Pith. sign in

REVIEW 2 major objections 5 minor 83 references

Engineering Nonclassical States via the Dynamical Casimir Effect

T0 review · 2 major / 5 minor · reviewed 2026-07-10 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Optimal drives of a qubit frequency can turn dynamical Casimir photon pairs into high-fidelity Fock, squeezed, and cat cavity states from vacuum.

desk verdict Solid numerical demonstration that hybrid optimal control can turn parametric DCE into a practical resource for high-fidelity cavity Fock, squeezed, and cat states; modeling caveats are real but already flagged and do not sink the claim. read the letter →

arxiv 2607.08275 v1 pith:TVM6FX2I submitted 2026-07-09 quant-ph

Maristella Crotti , Luca Razzoli , Giacomo Guarnieri , Luigi Giannelli , Giuseppe A. Falci , Giuliano Benenti This is my paper · ORCID
classification quant-ph
keywords dynamicalCasimireffectultrastrongcouplingoptimalquantumcontrolnonclassicallightFockstatessqueezedSchrödingercatcircuitQED
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Nonadiabatic driving in ultrastrong light–matter systems is usually treated as an error source because counter-rotating terms turn vacuum fluctuations into real photons (the dynamical Casimir effect). This paper argues the opposite: those same processes can be deliberately shaped into a resource. By modulating only the frequency of a qubit ultrastrongly coupled to a cavity mode, and by designing the modulation with hybrid optimal control (CRAB followed by GRAPE), the authors convert the vacuum into targeted nonclassical cavity states—Fock states up to n=10, squeezed vacua, and Schrödinger-cat superpositions—with high final fidelities and short preparation times set by the strong coupling. The protocols remain usable under moderate classical control noise and weak thermal dissipation, and they operate on nanosecond scales accessible to existing superconducting hardware. If the claim holds, the dynamical Casimir effect becomes a practical tool for on-demand bosonic-state engineering rather than a nuisance to be suppressed.

What carries the argument

Hybrid optimal control of the qubit-frequency drive Ω_D(t): a CRAB Fourier parametrization that yields a smooth, power-constrained guess, refined by amplitude-bounded GRAPE and final interpolation. The objective is final-state fidelity of the reduced cavity state, exploiting parity conservation so that photon pairs generated by counter-rotating terms land in the desired even- or odd-parity target.

What would settle it

Implement the optimized qubit-frequency pulse for |n=6⟩ (or a 3 dB squeezed vacuum) in a circuit-QED device with g/ω_c ≈ 0.3 and measure the cavity Wigner function; if the reconstructed fidelity falls well below the simulated unitary value ~0.99 (or the dissipative value ~0.9 at η=10^{-4}), the modeling premises fail.

Watch

Extended reading notes

Core claim

In a cavity mode ultrastrongly coupled to a frequency-tunable qubit, optimally designed nonadiabatic drives of the qubit frequency can harness the dynamical Casimir effect to deterministically prepare targeted nonclassical cavity states (Fock, squeezed, and Schrödinger-cat superpositions) from vacuum with high fidelity, remaining robust against moderate classical control noise and weak thermal dissipation.

Load-bearing premise

That a pure two-level qubit and a Markovian master equation built from the joint system’s instantaneous eigenstates remain accurate under the strong, broadband, nonadiabatic frequency drives found by the optimizer.

