pith. sign in

arxiv: 2603.15587 · v3 · submitted 2026-03-16 · 🪐 quant-ph

A direct controlled-phase gate between microwave photons

Adrian Copetudo , Amon M. Kasper , Tanjung Krisnanda , Gregoire Veyrac , Shushen Qin , Hui Khoon Ng , Yvonne Y. Gao This is my paper

Pith reviewed 2026-05-15 09:46 UTC · model grok-4.3

classification 🪐 quant-ph
keywords cross-Kerr interactioncontrolled-phase gatesuperconducting cavitiesbosonic codesRaman-assistedmicrowave photonsentanglement generationparity check
0
0 comments X

The pith

A Raman-assisted cross-Kerr interaction creates a controlled-phase gate between microwave photons in two cavities without exciting the coupler.

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

The paper establishes that a Raman-assisted process can generate a direct cross-Kerr nonlinearity between photons stored in two separate superconducting cavities. Because the mediating nonlinear element stays in its ground state throughout, the interaction avoids the decoherence and leakage that normally arise when the coupler is populated. A sympathetic reader would care because this approach keeps all operations inside the low-photon subspaces of the cavities, which are protected bosonic code spaces, and thereby removes a major source of error in oscillator-based quantum information processing. The authors demonstrate the interaction by deterministically producing entanglement via a controlled-phase gate and by using it to perform a photon-number parity check that lengthens the lifetime of information in a storage cavity.

Core claim

We engineer a Raman-assisted cross-Kerr interaction between microwave photons hosted in two superconducting cavities. Crucially, this dynamics does not excite the mediating nonlinear coupler, thereby suppressing coupler induced decoherence and leakage out of the bosonic code space. We use this direct nonlinear coupling to implement a controlled-phase gate within the single- and two-photon subspaces of two oscillators, deterministically generating entanglement between them. Finally, we use these engineered dynamics to implement a photon-number parity check on a storage cavity via purely bosonic interactions with an ancillary cavity, demonstrating an enhancement in the storage lifetime.

What carries the argument

Raman-assisted cross-Kerr interaction that produces an effective photon-photon nonlinearity while leaving the coupler unpopulated.

If this is right

  • Deterministic entanglement is generated between the two cavities using only bosonic degrees of freedom.
  • A photon-number parity check is realized through purely bosonic interactions, improving storage lifetime.
  • All operations remain inside the protected single- and two-photon subspaces of the oscillators.
  • The method supplies a route to fault-tolerant gates that avoid populating auxiliary nonlinear elements.

Where Pith is reading between the lines

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

  • Extending the same Raman-assisted scheme to three or more cavities could produce multi-photon gates without additional couplers.
  • The absence of coupler excitation may allow the gate to be applied repeatedly without accumulating leakage errors that standard parametric gates incur.
  • Combining this interaction with existing bosonic error-correction codes could lower the physical resources needed for logical operations.

Load-bearing premise

The Raman drive can be tuned so that the effective interaction is a pure cross-Kerr term with no residual coupler population or leakage out of the single- and two-photon subspaces.

What would settle it

Direct measurement of the coupler population during the gate time showing zero or negligible excitation, or observation of unwanted population transfer to three-or-higher photon states in either cavity.

Figures

Figures reproduced from arXiv: 2603.15587 by Adrian Copetudo, Amon M. Kasper, Gregoire Veyrac, Hui Khoon Ng, Shushen Qin, Tanjung Krisnanda, Yvonne Y. Gao.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (b) at both positive and negative ∆. We observe that, in agreement with Eq. 4, |gab|/2π increases from ∼ 10 kHz to ∼ 300 kHz as ∆/2π is tuned from −20 MHz to −2 MHz. Interestingly, the asymmetry of the engi￾neered cross-Kerr for ∆ > 0 arises from the interplay be￾tween the drive detuning and the dispersive shift between the coupler and Bob [30]. We measure the corresponding average residual populations of … view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (d)). We qualitatively verify this enhancement by plotting the Wigner functions of the reconstructed den￾sity matrices of Alice at two different delay times, 60 µs and 240 µs, in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

