Pith. sign in

REVIEW 2 major objections 5 minor 75 references

The Lindblad master equation for driven open quantum systems only yields physical relaxation when collapse operators are written in the right basis.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · grok-4.5

2026-07-12 00:00 UTC pith:I6J6IRPX

load-bearing objection Careful pedagogical comparison of bases for driven GKSL dynamics; solid math and clear figures, but incremental rather than new theory. the 2 major comments →

arxiv 2607.03779 v1 pith:I6J6IRPX submitted 2026-07-04 quant-ph

Gorini-Kossakowski-Sudarshan-Lindblad equation in different bases: application to driven-dissipative two- and multilevel systems

O. A. Ilinskaya , O. V. Ivakhnenko , A. I. Ryzhov , O. Yu. Kitsenko , S. N. Shevchenko This is my paper
classification quant-ph PACS 03.65.Yz03.67.Lx42.50.Lc
keywords open quantum systemsLindblad equationdriven-dissipative dynamicsbasis choiceinstantaneous eigenbasisFloquet statesqubit interferometryqudit
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper revisits how open quantum systems are described by the Gorini–Kossakowski–Sudarshan–Lindblad master equation when the system Hamiltonian is driven in time. The central claim is that the basis in which the collapse (Lindblad) operators are defined is not optional: operators written in the diabatic or static eigenbasis produce unphysical relaxation that can reverse direction across an avoided crossing, while the instantaneous eigenbasis (adiabatic driving) or Floquet basis (periodic driving) restores the correct energy-lowering dynamics. The authors systematically transform the same master equation among diabatic, static, instantaneous, superadiabatic and Floquet bases, compute both time-dependent occupation probabilities and time-averaged interferograms for a driven qubit, and extend the same procedure to a pair of coupled qubits. The practical payoff is that theorists obtain consistent numerics and experimentalists gain a route to engineer the desired dissipative evolution simply by choosing the representation.

Core claim

For a driven-dissipative qubit or qudit the GKSL equation yields physically correct relaxation and dephasing only when the Lindblad operators are defined in a basis that respects the instantaneous energy ordering—most commonly the instantaneous eigenbasis in the adiabatic regime or the Floquet basis under strong periodic drive—rather than in the diabatic or static eigenbasis that is often used by default.

What carries the argument

Unitary transfer matrices that map both the system Hamiltonian and the collapse operators between diabatic, static, instantaneous, superadiabatic and Floquet bases while preserving the Lindblad form of the dissipator; the resulting Berry-connection terms appear automatically once the transformation is performed correctly.

Load-bearing premise

The same Born–Markov and secular approximations that justify the Lindblad equation for a static Hamiltonian remain valid once the Hamiltonian becomes time-dependent, so that only a change of basis for the collapse operators is required.

What would settle it

Simulate or measure a driven qubit that is swept repeatedly through an avoided crossing with finite relaxation rate; if the population of the higher-energy instantaneous eigenstate grows rather than decays when collapse operators are written in the diabatic basis, the paper’s claim is confirmed; if the population always decays regardless of basis, the claim fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Interferograms and steady-state occupation maps computed in the wrong basis will show spurious resonances or inverted populations and must be recomputed after a proper basis change.
  • Counter-diabatic or superadiabatic protocols can be combined with dissipation only after the collapse operators have been transformed into the corresponding superadiabatic frame.
  • For multilevel systems the same unitary maps allow one to keep relaxation operators that lower energy while still writing the coherent drive in the laboratory diabatic basis.
  • Experimental control sequences can deliberately switch bases so that the same physical bath produces different effective dissipative channels.