Editorial extensions

If this is right

  • Fock, squeezed, and cat states become preparable on demand in a few nanoseconds, well below typical superconducting gate times.
  • State-preparation steps that currently rely on heralding or multi-gate sequences can be replaced by a single shaped microwave pulse on the qubit.
  • The same control pipeline extends, in principle, to multi-qubit cavity architectures for larger bosonic encodings or reservoir-computing nodes.
  • Control-power constraints can be built into the optimization, making the pulses compatible with existing microwave hardware limits.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because excitations are created in pairs, the same machinery could be retargeted at even-parity logical codes without extra parity-projection steps.
  • The reported speed-up relative to weak-coupling protocols suggests that USC platforms could serve as fast ‘state factories’ feeding slower error-corrected processors.
  • If higher qubit levels prove non-negligible, the same optimal-control loop could be re-run on a multi-level artificial atom to recover fidelity.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The manuscript shows that the dynamical Casimir effect in an ultrastrongly coupled cavity–qubit system can be turned from an error source into a resource for deterministic nonclassical-state preparation. Starting from the vacuum of a driven Rabi Hamiltonian, hybrid CRAB–GRAPE optimal control of the qubit frequency is used to generate high-fidelity Fock states (e.g., F≈0.995 for |n=6⟩ under unitary evolution; average F≳0.96 for n≤10), single-mode squeezed vacua, and Schrödinger-cat superpositions. Performance is quantified via reduced-cavity fidelity, Wigner functions, a control-cost functional C2, and systematic scans versus photon number, squeezing strength, and cat amplitude. Robustness is assessed against additive white/colored control noise and against weak thermal dissipation treated with a time-dependent GKLS master equation built from instantaneous joint eigenstates. Experimental feasibility in circuit QED is argued via order-of-magnitude comparisons with existing microwave control and gate-based preparation times.

Significance. If the numerical results hold under realistic device constraints, the work reframes parametric DCE as a practical tool for ultrafast, on-demand bosonic-state engineering in the USC regime—relevant to continuous-variable encodings, bosonic error correction, and quantum metrology. Strengths include an explicit hybrid optimal-control pipeline (CRAB Fourier ansatz → constrained GRAPE → smoothing), parity-consistent target embedding, direct Wigner-function validation, scaling studies over n, r_dB, and α, and systematic classical- and quantum-noise scans. The control-cost functional C2 and amplitude-constrained refinement provide a concrete handle on energetic resources. Within the driven Rabi model the demonstration is reproducible in principle and free of circular target definitions.

major comments (2)
  1. [Model / SM §S4] Model, Eqs. (1)–(2) and SM §S4: The optimized drives reach amplitudes of order ωc with broadband content (Nf=20, κ∼2–3). Flux-qubit platforms cited for experimental feasibility have higher levels that become relevant under such strong, nonadiabatic frequency modulation. The central claim of high-fidelity preparation and the reported two-order-of-magnitude speedup relative to Jaynes–Cummings gate sequences rest on the pure two-level Rabi model remaining quantitatively accurate. A quantitative estimate (or literature bound) of leakage out of the computational subspace under the reported pulse amplitudes and bandwidths is needed to underwrite the experimental conclusions; without it the feasibility argument remains qualitative.
  2. [Robustness against noise / Eq. (5) / SM §S3] Eq. (5) and SM §S3: The open-system treatment employs a time-dependent GKLS equation whose Lindblad operators are built from instantaneous eigenstates of HS(t). Standard derivations of such master equations assume weak coupling and sufficiently slow variation of the system Hamiltonian relative to bath correlation times. The optimized DCE protocols are strongly nonadiabatic by design (T∼20τs with large ΩD). The robustness claims (F≳0.9 at η=10−4; Wigner function in Fig. 2e) therefore inherit an unquantified modeling uncertainty. The manuscript should either justify the instantaneous-eigenstate Markovian form for these drive rates (e.g., via adiabaticity parameters or references) or clearly delimit the fidelity results as conditional on that approximation.
minor comments (5)
  1. [Optimal control strategy] Optimal control strategy section: typographical duplication “minimize the the cost function”.
  2. [Throughout] Throughout: inconsistent spacing/encoding of “Schrödinger” (e.g., “Schr¨ odinger”) and similar diacritics; clean for production.
  3. [Fig. 2 / Fig. 5] Fig. 2 and End Matter figures: color-bar ranges for Wigner functions differ slightly between target and prepared panels; a common scale would ease visual comparison of residual error.
  4. [SM §S1] SM §S1: CRAB fidelity is defined on the reduced cavity state while GRAPE optimizes a full bipartite overlap with a parity-selected product target. The main text already notes consistency of reported fidelities; a one-sentence reminder near Eq. (S4)–(S7) would help readers who skip the SM.
  5. [SM §S4 / Conclusions] SM §S4: the numerical speedup comparison (∼2.54 ns vs ∼190 ns for |n=6⟩) is useful; stating the cavity frequency assumed for the conversion of τs into nanoseconds in the main text (or a footnote) would make the claim self-contained.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: numerical optimal-control maximization of fidelity to independent external target states under a fixed Hamiltonian.