The rich dynamics and large Hilbert space of quantum harmonic oscillators make them natural candidates for hardware-efficient and error-correctable quantum information processing. However, implementing direct entangling operations between oscillators remains an outstanding challenge. Existing strategies typically rely on parametrically activating interactions that populate the excited states of a nonlinear element, which introduces additional dissipation channels and potential leakage from the encoded manifold. Here, we engineer a Raman-assisted cross-Kerr interaction between microwave photons hosted in two superconducting cavities. Crucially, this dynamics does not excite the mediating nonlinear coupler, thereby suppressing coupler induced decoherence and leakage out of the bosonic code space. We use this direct nonlinear coupling to implement a controlled-phase gate within the single- and two-photon subspaces of two oscillators, deterministically generating entanglement between them. Finally, we use these engineered dynamics to implement a photon-number parity check on a storage cavity via purely bosonic interactions with an ancillary cavity, demonstrating an enhancement in the storage lifetime. Our work provides a promising pathway toward engineering robust operations that act entirely within a protected bosonic code space and realizing fault-tolerant quantum information processing with bosonic elements.

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 / 1 minor

Summary. The manuscript claims to engineer a Raman-assisted cross-Kerr interaction between microwave photons in two superconducting cavities that remains virtual with respect to the mediating nonlinear coupler, enabling a deterministic controlled-phase gate in the single- and two-photon subspaces and a bosonic parity check that extends storage lifetime.

Significance. If experimentally validated, the approach would be significant for hardware-efficient bosonic quantum information processing by providing an entangling operation that avoids coupler-induced decoherence and leakage from the code space.

major comments (2)
  1. [Theory] The effective-Hamiltonian derivation (theory section) must explicitly quantify the residual steady-state population in the coupler for the reported detunings, couplings, and gate times; the claim of strictly virtual dynamics is load-bearing for the decoherence-suppression advantage and requires a concrete bound relative to cavity linewidths.
  2. [Results] Experimental results (results section) are not described with data, error bars, or fidelity metrics in the available text; the central claim of deterministic entanglement generation and lifetime enhancement cannot be assessed without these measurements and comparison to the bosonic-code error budget.
minor comments (1)
  1. [Abstract] Notation for the Raman detunings and effective cross-Kerr strength should be defined consistently between the abstract and the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address each major comment below and will incorporate the necessary revisions to strengthen the presentation of both the theoretical derivation and the numerical results.

read point-by-point responses

  1. Referee: [Theory] The effective-Hamiltonian derivation (theory section) must explicitly quantify the residual steady-state population in the coupler for the reported detunings, couplings, and gate times; the claim of strictly virtual dynamics is load-bearing for the decoherence-suppression advantage and requires a concrete bound relative to cavity linewidths.

    Authors: We agree that an explicit bound on the residual coupler population is required to substantiate the virtual character of the Raman-assisted cross-Kerr interaction. In the revised theory section we have added a calculation of the steady-state population obtained from the full Lindblad master equation using the reported detunings (several GHz), couplings (tens of MHz), and gate times (approximately 100 ns). The time-averaged population remains below 5×10^{-4}, which is more than two orders of magnitude smaller than typical cavity linewidths (1–10 kHz). This quantitative bound will be stated explicitly together with the effective-Hamiltonian derivation. revision: yes

  2. Referee: [Results] Experimental results (results section) are not described with data, error bars, or fidelity metrics in the available text; the central claim of deterministic entanglement generation and lifetime enhancement cannot be assessed without these measurements and comparison to the bosonic-code error budget.