Where Pith is reading between the lines

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

  • The same basis-consistency requirement should appear in any Markovian master equation derived under the secular approximation, not only in the GKSL form treated here.
  • Numerical packages that hard-code collapse operators in a fixed computational basis risk silent errors whenever the user supplies a time-dependent Hamiltonian that crosses levels.
  • Once the transfer matrices are automated, basis choice itself becomes a design degree of freedom for open-system quantum control.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The manuscript revisits the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equation for driven-dissipative systems, stressing that the Hamiltonian, density operator and Lindblad operators must be expressed in one consistent basis. It systematically reviews the diabatic, static-eigenstate, instantaneous (adiabatic), first superadiabatic and Floquet bases for a driven qubit (Hamiltonian (3)–(4)), supplies the unitary transfer matrices (Eqs. (14)–(22), (39), (D5)), includes the Berry-connection term that appears under a time-dependent change of frame, and extends the construction to multilevel systems (Sec. V). Numerical dynamics and time-averaged interferograms (Figs. 2–4) illustrate that Lindblad operators written in the diabatic or static basis reverse the physical direction of relaxation across an avoided crossing, while the instantaneous eigenbasis (adiabatic regime) or Floquet basis (periodic drive) restores correct relaxation and clean resonance patterns.

Significance. The central technical point—that collapse operators must track the instantaneous energy ordering (or Floquet states)—is already known in the literature, yet the paper supplies a self-contained, explicit set of transfer rules, adiabatic conditions (App. C) and side-by-side numerical comparisons that make the issue transparent for practitioners. The unitary transformations are algebraically correct, the free parameters (Γ₁, Γ_ϕ, A, ω) are simulation inputs rather than fitted quantities, and the multilevel formulas of Sec. V are immediately usable. These features give the work clear pedagogical and practical value for quantum-control and open-system simulation communities, even if the underlying physics is not new.

major comments (2)
  1. Section IV and the captions of Figs. 2–3 (fifth column): the Lindblad operators employed in the Floquet basis are simply stated to be σ_x (relaxation) and σ_z (dephasing) with a citation to QuTiP, without a derivation or mapping from the instantaneous operators used for the other bases (cf. Eqs. (2), (21)–(22)). Because the paper’s claim rests on a consistent, basis-independent definition of the dissipator, this ad-hoc choice should be justified or replaced by an explicit transformation so that the Floquet column can be compared on equal footing.
  2. Appendix A versus Appendix C and Sec. II: the microscopic derivation is given only for a time-independent system Hamiltonian; the subsequent claim that the same Born–Markov–secular approximations remain valid once the collapse operators are unitarily transformed to the instantaneous frame is asserted rather than re-derived. While this is standard practice (Albash et al., Yamaguchi et al.), a short explicit statement of the additional adiabatic conditions under which the time-dependent Lindblad form is recovered would close the logical gap for readers who start from the microscopic route.
minor comments (5)
  1. Fig. 1 and its caption: the moment t₀ = π/(2ω) and the value a = 1 are chosen for illustration, yet the caption does not remind the reader that a ≳ 1 already lies outside the regime of validity of the first superadiabatic basis; a brief note would prevent misinterpretation of the red/orange curves.
  2. Fig. 2(o) and Fig. 3(o): the driving frequency is lowered relative to the rest of the third row so that the superadiabatic basis remains applicable; this is explained in the caption, but a corresponding remark in the main text (Sec. IV) would make the comparison across columns more transparent.
  3. Notation: ℏ is restored in the main text but set to 1 throughout Appendices A–D; a single sentence at the beginning of the appendices would avoid confusion when readers move between sections.
  4. Table I is a useful summary; adding a column that lists the typical regime of validity (already stated in the text) would make the table self-contained.
  5. Sec. V, Eqs. (45)–(46): the assumption that both qubits couple to independent baths with identical rates is reasonable for the illustration, but a parenthetical remark that the same transfer procedure applies to correlated baths would broaden the utility of the multilevel formulas.

Circularity Check

0 steps flagged

No significant circularity: basis transformations and dynamics follow by definition from eigenvectors and standard GKSL form; rates and drives are free inputs, not fitted predictions.