full rationale

The paper's central results are obtained by hybrid CRAB+GRAPE numerical maximization of the fidelity of the reduced cavity state to externally defined target states (Fock |n>, single-mode squeezed vacuum S(r, heta)|0>, and the cat superposition of Eq. (B4)). The targets are standard textbook states, not quantities defined by or fitted from the control pulses. The system Hamiltonian (Rabi + drive, Eqs. (1)–(2)) and the cost C=1-F are fixed a priori; the optimization merely searches for drives that achieve high F under those dynamics. Hyperparameters (Nf, T, P, amplitude bounds) shape the search landscape but do not force the reported fidelities by construction. Self-citations (e.g., prior DCE optimal-control work [19] and the cost functional reference [58]) supply background methods or metrics and are not load-bearing uniqueness theorems or ansätze that reduce the main claim to an input. Parity conservation, Wigner-function agreement, and noise scans are independent consistency checks, not circular redefinitions. The derivation chain is therefore self-contained numerical demonstration, not circular.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard quantum optics (Rabi model, DCE from counter-rotating terms, parity conservation), standard optimal-control algorithms (CRAB, GRAPE), and a standard weak-coupling Markovian open-system model. No new particles or forces are introduced. Free parameters are protocol and model choices (coupling, times, Fourier content, power bounds, bath parameters) selected to demonstrate high fidelity rather than fitted to experimental data. Invented entities are absent; the contribution is a control protocol and numerical demonstration.

free parameters (6)
  • g/ωc (light–matter coupling ratio)
    Chosen in the USC regime (e.g. 0.3, also scanned at 0.6 in SM); sets the characteristic time τs=π/2g and the strength of counter-rotating photon generation. Not fitted to data; hand-selected for demonstration.
  • Protocol duration T (in units of τs)
    Main results use T=20τs after SM landscape scan; longer T improves fidelity at higher control cost. Hand-chosen compromise, not data-fitted.
  • Number of CRAB harmonics Nf and frequency bandwidth κ
    Nf≈20 and κ≈2–3 selected after systematic scans (SM §S2) to balance expressivity and convergence; free design parameters of the control ansatz.
  • Total control power proxy P and GRAPE amplitude bounds
    P and Ωmin/Ωmax constrain realistic drives; best CRAB seeds with moderate P are refined under bounds. Chosen for physical realism, not fitted to experiment.
  • Bath parameters η, ωB/ωc, βωc
    Open-system robustness uses η~10^{-4}, ωB/ωc=10, βωc=5 as representative superconducting-device values; illustrative, not fitted to a specific device dataset in the paper.
  • ωq/ωc (qubit–cavity detuning)
    Main figures use ωq/ωc=2 (off-resonant USC); a free model choice affecting the control landscape.
assumptions (5)
  • domain assumption The cavity–qubit system is accurately described by the driven quantum Rabi Hamiltonian with a two-level qubit and a single bosonic mode, including counter-rotating terms that enable parametric DCE.
    Invoked in Model section, Eqs. (1)–(2); underpins all unitary and open-system simulations.
  • standard math Total excitation parity Π=exp(iπ n_ex) is conserved, so targets must lie in the even-parity subspace consistent with the initial |0⟩|g⟩ state.
    Used to embed GRAPE targets (SM §S1.B, Eq. (S7)); standard for the Rabi model with σz drive.
  • domain assumption CRAB (truncated random Fourier basis + derivative-free optimization) and GRAPE (piecewise-constant controls + analytic gradients) can find high-fidelity open-loop controls for this landscape.
    Methodological premise of Optimal control strategy and SM §S1; standard in quantum optimal control but not a guarantee of global optimality.
  • domain assumption Open-system dynamics under weak system–bath coupling and Markovian conditions are described by a time-dependent GKLS master equation with Lindblad operators from instantaneous eigenstates and Ohmic J(ω).
    Eq. (5) and SM §S3; used for robustness claims in Fig. 4(b) and Fig. 2(e).
  • domain assumption Microwave control technology can implement the optimized ΩD(t) amplitudes and timescales while preserving an effective two-level qubit and USC coupling.
    SM §S4 experimental feasibility discussion; supports the claim of practical relevance but is not demonstrated in this work.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Engineering Nonclassical States via the Dynamical Casimir Effect." pith.science (2026). https://pith.science/paper/TVM6FX2I