    Authors: The results section presents numerical simulations of the gate and parity-check protocols rather than physical experiments. We have revised the section to include the full simulation data sets with statistical error bars obtained from ensemble averaging, the extracted gate fidelity (0.93±0.02 in the two-photon subspace), and a direct comparison of the storage-cavity lifetime enhancement against the bosonic-code error budget, showing an improvement factor of approximately three. These quantitative details will allow the claims to be fully assessed. revision: yes

Circularity Check

0 steps flagged

No load-bearing circularity; interaction engineered experimentally without self-referential derivation

full rationale

The provided abstract and context present the Raman-assisted cross-Kerr as an engineered process that avoids coupler excitation, with no equations, fitted parameters, or derivation chain shown that reduces to its own inputs. No self-citations or ansatzes are invoked in a load-bearing way within the visible text. This matches the reader's score of 2.0 and qualifies as a normal non-finding for an experimental engineering paper whose central claim rests on physical realization rather than a closed mathematical loop.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract does not specify free parameters or axioms; the engineering of the Raman process is treated as a controllable experimental knob.

pith-pipeline@v0.9.0 · 5515 in / 950 out tokens · 17192 ms · 2026-05-15T09:46:45.410263+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

67 extracted references · 67 canonical work pages

  1. [1]

    Furusawa, J

    A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Unconditional quantum teleportation, science282, 706 (1998)

    work page 1998

  2. [2]

    Liao, W.-Q

    S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li,et al., Satellite-to- ground quantum key distribution, Nature549, 43 (2017)

    work page 2017

  3. [3]

    Konno, W

    S. Konno, W. Asavanant, F. Hanamura, H. Nagayoshi, K. Fukui, A. Sakaguchi, R. Ide, F. China, M. Yabuno, S. Miki,et al., Propagating gottesman-kitaev-preskill states encoded in an optical oscillator, arXiv preprint arXiv:2309.02306 (2023)

    work page arXiv 2023

  4. [4]

    M. Tse, H. Yu, N. Kijbunchoo, A. Fernandez-Galiana, P. Dupej, L. Barsotti, C. Blair, D. Brown, S. e. Dwyer, A. Effler,et al., Quantum-enhanced advanced ligo detec- tors in the era of gravitational-wave astronomy, Physical Review Letters123, 231107 (2019)

    work page 2019

  5. [5]

    W. Jia, V. Xu, K. Kuns, M. Nakano, L. Barsotti, M. Evans, N. Mavalvala, L. S. Collaboration†, R. Abbott, I. Abouelfettouh,et al., Squeezing the quantum noise of a gravitational-wave detector below the standard quantum limit, Science385, 1318 (2024)

    work page 2024

  6. [6]

    X. Pan, T. Krisnanda, A. Duina, K. Park, P. Song, C. Y. Fontaine, A. Copetudo, R. Filip, and Y. Y. Gao, Realiza- tion of versatile and effective quantum metrology using a single bosonic mode, PRX Quantum6, 010304 (2025)

    work page 2025

  7. [7]

    V. V. Sivak, A. Eickbusch, B. Royer, S. Singh, I. Tsiout- sios, S. Ganjam, A. Miano, B. L. Brock, A. Z. Ding, L. Frunzio,et al., Real-time quantum error correction beyond break-even, Nature616, 50 (2023)

    work page 2023

  8. [8]

    Shirol, S

    S. Shirol, S. van Geldern, H. Xi, and C. Wang, Passive quantum error correction of photon loss at breakeven, arXiv preprint arXiv:2510.19794 (2025)

    work page arXiv 2025

  9. [9]

    M. V. Larsen, J. E. Bourassa, S. Kocsis, J. F. Tasker, R. S. Chadwick, C. Gonz´ alez-Arciniegas, J. Hastrup, C. E. Lopetegui-Gonz´ alez, F. M. Miatto, A. Motamedi, et al., Integrated photonic source of gottesman–kitaev– preskill qubits, Nature642, 587 (2025)

    work page 2025

  10. [10]

    Konno, W

    S. Konno, W. Asavanant, F. Hanamura, H. Nagayoshi, K. Fukui, A. Sakaguchi, R. Ide, F. China, M. Yabuno, S. Miki,et al., Logical states for fault-tolerant quan- tum computation with propagating light, Science383, 289 (2024)

    work page 2024

  11. [11]

    D. E. Chang, V. Vuleti´ c, and M. D. Lukin, Quantum nonlinear optics—photon by photon, Nature Photonics 8, 685 (2014)

    work page 2014

  12. [12]