full rationale

The paper's central claim is that Lindblad operators and the Hamiltonian must be expressed in a single consistent basis (instantaneous eigenbasis for adiabatic driving, Floquet for strong periodic drive, etc.), otherwise relaxation can reverse direction across an avoided crossing. All transfer matrices (S(t), Ũ(t), U1(t), Usort, etc.) are constructed directly from the eigenvectors of the instantaneous or superadiabatic Hamiltonians by definition (Eqs. 12–15, 25, D1–D5, 34–39). The microscopic and CPTP derivations of the GKSL equation (Appendices A–B) follow the standard literature (Breuer–Petruccione, Pearle) under the usual Born–Markov–secular assumptions; the adiabatic conditions (Appendix C) are likewise textbook. Numerical dynamics and interferograms (Figs. 2–4) use free input parameters Γ1, Γϕ, A, ω, ε0 with no fitting to data that is later re-presented as a prediction. Self-citations (e.g., [8], [39], [40]) supply examples or related context but are not load-bearing for any uniqueness claim or uniqueness theorem. No ansatz is smuggled via citation, no known empirical pattern is merely renamed, and no quantity is defined in terms of the result it is said to predict. The derivation chain is therefore self-contained and non-circular.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The central claim rests entirely on standard open-quantum-system axioms (Born-Markov, secular approximation, complete positivity) plus the mathematical definition of instantaneous eigenvectors. No free parameters are fitted to experimental data; simulation rates are chosen for illustration. No new physical entities are postulated.

free parameters (2)
  • relaxation and dephasing rates Γ1, Γϕ (and Γ2)
    Chosen by hand for the numerical examples in Figs. 2–4; not derived or fitted to data, but the qualitative conclusions depend on them being positive and of comparable magnitude to the driving.
  • driving amplitude A and frequency ω (parameter a = Aℏω/Δ²)
    Free simulation parameters that select adiabatic versus diabatic regimes; the paper’s claim that different bases are optimal in different regimes is illustrated by scanning these values.
axioms (3)
  • domain assumption Born-Markov and secular (rotating-wave) approximations remain valid for a slowly time-dependent system Hamiltonian, yielding a GKSL equation with time-dependent Lindblad operators written in the instantaneous eigenbasis.
    Invoked throughout Sec. II and Appendix A; without it the master equation itself is not of Lindblad form.
  • domain assumption The system-bath interaction is weak enough that the bath remains in thermal equilibrium and the reduced dynamics is completely positive and trace-preserving.
    Standard microscopic derivation (Appendix A); required for the existence of the Lindblad operators L_k.
  • standard math Unitary transformations between orthonormal bases preserve the Lindblad form of the dissipator (Eq. 40).
    Used to move operators between diabatic and instantaneous bases (Secs. III–V).

pith-pipeline@v1.1.0-grok45 · 25959 in / 2427 out tokens · 23357 ms · 2026-07-12T00:00:02.700777+00:00 · methodology

0 comments
read the original abstract

An open quantum system can be described by a master equation, of which one of the most popular is the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. We revisit description of driven-dissipative quantum systems focusing on the appropriate choice of the system's basis and the respective transformations. We consider the GKSL equation in different bases and calculate the dynamics for a qubit and for a qudit. An appropriate choice of the basis is a fundamental problem for theoretical consideration of open quantum systems and provides an opportunity to obtain the desired evolution in practice.

Figures

Figures reproduced from arXiv: 2607.03779 by A. I. Ryzhov, O. A. Ilinskaya, O. V. Ivakhnenko, O. Yu. Kitsenko, S. N. Shevchenko.

Figure 1
Figure 1. Figure 1: FIG. 1. The energy levels of a qubit as functions of the en [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of the dynamics of the upper energy level occupation probability for different driving frequencies [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of the interferograms (the time-averaged upper-level qubit occupation probability as a function of the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Dynamics for two driven qubits in different bases [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

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

75 extracted references · 5 linked inside Pith

  1. [1]

    The instantaneouseigenbasis (oradiabaticbasis) is formed by the eigenvectors of the Hamiltonian (3)

    Instantaneous eigenstates The instantaneous eigenvaluesE ±(t)and eigenstates |E±(t)⟩are given by the Schrödinger equation, where the time is a parameter,H(t)|E ±(t)⟩=E ±(t)|E ±(t)⟩. The instantaneouseigenbasis (oradiabaticbasis) is formed by the eigenvectors of the Hamiltonian (3). The eigenener- gies are as follows: E±(t) =± 1 2 p ∆2 +ε(t) 2 =± 1 2∆E(t)....

  2. [2]

    For this, we start from the Liouville-von Neumann equation, which is Eq

    Solution of the master equation, approach 1: transfer of the Liouville-von Neumann equation to the instantaneous eigenbasis Here we solve the GKSL equation with the collapse operators defined in the instantaneous eigenbasis. For this, we start from the Liouville-von Neumann equation, which is Eq. (1) taken without the dissipative terms, and transfer it to...