@misc{pith2026260708275,
  author       = {Pith},
  title        = {Pith review of: Engineering Nonclassical States via the Dynamical Casimir Effect},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TVM6FX2I}},
  note         = {Machine review of arXiv:2607.08275}
}
read the original abstract

Nonadiabatic driving in ultrastrongly coupled light--matter systems is commonly regarded as a source of errors, as counter-rotating interactions convert vacuum fluctuations into real excitations through the dynamical Casimir effect (DCE). Here we show that, instead, the DCE can be harnessed as a resource for engineering nonclassical states of light. Considering a cavity mode ultrastrongly coupled to a frequency-tunable qubit, we employ optimal quantum control to design driving protocols that convert vacuum fluctuations into targeted states. Numerical optimization reveals a versatile and robust approach for the deterministic preparation of a broad class of nonclassical states, illustrated here through Fock states, squeezed states, and Schr\"odinger-cat-state superpositions.

Figures

Figures reproduced from arXiv: 2607.08275 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic representation of a single-mode cavity of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Optimal control strategy for the generation of the Fock state [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Performance scaling of Fock-state generation with [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Optimal control strategy for the generation of squeezed and cat states. (a, b) Optimized control drives Ω [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Performance scaling of squeezed and cat-state generation. (a, b) Squeezed-vacuum state generation as a function of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

83 extracted references · 83 canonical work pages

  1. [1]

    QUANTUM”. L.R. acknowledges support from University of Pavia through the project “Termodinamica di precisione per sistemi aperti quantistici

    System and control parameters areg/ω c = 0.3,T= 20τ s ≡20π/2g,ω q/ωc = 2 (corresponding to the off-resonance regime|ω c −ω q| ≫g), andN f = 20. The number of time intervals for the GRAPE refinement isN t = 300. Environmental parameters areω B/ωc = 10,β ω c = 5, andη= 10 −4 (see sectionRobustness against noisefor details). nonclassical Fock state withn= 6 ...

    work page 2024

  2. [2]

    M. A. Nielsen and I. L. Chuang,Quantum Computa- tion and Quantum Information: 10th Anniversary Edi- tion(Cambridge University Press, 2010)

    work page 2010

  3. [3]

    Benenti, G

    G. Benenti, G. Casati, D. Rossini, and G. Strini,Princi- ples of Quantum Computation and Information, 2nd ed. (World Scientific, Singapore, 2018)

    work page 2018

  4. [4]

    Walls and G

    D. Walls and G. J. Milburn, Generation and applications of squeezed light, inQuantum Optics, edited by D. Walls and G. J. Milburn (Springer Berlin Heidelberg, Berlin, Heidelberg, 2008) pp. 143–175

    work page 2008

  5. [5]

    Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, Shortcuts to adiabaticity for the quantum rabi model: Efficient generation of giant entangled cat states via parametric amplification, Phys. Rev. Lett.126, 023602 (2021)

    work page 2021

  6. [6]

    Aasiet al., Enhanced sensitivity of the ligo gravita- tional wave detector by using squeezed states of light, Nature Photonics7, 613 (2013)

    J. Aasiet al., Enhanced sensitivity of the ligo gravita- tional wave detector by using squeezed states of light, Nature Photonics7, 613 (2013)

    work page 2013

  7. [7]

    Descamps, A

    E. Descamps, A. Saharyan, A. Chivet, A. Keller, and P. Milman, Unified framework for bosonic quantum in- formation encoding, resources, and universality from su- perselection rules, Optica Quantum4, 148 (2026)

    work page 2026

  8. [8]

    Kurman, K

    Y. Kurman, K. Hymas, A. Fedorov, W. J. Munro, and J. Quach, Powering quantum computation with quantum batteries, Phys. Rev. X16, 011016 (2026)

    work page 2026

Show all 83 references
  1. [9]

    M. H. Michael, M. Silveri, R. T. Brierley, V. V. Albert, J. Salmilehto, L. Jiang, and S. M. Girvin, New class of quantum error-correcting codes for a bosonic mode, Phys. Rev. X6, 031006 (2016)

