu, A. Maiti, K. Sahay, N. Thakur, T. Tsun- oda, S. H. Xue, L. Frunzio, S. M. Girvin, S. Puri, and R. J. Schoelkopf, Dual-rail encoding with super- conducting cavities, Proc. Natl. Acad. Sci. U.S.A120, e2221736120 (2023)

    2023

  34. [34]

    Kubica, A

    A. Kubica, A. Haim, Y. Vaknin, H. Levine, F. Brand˜ ao, and A. Retzker, Erasure Qubits: Overcoming the T 1 Limit in Superconducting Circuits, Phys. Rev. X13, 041022 (2023)

    2023

  35. [35]

    Gammelmark, B

    S. Gammelmark, B. Julsgaard, and K. Mølmer, Past Quantum States of a Monitored System, Phys. Rev. Lett. 111, 160401 (2013)

    2013

  36. [36]

    L. S. Levitov, H. Lee, and G. B. Lesovik, Electron count- ing statistics and coherent states of electric current, J. Math. Phys.37, 4845 (1996)

    1996

  37. [37]

    D. A. Bagrets and Y. V. Nazarov, Full counting statistics of charge transfer in Coulomb blockade systems, Phys. Rev. B67, 085316 (2003)

    2003

  38. [38]

    Flindt, T

    C. Flindt, T. Novotn´ y, and A.-P. Jauho, Full counting 7 statistics of nano-electromechanical systems, EPL69, 475 (2005)

    2005

  39. [39]

    G. T. Landi, M. J. Kewming, M. T. Mitchison, and P. P. Potts, Current Fluctuations in Open Quantum Systems: Bridging the Gap Between Quantum Continuous Mea- surements and Full Counting Statistics, PRX Quantum 5, 020201 (2024)

    2024

  40. [40]

    Menczel, C

    P. Menczel, C. Flindt, F. Brange, F. Nori, and C. Gneit- ing, Full Counting Statistics and First-Passage Times in Quantum Markovian Processes: Ensemble Relations, Metastability, and Fluctuation Theorems, PRX Quan- tum7, 010304 (2026)

    2026

  41. [41]

    Guillaud, J

    J. Guillaud, J. Cohen, and M. Mirrahimi, Quantum com- putation with cat qubits, SciPost Phys. Lect. Notes , 72 (2023)

    2023

  42. [42]

    Dalibard, Y

    J. Dalibard, Y. Castin, and K. Mølmer, Wave-function approach to dissipative processes in quantum optics, Phys. Rev. Lett.68, 580 (1992)

    1992

  43. [43]

    Mølmer, Y

    K. Mølmer, Y. Castin, and J. Dalibard, Monte Carlo wave-function method in quantum optics, J. Opt. Soc. Am. B10, 524 (1993)

    1993

  44. [44]

    A. J. Daley, Quantum trajectories and open many-body quantum systems, Adv. Phys.63, 77 (2014)

    2014

  45. [45]

    Bartolo, F

    N. Bartolo, F. Minganti, J. Lolli, and C. Ciuti, Homodyne versus photon-counting quantum trajectories for dissipa- tive Kerr resonators with two-photon driving, Eur. Phys. J. Spec. Top.226, 2705 (2017)

    2017

  46. [46]

    Minganti,Out-of-Equilibrium Phase Transitions in Nonlinear Optical Systems, Ph.d

    F. Minganti,Out-of-Equilibrium Phase Transitions in Nonlinear Optical Systems, Ph.d. thesis, Universit´ e Paris Diderot (2018)

    2018

  47. [47]

    Bit flips, saturation, and quantum chaos in dissipative cat qubits

    F. Ferrari, J. Cohen, V. Savona, and F. Minganti, Bit flips, saturation, and quantum chaos in dissipative cat qubits (2026), arXiv:2605.24100 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  48. [48]

    For more details, see the Supplementary Information

  49. [49]

    Breuer and F

    H.-P. Breuer and F. Petruccione,The Theory of Open Quantum Systems, 1st ed. (Oxford University PressOx- ford, 2007)

    2007

  50. [50]

    Y.-F. Chen, D. Hover, S. Sendelbach, L. Maurer, S. T. Merkel, E. J. Pritchett, F. K. Wilhelm, and R. Mc- Dermott, Microwave photon counter based on josephson junctions, Phys. Rev. Lett.107, 217401 (2011)

    2011

  51. [51]

    Besse, S

    J.-C. Besse, S. Gasparinetti, M. C. Collodo, T. Wal- ter, P. Kurpiers, M. Pechal, C. Eichler, and A. Wallraff, Single-shot quantum nondemolition detection of individ- ual itinerant microwave photons, Phys. Rev. X8, 021003 (2018)

    2018

  52. [52]

    S. Kono, K. Koshino, Y. Tabuchi, A. Noguchi, and Y. Nakamura, Quantum non-demolition detection of an itinerant microwave photon, Nat. Phys.14, 546 (2018)

    2018

  53. [53]

    Dassonneville, R

    R. Dassonneville, R. Assouly, T. Peronnin, P. Rouchon, and B. Huard, Number-resolved photocounter for prop- agating microwave mode, Phys. Rev. App.14, 044022 (2020)

    2020

  54. [54]

    Lescanne, S

    R. Lescanne, S. Del´ eglise, E. Albertinale, U. R´ eglade, T. Capelle, E. Ivanov, T. Jacqmin, Z. Leghtas, and E. Flurin, Irreversible qubit-photon coupling for the de- tection of itinerant microwave photons, Phys. Rev. X10, 021038 (2020)