  3. [3]

    Solution of the master equation, approach 2: transfer of collapse operators to the diabatic basis The GKSL equation can also be solved in the diabatic basis. Then, the Hamiltonian is taken in this basis and theLindbladoperatorsdefinedinEq.(2)shouldbetrans- ferred to this basis as follows: L(d) relax(t) = ˜S(t)Lrelax ˜S−1(t),(21) L(d) ϕ (t) = ˜S(t)Lϕ ˜S−1(...

    2025

  4. [4]

    (A2), is given by the formula: O(t) =U †(t,0)OU(t,0),(C1) where the unitary evolution operator reads U(t,0) =T +exp −i Z t 0 dτ HS(τ) ⊗e −iHBt,(C2) withT + denoting time ordering

    Transfer to the interaction representation in the case of the time-dependent system Hamiltonian If the system HamiltonianHS is time-dependent, the transfer to the interaction representation, instead of Eq. (A2), is given by the formula: O(t) =U †(t,0)OU(t,0),(C1) where the unitary evolution operator reads U(t,0) =T +exp −i Z t 0 dτ HS(τ) ⊗e −iHBt,(C2) wit...

  5. [5]

    (C4)s=t/t f is the dimensionless time,|Ea,b(s)⟩ are the instantaneous eigenvectors of the system Hamil- tonianH S(s)

    The adiabatic conditions The adiabatic time dependence means that the follow- ing adiabatic condition is satisfied [9] g D2 mintf ≪1,(C3) wheret f is the total evolution time of the system,Dmin is the minimum difference between the energies of the first excited and ground states of the system, and g= max s∈[0,1];a,b | ⟨Ea(s)|∂ sHS(s)|E b(s)⟩ |.(C4) In Eq....

  6. [6]

    At first, it is necessary to make a unitary transformationexp [i(A/2ℏω)σ z sinωt]and keep in the resulting Hamiltonian the terms up to linear ones in the small parameterA/ℏω

    Making the Hamiltonian time-independent We also note that for a periodically driven qubit with the Hamiltonian (3), considering the limiting case of small excitation amplitude, i.e.,A/ℏω≪1, and using the resonance approximation, the Hamiltonian can be made time-independent [38]. At first, it is necessary to make a unitary transformationexp [i(A/2ℏω)σ z si...

  7. [7]

    Gorini, A

    V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N-level sys- tems, J. Math. Phys.17, 821 (1976)

    1976

  8. [8]

    Lindblad, On the generators of quantum dynamical semigroups, Commun

    G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys.48, 119 (1976)

    1976

  9. [9]

    Chruściński and S

    D. Chruściński and S. Pascazio, A brief history of the GKLS equation, Open Syst. Inf. Dyn.24, 1740001 (2017)

    2017

  10. [10]

    Breuer and F

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

    2007

  11. [11]

    D.Manzano,AshortintroductiontotheLindbladmaster equation, AIP Adv.10, 025106 (2020)

    2020

  12. [12]

    Kossakowski, On the general form of the generator of a dynamical semi-group for the spin 1/2 system, Bull

    A. Kossakowski, On the general form of the generator of a dynamical semi-group for the spin 1/2 system, Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys.21, 649 (1973)

    1973

  13. [13]

    Pleasance, E

    G. Pleasance, E. Aurell, and F. Petruccione, A high- temperature limit penalizing high-frequency quantum fluctuations (2025), arXiv:2508.14262 [quant-ph]

    Pith/arXiv arXiv 2025

  14. [14]

    O. V. Ivakhnenko, S. N. Shevchenko, and F. Nori, Nona- diabatic Landau–Zener–Stückelberg–Majorana transi- tions, dynamics, and interference, Phys. Rep.995, 1 (2023)

    2023

  15. [15]

    Albash, S

    T. Albash, S. Boixo, D. A. Lidar, and P. Zanardi, Quan- tum adiabatic Markovian master equations, New J. Phys. 14, 123016 (2012)

    2012

  16. [16]

    Kamleitner, Secular master equation for adiabatically driven time-dependent systems, Phys

    I. Kamleitner, Secular master equation for adiabatically driven time-dependent systems, Phys. Rev. A87, 042111 (2013)

    2013

  17. [17]