    2016

  2. [10]

    Y.-H. Chen, W. Qin, R. Stassi, X. Wang, and F. Nori, Fast binomial-code holonomic quantum computation with ultrastrong light-matter coupling, Phys. Rev. Res. 3, 033275 (2021)

    2021

  3. [11]

    Leghtas, G

    Z. Leghtas, G. Kirchmair, B. Vlastakis, R. J. Schoelkopf, M. H. Devoret, and M. Mirrahimi, Hardware-efficient au- tonomous quantum memory protection, Phys. Rev. Lett. 111, 120501 (2013)

    2013

  4. [12]

    N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Ex- tending the lifetime of a quantum bit with error correc- tion in superconducting circuits, Nature536, 441 (2016)

    2016

  5. [13]

    Beaudoin, J

    F. Beaudoin, J. M. Gambetta, and A. Blais, Dissipation and ultrastrong coupling in circuit QED, Phys. Rev. A 84, 043832 (2011)

    2011

  6. [14]

    Frisk Kockum, A

    A. Frisk Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, Ultrastrong coupling between light and matter, Nature Reviews Physics1, 19 (2019)

    2019

  7. [15]

    Forn-D´ ıaz, L

    P. Forn-D´ ıaz, L. Lamata, E. Rico, J. Kono, and E. Solano, Ultrastrong coupling regimes of light-matter interaction, Rev. Mod. Phys.91, 025005 (2019)

    2019

  8. [16]

    G. T. Moore, Quantum theory of the electromagnetic field in a variable-length one-dimensional cavity, Journal of Mathematical Physics11, 2679 (1970)

    1970

  9. [17]

    V. V. Dodonov, Current status of the dynamical casimir effect, Physica Scripta82, 038105 (2010)

    2010

  10. [18]

    C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Observation of the dynamical casimir effect in a superconducting circuit, Nature479, 376 (2011)

    2011

  11. [19]

    P. D. Nation, J. R. Johansson, M. P. Blencowe, and 6 F. Nori, Colloquium: Stimulating uncertainty: Amplify- ing the quantum vacuum with superconducting circuits, Rev. Mod. Phys.84, 1 (2012)

    2012

  12. [20]

    F. Hoeb, F. Angaroni, J. Zoller, T. Calarco, G. Strini, S. Montangero, and G. Benenti, Amplification of the parametric dynamical casimir effect via optimal control, Phys. Rev. A96, 033851 (2017)

    2017

  13. [21]

    Benenti, A

    G. Benenti, A. D’Arrigo, S. Siccardi, and G. Strini, Dy- namical casimir effect in quantum-information process- ing, Phys. Rev. A90, 052313 (2014)

    2014

  14. [22]

    Felicetti, M

    S. Felicetti, M. Sanz, L. Lamata, G. Romero, G. Johans- son, P. Delsing, and E. Solano, Dynamical casimir effect entangles artificial atoms, Phys. Rev. Lett.113, 093602 (2014)

    2014

  15. [23]

    C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Fil- ipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte- Herbr¨ uggen, D. Sugny, and F. K. Wilhelm, Quantum op- timal control in quantum technologies. Strategic report on current status, visions and goals for research in Eu...

    2022

  16. [26]

    Khaneja, T

    N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbr¨ uggen, and S. J. Glaser, Optimal control of coupled spin dy- namics: design of nmr pulse sequences by gradient as- cent algorithms, Journal of Magnetic Resonance172, 296 (2005)

    2005

  17. [27]

    Haroche and J.-M

    S. Haroche and J.-M. Raimond,Exploring the Quantum: Atoms, Cavities, and Photons(Oxford University Press, 2006)

    2006

  18. [28]

    Filipowicz, J

    P. Filipowicz, J. Javanainen, and P. Meystre, Quantum and semiclassical steady states of a kicked cavity mode, J. Opt. Soc. Am. B3, 906 (1986)

    1986

  19. [29]

    Braak, Integrability of the Rabi model, Phys

    D. Braak, Integrability of the Rabi model, Phys. Rev. Lett.107, 100401 (2011)

    2011

  20. [30]

    Q. Xie, H. Zhong, M. T. Batchelor, and C. Lee, The quantum rabi model: solution and dynamics, Journal of Physics A: Mathematical and Theoretical50, 113001 (2017)