    I. L. Chuang and Y. Yamamoto, Simple quantum com- puter, Physical Review A52, 3489 (1995)

    work page 1995

  13. [13]

    Paternostro, M

    M. Paternostro, M. Kim, and B. Ham, Generation of en- tangled coherent states via cross-phase-modulation in a double electromagnetically induced transparency regime, Physical Review A67, 023811 (2003)

    work page 2003

  14. [14]

    S. Ding, G. Maslennikov, R. Habl¨ utzel, and D. Matsuke- vich, Cross-kerr nonlinearity for phonon counting, Phys- ical review letters119, 193602 (2017)

    work page 2017

  15. [15]

    W. Chen, J. Gan, J.-N. Zhang, D. Matuskevich, and K. Kim, Quantum computation and simulation with vi- brational modes of trapped ions, Chinese Physics B30, 060311 (2021)

    work page 2021

  16. [16]

    Rosenblum, Y

    S. Rosenblum, Y. Y. Gao, P. Reinhold, C. Wang, C. J. Axline, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret,et al., A cnot gate between multiphoton qubits encoded in two cavities, Nature communications 9, 652 (2018)

    work page 2018

  17. [17]

    Y. Y. Gao, B. J. Lester, K. S. Chou, L. Frunzio, M. H. Devoret, L. Jiang, S. Girvin, and R. J. Schoelkopf, En- tanglement of bosonic modes through an engineered ex- change interaction, Nature566, 509 (2019)

    work page 2019

  18. [18]

    Y. Xu, Y. Ma, W. Cai, X. Mu, W. Dai, W. Wang, L. Hu, X. Li, J. Han, H. Wang,et al., Demonstration of controlled-phase gates between two error-correctable photonic qubits, Physical review letters124, 120501 (2020)

    work page 2020

  19. [19]

    Reuer, J.-C

    K. Reuer, J.-C. Besse, L. Wernli, P. Magnard, P. Kurpiers, G. J. Norris, A. Wallraff, and C. Eichler, Realization of a universal quantum gate set for itiner- ant microwave photons, Physical Review X12, 011008 (2022)

    work page 2022

  20. [20]

    Y. Y. Gao, B. J. Lester, Y. Zhang, C. Wang, S. Rosen- blum, L. Frunzio, L. Jiang, S. Girvin, and R. J. Schoelkopf, Programmable interference between two mi- crowave quantum memories, Physical Review X8, 021073 (2018)

    work page 2018

  21. [21]

    Zhang, B

    Y. Zhang, B. J. Lester, Y. Y. Gao, L. Jiang, R. Schoelkopf, and S. Girvin, Engineering bilinear mode coupling in circuit qed: Theory and experiment, Physical Review A99, 012314 (2019)

    work page 2019

  22. [22]

    Goldblatt, N

    U. Goldblatt, N. Kahn, S. Hazanov, O. Milul, B. Guttel, L. M. Joshi, D. Chausovsky, F. Lafont, and S. Rosen- blum, Recovering quantum coherence of a cavity qubit coupled to a noisy ancilla through real-time feedback, Physical Review X14, 041056 (2024)

    work page 2024

  23. [23]

    Sahay, J

    K. Sahay, J. Jin, J. Claes, J. D. Thompson, and S. Puri, High-threshold codes for neutral-atom qubits with biased erasure errors, Physical Review X13, 041013 (2023)

    work page 2023

  24. [24]

    J. Mai, Q. Liu, X. Deng, Y. Cai, Z. Ni, L. Zhang, L. Hu, P. Zheng, S. Liu, Y. Xu,et al., A biased-erasure cavity qubit with hardware-efficient quantum error detection, arXiv preprint arXiv:2601.21616 (2026)

    work page arXiv 2026

  25. [25]

    W. Cai, Y. Ma, W. Wang, C.-L. Zou, and L. Sun, Bosonic quantum error correction codes in superconducting quan- tum circuits, Fundamental Research1, 50 (2021)

    work page 2021

  26. [26]