    2020

  55. [55]

    S. Ma, G. Liu, P. Peng, B. Zhang, S. Jandura, J. Claes, A. P. Burgers, G. Pupillo, S. Puri, and J. D. Thompson, High-fidelity gates and mid-circuit erasure conversion in an atomic qubit, Nature622, 279 (2023)

    2023

  56. [56]

    Koottandavida, I

    A. Koottandavida, I. Tsioutsios, A. Kargioti, C. R. Smith, V. R. Joshi, W. Dai, J. D. Teoh, J. C. Curtis, L. Frunzio, R. J. Schoelkopf, and M. H. Devoret, Erasure Detection of a Dual-Rail Qubit Encoded in a Double-Post Superconducting Cavity, Phys. Rev. Lett.132, 180601 (2024)

    2024

  57. [57]

    Levineet al., Demonstrating a Long-Coherence Dual- Rail Erasure Qubit Using Tunable Transmons, Phys

    H. Levineet al., Demonstrating a Long-Coherence Dual- Rail Erasure Qubit Using Tunable Transmons, Phys. Rev. X14, 011051 (2024)

    2024

  58. [58]

    A. L. Shaw, P. Scholl, R. Finkelstein, R. B.-S. Tsai, J. Choi, and M. Endres, Erasure cooling, control, and hyperentanglement of motion in optical tweezers, Science 388, 845 (2025)

    2025

  59. [59]

    S. J. De Graaf, S. H. Xue, B. J. Chapman, J. D. Teoh, T. Tsunoda, P. Winkel, J. W. O. Garmon, K. M. Chang, L. Frunzio, S. Puri, and R. J. Schoelkopf, A mid- circuit erasure check on a dual-rail cavity qubit using the joint-photon number-splitting regime of circuit QED, npj Quantum Inf.11, 1 (2025)

    2025

  60. [60]

    Zhang, G

    B. Zhang, G. Liu, G. Bornet, S. P. Horvath, P. Peng, S. Ma, S. Huang, S. Puri, and J. D. Thompson, Logical qubits with erasure conversion using metastable neutral atoms, Nat. Phys.22, 910 (2026)

    2026

  61. [61]

    Z. K. Minev, S. O. Mundhada, S. Shankar, P. Reinhold, R. Guti´ errez-J´ auregui, R. J. Schoelkopf, M. Mirrahimi, H. J. Carmichael, and M. H. Devoret, To catch and re- verse a quantum jump mid-flight, Nature570, 200–204 (2019)

    2019

  62. [62]

    Mercurio, Y.-T

    A. Mercurio, Y.-T. Huang, L.-X. Cai, Y.-N. Chen, V. Savona, and F. Nori, QuantumToolbox.jl: An efficient Julia framework for simulating open quantum systems, Quantum9, 1866 (2025)

    2025

  63. [63]

    Johansson, P

    J. Johansson, P. Nation, and F. Nori, QuTiP: An open- source Python framework for the dynamics of open quan- tum systems, Comput. Phys. Commun.183, 1760 (2012)

    2012

  64. [64]

    Guilmin, A

    P. Guilmin, A. Bocquet, ´E. Genois, D. Weiss, and R. Gautier, Dynamiqs: an open-source python library for gpu-accelerated and differentiable simulation of quantum systems (2025)

    2025

  65. [65]

    H. M. Wiseman and G. J. Milburn, Quantum theory of field-quadrature measurements, Phys. Rev. A47, 642 (1993)

    1993

  66. [66]

    H. M. Wiseman and G. J. Milburn, Quantum theory of optical feedback via homodyne detection, Phys. Rev. Lett.70, 548 (1993)

    1993

  67. [67]

    H. M. Wiseman and G. J. Milburn,Quantum Measure- ment and Control, 1st ed. (Cambridge University Press, 2009)

    2009

  68. [68]

    H. J. Carmichael,Statistical Methods in Quantum Optics 1(Springer Berlin Heidelberg, Berlin, Heidelberg, 1999)

    1999

  69. [69]

    Polkovnikov, Phase space representation of quantum dynamics, Ann

    A. Polkovnikov, Phase space representation of quantum dynamics, Ann. Phys.325, 1790 (2010)

    2010

  70. [70]

    V. V. Albert and L. Jiang, Symmetries and conserved quantities in Lindblad master equations, Phys. Rev. A 89, 022118 (2014)

    2014

  71. [71]

    Macieszczak, M

    K. Macieszczak, M. Gut ¸˘ a, I. Lesanovsky, and J. P. Gar- rahan, Towards a Theory of Metastability in Open Quan- tum Dynamics, Phys. Rev. Lett.116, 240404 (2016)

    2016

  72. [72]

    code emission

    K. Macieszczak, D. C. Rose, I. Lesanovsky, and J. P. Gar- rahan, Theory of classical metastability in open quantum systems, Phys. Rev. Res.3, 033047 (2021). End Matter 8 P(n|Q ) 0 0.05 0.1 (a) n 0 10 20 30 P(E|n) 10−4 10−2 1 (b) ⟨a ̂†a ̂⟩= 2 ⟨a ̂†a ̂⟩= 4 ⟨a ̂†a ̂⟩= 6 ⟨a ̂†a ̂⟩= 8 ⟨â†a ̂⟩= 2 ⟨â†a ̂⟩= 4 ⟨â†a ̂⟩= 6 ⟨â†a ̂⟩= 8 𝜁 = 1 𝜁 = 10 𝜁 = 100 FIG. 6....

    2021