    2017

  21. [31]

    Dodonov, Fifty years of the dynamical casimir effect, Physics2, 67 (2020)

    V. Dodonov, Fifty years of the dynamical casimir effect, Physics2, 67 (2020)

    2020

  22. [32]

    In this work, we consider theparametricDCE, where photons are generated through the parametric amplifica- tion of vacuum fluctuations without moving or changing the boundaries [16]

  23. [33]

    Braak, Symmetries in the quantum rabi model, Sym- metry11, 1259 (2019)

    D. Braak, Symmetries in the quantum rabi model, Sym- metry11, 1259 (2019)

    2019

  24. [34]

    Further details on the specific fidelity definitions used—which depend on the adopted optimal control technique—are provided in the Supplemental Material (SM)

  25. [35]

    Zheng, S

    Y. Zheng, S. Campbell, G. De Chiara, and D. Poletti, Cost of counterdiabatic driving and work output, Phys. Rev. A94, 042132 (2016)

    2016

  26. [36]

    Campbell and S

    S. Campbell and S. Deffner, Trade-off between speed and cost in shortcuts to adiabaticity, Phys. Rev. Lett.118, 100601 (2017)

    2017

  27. [37]

    See [58] for the use of this metric beyond the counterdiabatic-driving regime

  28. [38]

    The timescaleτ s corresponds to the time required to perform half a vacuum Rabi oscillation in the reso- nant (ω q =ω c) Jaynes-Cummings limit [i.e., neglecting counter-rotating terms in the Rabi Hamiltonian (1)]

  29. [39]

    Depending on the specific experimental constraints, the fidelityF≈0.995 can be further enhanced up to≈0.999 by permitting larger control amplitudes (see SM)

  30. [41]

    Lindblad, On the generators of quantum dynamical semigroups, Communications in Mathematical Physics 48, 119 (1976)

    G. Lindblad, On the generators of quantum dynamical semigroups, Communications in Mathematical Physics 48, 119 (1976)

    1976

  31. [45]

    Deng, J.-L

    C. Deng, J.-L. Orgiazzi, F. Shen, S. Ashhab, and A. Lu- pascu, Observation of floquet states in a strongly driven artificial atom, Phys. Rev. Lett.115, 133601 (2015)

    2015

  32. [46]

    Niemczyk, F

    T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. H¨ ummer, E. Solano, A. Marx, and R. Gross, Circuit quantum electrodynamics in the ultrastrong-coupling regime, Nature Physics6, 772 (2010)

    2010

  33. [47]

    J. M. Fink, M. G¨ oppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, Climbing the Jaynes– Cummings ladder and observing its nonlinearity in a cav- ity QED system, Nature454, 315 (2008)

    2008

  34. [48]

    Yoshikawa, K

    J.-i. Yoshikawa, K. Makino, S. Kurata, P. van Loock, and A. Furusawa, Creation, storage, and on-demand release of optical quantum states with a negative wigner func- tion, Phys. Rev. X3, 041028 (2013)

    2013

  35. [49]

    Lau and M

    H.-K. Lau and M. B. Plenio, Universal quantum comput- ing with arbitrary continuous-variable encoding, Phys. Rev. Lett.117, 100501 (2016)

    2016

  36. [50]

    J. Lee, N. Kang, S.-H. Lee, H. Jeong, L. Jiang, and S.- W. Lee, Fault-tolerant quantum computation by hybrid qubits with bosonic cat code and single photons, PRX Quantum5, 030322 (2024)

    2024

  37. [51]

    Q. Xu, G. Zheng, Y.-X. Wang, P. Zoller, A. A. Clerk, and L. Jiang, Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits, npj Quantum Information9, 78 (2023)

    2023

  38. [52]

    Paparelle, F

    I. Paparelle, F. Mousavi, F. Scazza, A. Bassi, M. Paris, and A. Zavatta, Experimental direct quantum commu- nication with squeezed states, Opt. Express33, 28917 (2025)

    2025

  39. [53]

    Reiserer and G

    A. Reiserer and G. Rempe, Cavity-based quantum net- works with single atoms and optical photons, Rev. Mod. Phys.87, 1379 (2015)

    2015

  40. [54]