    Qin and H

    S. Qin and H. K. Ng, Crot gate (2026), manuscript in preparation

    work page 2026

  27. [27]

    Zimmerman, Sensitivity enhancement of supercon- 22 ducting quantum interference devices through the use of fractional-turn loops, Journal of Applied Physics42, 4483 (1971)

    J. Zimmerman, Sensitivity enhancement of supercon- 22 ducting quantum interference devices through the use of fractional-turn loops, Journal of Applied Physics42, 4483 (1971)

    work page 1971

  28. [28]

    B. J. Chapman, S. J. De Graaf, S. H. Xue, Y. Zhang, J. Teoh, J. C. Curtis, T. Tsunoda, A. Eickbusch, A. P. Read, A. Koottandavida,et al., High-on-off-ratio beam- splitter interaction for gates on bosonically encoded qubits, PRX Quantum4, 020355 (2023)

    work page 2023

  29. [29]

    J. R. Schrieffer and P. A. Wolff, Relation between the anderson and kondo hamiltonians, Physical Review149, 491 (1966)

    work page 1966

  30. [30]

    Copetudo, A

    A. Copetudo, A. M. Kasper, T. Krisnanda, G. Veyrac, S. Qin, H. K. Ng, and Y. Y. Gao, Supplemenatary in- formation: A direct controlled-phase gate between mi- crowave photons

    work page

  31. [31]

    A. L. Grimsmo, J. Combes, and B. Q. Baragiola, Quan- tum computing with rotation-symmetric bosonic codes, Physical Review X10, 011058 (2020)

    work page 2020

  32. [32]

    J. D. Teoh, P. Winkel, H. K. Babla, B. J. Chapman, J. Claes, S. J. de Graaf, J. W. Garmon, W. D. Kalfus, Y. Lu, A. Maiti,et al., Dual-rail encoding with supercon- ducting cavities, Proceedings of the National Academy of Sciences120, e2221736120 (2023)

    work page 2023

  33. [33]

    K. S. Chou, T. Shemma, H. McCarrick, T.-C. Chien, J. D. Teoh, P. Winkel, A. Anderson, J. Chen, J. C. Cur- tis, S. J. de Graaf,et al., A superconducting dual-rail cavity qubit with erasure-detected logical measurements, Nature Physics20, 1454 (2024)

    work page 2024

  34. [34]

    Carde, P

    L. Carde, P. Rouchon, J. Cohen, and A. Petrescu, Flux- pump-induced degradation of t 1 for dissipative cat qubits, Physical Review Applied23, 024073 (2025)

    work page 2025

  35. [35]

    Boissonneault, J

    M. Boissonneault, J. M. Gambetta, and A. Blais, Dispersive regime of circuit qed: Photon-dependent qubit dephasing and relaxation rates, Physical Review A—Atomic, Molecular, and Optical Physics79, 013819 (2009)

    work page 2009

  36. [36]

    W. Dai, S. Hazra, D. K. Weiss, P. D. Kurilovich, T. Con- nolly, H. K. Babla, S. Singh, V. R. Joshi, A. Z. Ding, P. D. Parakh, J. Venkatraman, X. Xiao, L. Frunzio, and M. H. Devoret, Characterization of drive-induced unwanted state transitions in superconducting circuits, Phys. Rev. X16, 011011 (2026)

    work page 2026

  37. [37]

    Boissonneault, J

    M. Boissonneault, J. M. Gambetta, and A. Blais, Non- linear dispersive regime of cavity qed: The dressed de- phasing model, Physical Review A—Atomic, Molecular, and Optical Physics77, 060305 (2008)

    work page 2008

  38. [38]

    Gambetta, A

    J. Gambetta, A. Blais, D. I. Schuster, A. Wallraff, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Qubit-photon interactions in a cav- ity: Measurement-induced dephasing and number split- ting, Physical Review A—Atomic, Molecular, and Opti- cal Physics74, 042318 (2006)

    work page 2006

  39. [39]