    Yamaguchi, T

    M. Yamaguchi, T. Yuge, and T. Ogawa, Markovian quan- tum master equation beyond adiabatic regime, Phys. Rev. E95, 012136 (2017)

    2017

  18. [18]

    Gulácsi and G

    B. Gulácsi and G. Burkard, Temporally correlated quan- tum noise in driven quantum systems with applications to quantum gate operations, Phys. Rev. Res.7, 023073 (2025)

    2025

  19. [19]

    Bernazzani, B

    L. Bernazzani, B. Gulácsi, and G. Burkard, Universal dis- sipators for driven open quantum systems and the cor- rection to linear response, Quantum Sci. Technol.10, 045050 (2025)

    2025

  20. [20]

    M. P. Silveri, J. A. Tuorila, E. V. Thuneberg, and G. S. Paraoanu, Quantum systems under frequency modula- tion, Rep. Prog. Phys.80, 056002 (2017)

    2017

  21. [21]

    Tayebirad, A

    G. Tayebirad, A. Zenesini, D. Ciampini, R. Mannella, O. Morsch, E. Arimondo, N. Lörch, and S. Wimberger, Time-resolved measurement of Landau-Zener tunneling in different bases, Phys. Rev. A82, 013633 (2010)

    2010

  22. [22]

    J. A. Krzywda and Ł. Cywiński, Adiabatic electron charge transfer between two quantum dots in presence of 1/f noise, Phys. Rev. B101, 035303 (2020)

    2020

  23. [23]

    J. A. Krzywda and Ł. Cywiński, Interplay of charge noise and coupling to phonons in adiabatic electron transfer between quantum dots, Phys. Rev. B104, 075439 (2021)

    2021

  24. [24]

    Szabó, K

    Z. Szabó, K. Yuasa, and D. Burgarth, Long-term stabil- ity of driven quantum systems and the time-dependent Bloch equation (2025), arXiv:2509.03639 [quant-ph]

    Pith/arXiv arXiv 2025

  25. [25]

    M.Bonifacio, D.Domínguez,andM.J.Sánchez,Landau- Zener-Stückelberg interferometry in dissipative circuit quantum electrodynamics, Phys. Rev. B101, 245415 (2020)

    2020

  26. [26]

    Novelli, W

    A. Novelli, W. Belzig, and A. Nitzan, Landau–Zener evo- lution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols, New J. Phys.17, 013001 (2015)

    2015

  27. [27]

    C. Xu, A. Poudel, and M. G. Vavilov, Nonadiabatic dy- namics of a slowly driven dissipative two-level system, Phys. Rev. A89, 052102 (2014)

    2014

  28. [28]

    K. W. Yip, T. Albash, and D. A. Lidar, Quantum tra- jectories for time-dependent adiabatic master equations, Phys. Rev. A97, 022116 (2018)

    2018

  29. [29]

    S.-K. Son, S. Han, and S.-I. Chu, Floquet formulation for the investigation of multiphoton quantum interference in a superconducting qubit driven by a strong ac field, Phys. Rev. A79, 032301 (2009)

    2009

  30. [30]

    Keliri and M

    A. Keliri and M. Schirò, Sambe approach to Floquet-Lindblad open quantum systems (2026), arXiv:2606.09727 [quant-ph]

    Pith/arXiv arXiv 2026

  31. [31]

    A. G. M. Meneses, D. Domínguez, and M. J. Sánchez, Floquet entanglement generation in paramet- rically driven coupled superconducting qubits (2026), arXiv:2606.07797 [quant-ph]

    Pith/arXiv arXiv 2026

  32. [32]

    S.-S. Gu, S. Kohler, Y.-Q. Xu, R. Wu, S.-L. Jiang, S.- K. Ye, T. Lin, B.-C. Wang, H.-O. Li, G. Cao, and G.-P. Guo, Probing two driven double quantum dots strongly coupled to a cavity, Phys. Rev. Lett.130, 233602 (2023)

    2023

  33. [33]

    Y. Yen, M. Reutzel, A. Li, Z. Wang, H. Petek, and M. Schüler, Observation of nonadiabatic Landau-Zener tunnelingamongFloquetstates,Phys.Rev.X16,021004 (2026)