    Schnabel, Squeezed states of light and their appli- cations in laser interferometers, Physics Reports684, 1 (2017)

    R. Schnabel, Squeezed states of light and their appli- cations in laser interferometers, Physics Reports684, 1 (2017)

    2017

  41. [55]

    Mart´ ınez-Pe˜ na, J

    R. Mart´ ınez-Pe˜ na, J. Nokkala, G. L. Giorgi, R. Zambrini, and M. C. Soriano, Information processing capacity of spin-based quantum reservoir computing systems, Cog- 7 nitive Computation15, 1440 (2023)

    2023

  42. [56]

    Sannia, R

    A. Sannia, R. Mart´ ınez-Pe˜ na, M. C. Soriano, G. L. Giorgi, and R. Zambrini, Dissipation as a resource for Quantum Reservoir Computing, Quantum8, 1291 (2024)

    2024

  43. [57]

    C. Zhu, P. J. Ehlers, H. I. Nurdin, and D. Soh, Minimal- istic and scalable quantum reservoir computing enhanced with feedback, npj Quantum Information11, 195 (2025)

    2025

  44. [58]

    S. Das, G. L. Giorgi, and R. Zambrini, Quantum reser- voir computing in Jaynes-Cummings models: Nonlinear memory and time-series prediction, Phys. Rev. Res.8, 023148 (2026)

    2026

  45. [59]

    Tumbiolo, L

    E. Tumbiolo, L. Maccone, C. Macchiavello, M. G. A. Paris, and G. Guarnieri, Shake before use: Universal en- hancement of quantum thermometry by unitary driving, Phys. Rev. Lett. (2026)

    2026

  46. [60]

    Vahlbruch, M

    H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schn- abel, Detection of 15 db squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency, Phys. Rev. Lett.117, 110801 (2016)

    2016

  47. [61]

    Dassonneville, R

    R. Dassonneville, R. Assouly, T. Peronnin, A. Clerk, A. Bienfait, and B. Huard, Dissipative stabilization of squeezing beyond 3 db in a microwave mode, PRX Quan- tum2, 020323 (2021)

    2021

  48. [62]

    Eickbusch, V

    A. Eickbusch, V. Sivak, A. Z. Ding, S. S. Elder, S. R. Jha, J. Venkatraman, B. Royer, S. M. Girvin, R. J. Schoelkopf, and M. H. Devoret, Fast universal control of an oscillator with weak dispersive coupling to a qubit, Nature Physics 18, 1464 (2022)

    2022

  49. [63]

    Engineering Nonclassical States via the Dynamical Casimir Effect

    Y. Cai, X. Deng, L. Zhang, Z. Ni, J. Mai, P. Huang, P. Zheng, L. Hu, S. Liu, Y. Xu, and D. Yu, Quantum squeezing amplification with a weak kerr nonlinear oscil- lator, Nature Communications17, 970 (2025). 8 END MA TTER Appendix A: Squeezed state generation.—To illustrate how o...

    2025

  50. [64]

    Caneva, T

    T. Caneva, T. Calarco, and S. Montangero, Chopped random-basis quantum optimization, Phys. Rev. A84, 022326 (2011)

    2011

  51. [65]

    M. M. M¨ uller, R. S. Said, F. Jelezko, T. Calarco, and S. Montangero, One decade of quantum optimal control in the chopped random basis, Reports on Progress in Physics85, 076001 (2022)

    2022

  52. [66]

    Khaneja, T

    N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbr¨ uggen, and S. J. Glaser, Optimal control of coupled spin dynamics: design of nmr pulse sequences by gradient ascent algorithms, Journal of Magnetic Resonance172, 296 (2005)

    2005

  53. [67]

    J. R. Johansson, P. D. Nation, and F. Nori, QuTiP: An open-source Python framework for the dynamics of open quantum systems, Computer Physics Communications183, 1760 (2012)

    2012

  54. [68]

    J. R. Johansson, P. D. Nation, and F. Nori, QuTiP 2: A Python framework for the dynamics of open quantum systems, Computer Physics Communications184, 1234 (2013)

    2013

  55. [69]

    Gao and L

    F. Gao and L. Han, Implementing the nelder-mead simplex algorithm with adaptive parameters, Computational Opti- mization and Applications51, 259 (2012)

    2012

  56. [70]

    Virtanen, R

    P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, ˙I. Polat, Y. Feng...