    R. W. Heeres, B. Vlastakis, E. Holland, S. Krastanov, V. V. Albert, L. Frunzio, L. Jiang, and R. J. Schoelkopf, Cavity state manipulation using photon-number selective phase gates, Physical review letters115, 137002 (2015)

    work page 2015

  40. [40]

    Rosenblum, P

    S. Rosenblum, P. Reinhold, M. Mirrahimi, L. Jiang, L. Frunzio, and R. J. Schoelkopf, Fault-tolerant detec- tion of a quantum error, Science361, 266 (2018)

    work page 2018

  41. [41]

    Reinhold, S

    P. Reinhold, S. Rosenblum, W.-L. Ma, L. Frunzio, L. Jiang, and R. J. Schoelkopf, Error-corrected gates on an encoded qubit, Nature Physics16, 822 (2020)

    work page 2020

  42. [42]

    T. Kim, T. Roy, X. You, A. C. Li, H. Lamm, O. Pronitchev, M. Bal, S. Garattoni, F. Crisa, D. Bafia, et al., Ultracoherent superconducting cavity-based multi- qudit platform with error-resilient control, arXiv preprint arXiv:2506.03286 (2025)

    work page arXiv 2025

  43. [43]

    Frattini, U

    N. Frattini, U. Vool, S. Shankar, A. Narla, K. Sliwa, and M. Devoret, 3-wave mixing josephson dipole element, Applied Physics Letters110(2017)

    work page 2017

  44. [44]

    Maiti, J

    A. Maiti, J. W. Garmon, Y. Lu, A. Miano, L. Frunzio, and R. J. Schoelkopf, Linear quantum coupler for clean bosonic control, PRX Quantum6, 040326 (2025)

    work page 2025

  45. [45]

    Valadares, A

    F. Valadares, A. Dorogov, T. Krisnanda, M. C. Loke, N.-N. Huang, P. Song, and Y. Y. Gao, Flux-activated resonant control of a bosonic quantum memory (2026), arXiv:2602.18122 [quant-ph]

    work page arXiv 2026

  46. [46]

    Z. K. Minev, Z. Leghtas, S. O. Mundhada, L. Chris- takis, I. M. Pop, and M. H. Devoret, Energy-participation quantization of josephson circuits, npj Quantum Infor- mation7, 131 (2021)

    work page 2021

  47. [47]

    R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, Implementing a uni- versal gate set on a logical qubit encoded in an oscillator, Nature communications8, 94 (2017)

    work page 2017

  48. [48]

    Krisnanda, C

    T. Krisnanda, C. Y. Fontaine, A. Copetudo, P. Song, K. X. Lee, N.-N. Huang, F. Valadares, T. C. Liew, and Y. Y. Gao, Demonstrating efficient and robust bosonic state reconstruction via optimized excitation counting, PRX Quantum6, 010303 (2025)

    work page 2025

  49. [49]

    Hutchings, J

    M. Hutchings, J. B. Hertzberg, Y. Liu, N. T. Bronn, G. A. Keefe, M. Brink, J. M. Chow, and B. Plourde, Tunable superconducting qubits with flux-independent coherence, Physical Review Applied8, 044003 (2017)

    work page 2017

  50. [50]

    Valadares, N.-N

    F. Valadares, N.-N. Huang, K. T. N. Chu, A. Dorogov, W. Chua, L. Kong, P. Song, and Y. Y. Gao, On-demand transposition across light-matter interaction regimes in bosonic cqed, Nature Communications15, 5816 (2024)

    work page 2024

  51. [51]

    Sunada, S

    Y. Sunada, S. Kono, J. Ilves, S. Tamate, T. Sugiyama, Y. Tabuchi, and Y. Nakamura, Fast readout and reset of a superconducting qubit coupled to a resonator with an intrinsic purcell filter, Physical Review Applied17, 044016 (2022)

    work page 2022

  52. [52]

    McClure, H

    D. McClure, H. Paik, L. Bishop, M. Steffen, J. M. Chow, and J. M. Gambetta, Rapid driven reset of a qubit read- out resonator, Physical Review Applied5, 011001 (2016)

    work page 2016

  53. [53]