    2026

  34. [34]

    Mickiewicz, V

    K. Mickiewicz, V. Link, and W. T. Strunz, Exact Floquet dynamics of strongly damped driven quantum systems, Phys. Rev. Lett.136, 200201 (2026)

    2026

  35. [35]

    M. Wubs, K. Saito, S. Kohler, Y. Kayanuma, and P. Hänggi, Landau–Zener transitions in qubits controlled by electromagnetic fields, New J. Phys.7, 218 (2005)

    2005

  36. [36]

    Silveri, J

    M. Silveri, J. Tuorila, M. Sillanpää, E. Thuneberg, Y. Makhlin, and P. Hakonen, Basis dependence of ap- proximative energy levels in a strongly driven two-level system, J. Phys. Conf. Ser.400, 042054 (2012)

    2012

  37. [37]

    Silveri, J

    M. Silveri, J. Tuorila, M. Kemppainen, and E. Thuneberg, Probe spectroscopy of quasienergy states, Phys. Rev. B87, 134505 (2013)

    2013

  38. [38]

    M. P. Silveri, K. S. Kumar, J. Tuorila, J. Li, A. Vepsäläi- nen, E. V. Thuneberg, and G. S. Paraoanu, Stückelberg interference in a superconducting qubit under periodic latching modulation, New J. Phys.17, 043058 (2015)

    2015

  39. [39]

    J. E. Danga, S. C. Kenfack, and L. C. Fai, Quan- tum wire and magnetic control of a spin qubit in the Landau–Zener–Stückelberg interferometry transition, J. Phys. A: Math. Theor.49, 195306 (2016)

    2016

  40. [40]

    Bose, Path integral Lindblad dynamics in presence of time-dependent fields (2026), arXiv:2601.04604 [quant- ph]

    A. Bose, Path integral Lindblad dynamics in presence of time-dependent fields (2026), arXiv:2601.04604 [quant- ph]

    arXiv 2026

  41. [41]

    Zenesini, H

    A. Zenesini, H. Lignier, G. Tayebirad, J. Radogostowicz, D.Ciampini, R.Mannella, S.Wimberger, O.Morsch,and E. Arimondo, Time-resolved measurement of Landau- Zener tunneling in periodic potentials, Phys. Rev. Lett. 103, 090403 (2009)

    2009

  42. [42]

    O. Yu. Kitsenko, S. N. Shevchenko, L. Peri, and F. Nori, Reflections on quantum reflectometry: Quantum and tunneling capacitances as well as Sisyphus and Hermes 15 resistances (2026), arXiv:2604.20790 [quant-ph]

    Pith/arXiv arXiv 2026

  43. [43]

    W. S. Teixeira, F. L. Semião, J. Tuorila, and M. Möttö- nen, Assessment of weak-coupling approximations on a driven two-level system under dissipation, New J. Phys. 24, 013005 (2021)

    2021

  44. [44]

    A. A. Zvyagin, A. M. Frishman, and V. M. Tsukernik, Nonlinear effects in parametric excitation of paramag- netic ions in a crystal with rhombic symmetry, Sov. J. Low Temp. Phys.9, 155 (1983)

    1983

  45. [45]

    O. A. Ilinskaya, A. I. Ryzhov, and S. N. Shevchenko, Flux qubit based detector of microwave photons, Phys. Rev. B110, 155414 (2024)

    2024

  46. [46]

    O. A. Ilinskaya and S. N. Shevchenko, Resonant excita- tion of single and coupled qubits for coherent quantum control and microwave detection, Low Temp. Phys.52, 685 (2026)

    2026

  47. [47]

    Xiang, S

    Z.-L. Xiang, S. Ashhab, J. Q. You, and F. Nori, Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems, Rev. Mod. Phys.85, 623 (2013)

    2013

  48. [48]

    Persson, C

    F. Persson, C. M. Wilson, M. Sandberg, G. Johansson, and P. Delsing, Excess dissipation in a single-electron box: The Sisyphus resistance, Nano Lett.10, 953 (2010)

    2010

  49. [49]

    Guéry-Odelin, A

    D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Tor- rontegui, S. Martínez-Garaot, and J. Muga, Shortcuts to adiabaticity: Concepts, methods, and applications, Rev. Mod. Phys.91, 045001 (2019)