    2020

  57. [71]

    R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, A limited memory algorithm for bound constrained optimization, SIAM Journal on Scientific Computing16, 1190 (1995)

    1995

  58. [72]

    M. O. Scully and M. S. Zubairy,Quantum Optics(Cambridge University Press, 1997)

    1997

  59. [73]

    Carrega, L

    M. Carrega, L. Razzoli, P. A. Erdman, F. Cavaliere, G. Benenti, and M. Sassetti, Dissipation-induced collective advantage of a quantum thermal machine, AVS Quantum Science6, 025001 (2024)

    2024

  60. [74]

    Breuer and F

    H.-P. Breuer and F. Petruccione,The Theory of Open Quantum Systems(Oxford University Press, 2007)

    2007

  61. [75]

    Manzano, A short introduction to the Lindblad master equation, AIP Advances10, 025106 (2020)

    D. Manzano, A short introduction to the Lindblad master equation, AIP Advances10, 025106 (2020)

    2020

  62. [76]

    Campaioli, J

    F. Campaioli, J. H. Cole, and H. Hapuarachchi, Quantum master equations: Tips and tricks for quantum optics, quantum computing, and beyond, PRX Quantum5, 020202 (2024)

    2024

  63. [77]

    Vacchini,Open Quantum Systems: Foundations and Theory, 1st ed., Graduate Texts in Physics (Springer, Cham, 2024)

    B. Vacchini,Open Quantum Systems: Foundations and Theory, 1st ed., Graduate Texts in Physics (Springer, Cham, 2024)

    2024

  64. [78]

    Kossakowski, On quantum statistical mechanics of non-Hamiltonian systems, Reports on Mathematical Physics3, 247 (1972)

    A. Kossakowski, On quantum statistical mechanics of non-Hamiltonian systems, Reports on Mathematical Physics3, 247 (1972)

    1972

  65. [79]

    Lindblad, On the generators of quantum dynamical semigroups, Communications in Mathematical Physics48, 119 (1976)

    G. Lindblad, On the generators of quantum dynamical semigroups, Communications in Mathematical Physics48, 119 (1976)

    1976

  66. [80]

    Gorini, A

    V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups ofN-level systems, Journal of Mathematical Physics17, 821 (1976)

    1976

  67. [81]

    Yoshihara, T

    F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime, Nature Physics13, 44 (2017)

    2017

  68. [82]

    Yoshihara, T

    F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong- to the deep-strong-coupling regime, Phys. Rev. A95, 053824 (2017)

    2017

  69. [83]

    Deng, J.-L

    C. Deng, J.-L. Orgiazzi, F. Shen, S. Ashhab, and A. Lupascu, Observation of floquet states in a strongly driven artificial atom, Phys. Rev. Lett.115, 133601 (2015)

    2015

  70. [84]

    Hofheinz, E

    M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, Generation of fock states in a superconducting quantum circuit, Nature454, 310 (2008)

    2008

  71. [85]

    Kjaergaard, M

    M. Kjaergaard, M. E. Schwartz, J. Braum¨ uller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver, Superconducting qubits: Current state of play, Annual Review of Condensed Matter Physics11, 369 (2020)

    2020

  72. [86]

    Krantz, M

    P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A quantum engineer’s guide to superconducting qubits, Applied Physics Reviews6, 021318 (2019)

    2019

  73. [87]

    Leghtas, G

    Z. Leghtas, G. Kirchmair, B. Vlastakis, R. J. Schoelkopf, M. H. Devoret, and M. Mirrahimi, Hardware-efficient autonomous quantum memory protection, Phys. Rev. Lett.111, 120501 (2013)

    2013

  74. [88]

    Niemczyk, F

    T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. H¨ ummer, E. Solano, A. Marx, and R. Gross, Circuit quantum electrodynamics in the ultrastrong-coupling regime, Nature Physics 6, 772 (2010)

    2010

  75. [89]

    J. M. Fink, M. G¨ oppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system, Nature454, 315 (2008)

    2008

Pith tools

Reviewed July 10, 2026 · model on record in the stance chip above.