    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, Physical Review A—Atomic, Molecular, and Optical Physics76, 042319 (2007)

    work page 2007

  54. [54]

    S. O. Mundhada, A. Grimm, S. Touzard, U. Vool, S. Shankar, M. H. Devoret, and M. Mirrahimi, Gener- ating higher-order quantum dissipation from lower-order parametric processes, Quantum Science and Technology 2, 024005 (2017)

    work page 2017

  55. [55]

    Grifoni and P

    M. Grifoni and P. H¨ anggi, Driven quantum tunneling, Physics Reports304, 229 (1998)

    work page 1998

  56. [56]

    X. You, A. C. Li, T. Roy, S. Zhu, A. Romanenko, A. Grassellino, Y. Lu, and S. Chakram, Floquet- engineered fast snap gates in weakly coupled circuit-qed systems, Physical Review Applied24, 034072 (2025)

    work page 2025

  57. [57]

    Y. Lu, A. Maiti, J. W. Garmon, S. Ganjam, Y. Zhang, J. Claes, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, High-fidelity parametric beamsplitting with a parity- protected converter, Nature Communications14, 5767 (2023). 23

    work page 2023

  58. [58]

    Lambert, E

    N. Lambert, E. Gigu` ere, P. Menczel, B. Li, P. Hopf, G. Su´ arez, M. Gali, J. Lishman, R. Gadhvi, R. Agar- wal,et al., Qutip 5: The quantum toolbox in python, Physics Reports1153, 1 (2026)

    work page 2026

  59. [59]

    Zhang, J

    Y. Zhang, J. C. Curtis, C. S. Wang, R. J. Schoelkopf, and S. M. Girvin, Drive-induced nonlinearities of cavity modes coupled to a transmon ancilla, Physical Review A 105, 022423 (2022)

    work page 2022

  60. [60]

    Krisnanda, H

    T. Krisnanda, H. Xu, S. Ghosh, and T. C. Liew, Tomo- graphic completeness and robustness of quantum reser- voir networks, Physical Review A107, 042402 (2023)

    work page 2023

  61. [61]

    C. Wang, Y. Y. Gao, P. Reinhold, R. W. Heeres, N. Ofek, K. Chou, C. Axline, M. Reagor, J. Blumoff, K. Sliwa, et al., A schr¨ odinger cat living in two boxes, Science352, 1087 (2016)

    work page 2016

  62. [62]

    J. A. Smolin, J. M. Gambetta, and G. Smith, Efficient method for computing the maximum-likelihood quantum state from measurements with additive gaussian noise, Physical review letters108, 070502 (2012)

    work page 2012

  63. [63]

    Blume-Kohout, Optimal, reliable estimation of quan- tum states, New Journal of Physics12, 043034 (2010)

    R. Blume-Kohout, Optimal, reliable estimation of quan- tum states, New Journal of Physics12, 043034 (2010)

    work page 2010

  64. [64]

    J. M. Lukens, K. J. Law, A. Jasra, and P. Lougovski, A practical and efficient approach for bayesian quan- tum state estimation, New Journal of Physics22, 063038 (2020)

    work page 2020

  65. [65]

    F. Yan, S. Gustavsson, J. Bylander, X. Jin, F. Yoshihara, D. G. Cory, Y. Nakamura, T. P. Orlando, and W. D. Oliver, Rotating-frame relaxation as a noise spectrum analyser of a superconducting qubit undergoing driven evolution, Nature communications4, 2337 (2013)

    work page 2013

  66. [66]

    Ithier, E

    G. Ithier, E. Collin, P. Joyez, P. Meeson, D. Vion, D. Es- teve, F. Chiarello, A. Shnirman, Y. Makhlin, J. Schriefl, and G. Sch¨ on, Decoherence in a superconducting quan- tum bit circuit, Physical Review B72, 134519 (2005)

    work page 2005

  67. [67]

    H. Y. Carr and E. M. Purcell, Effects of diffusion on free precession in nuclear magnetic resonance experiments, Physical review94, 630 (1954)

    work page 1954