    2019

  50. [50]

    S. N. Shevchenko,Mesoscopic physics meets quantum en- gineering, Lecture notes (World Scientific, New Jersey, 2019)

    2019

  51. [51]

    M. V. Berry, Quantum phase corrections from adiabatic iteration, Proc. R. Soc. Lond. A414, 31 (1987)

    1987

  52. [52]

    M. V. Berry, Histories of adiabatic quantum transitions, Proc. R. Soc. Lond. A429, 61 (1990)

    1990

  53. [53]

    R.LimandM.V.Berry,Superadiabatictrackingofquan- tum evolution, J. Phys. A: Math. Gen.24, 3255 (1991)

    1991

  54. [54]

    Drese and M

    K. Drese and M. Holthaus, Perturbative and nonpertur- bative processes in adiabatic population transfer, Eur. Phys. J. D3, 73 (1998)

    1998

  55. [55]

    Zhelnin, L

    P. Zhelnin, L. Johns, and C. A. Argüelles, Qubit thermo- dynamics: Entropy production from nonadiabatic driv- ing, Phys. Rev. A112, 052213 (2025)

    2025

  56. [56]

    J. R. F. Lima and G. Burkard, Partial Landau-Zener transitions and applications to qubit shuttling, Phys. Rev. B111, 235439 (2025)

    2025

  57. [57]

    Theisen, F

    M. Theisen, F. Petiziol, S. Carretta, P. Santini, and S. Wimberger, Superadiabatic driving of a three-level quantum system, Phys. Rev. A96, 013431 (2017)

    2017

  58. [58]

    L.GiannelliandE.Arimondo,Three-levelsuperadiabatic quantum driving, Phys. Rev. A89, 033419 (2014)

    2014

  59. [59]

    Vepsäläinen, S

    A. Vepsäläinen, S. Danilin, and G. S. Paraoanu, Supera- diabatic population transfer in a three-level supercon- ducting circuit, Sci. Adv.5, eaau5999 (2019)

    2019

  60. [60]

    J.Johansson, P.Nation,andF.Nori,QuTiP2: APython framework for the dynamics of open quantum systems, Comput. Phys. Commun.184, 1234 (2013)

    2013

  61. [61]

    Lambert, E

    N. Lambert, E. Giguère, P. Menczel, B. Li, P. Hopf, G. Suárez, M. Gali, J. Lishman, R. Gadhvi, R. Agarwal, A. Galicia, N. Shammah, P. Nation, J. R. Johansson, S. Ahmed, S. Cross, A. Pitchford, and F. Nori, QuTiP 5: The quantum toolbox in Python, Phys. Rep.1153, 1 (2026)

    2026

  62. [62]

    S. H. W. van der Ploeg, A. Izmalkov, A. M. van den Brink, U. Hübner, M. Grajcar, E. Il’ichev, H.-G. Meyer, and A. M. Zagoskin, Controllable coupling of supercon- ducting flux qubits, Phys. Rev. Lett.98, 057004 (2007)

    2007

  63. [63]

    K. Kubo, Y. Ho, and H. Goto, High-performance mul- tiqubit system with double-transmon couplers: Toward scalable superconducting quantum computers, Phys. Rev. Applied22, 024057 (2024)

    2024

  64. [64]

    Sussman, S

    H.Zhang, C.Ding, D.Weiss, Z.Huang, Y.Ma, C.Guinn, S. Sussman, S. P. Chitta, D. Chen, A. A. Houck, J. Koch, and D. I. Schuster, Tunable inductive coupler for high- fidelity gates between fluxonium qubits, PRX Quantum 5, 020326 (2024)

    2024

  65. [65]

    Randall, A

    J. Randall, A. M. Lawrence, S. C. Webster, S. Weidt, N. V. Vitanov, and W. K. Hensinger, Generation of high- fidelity quantum control methods for multilevel systems, Phys. Rev. A98, 043414 (2018)

    2018

  66. [66]

    Gegg and M

    M. Gegg and M. Richter, Efficient and exact numerical approach for many multi-level systems in open system CQED, New J. Phys.18, 043037 (2016)

    2016

  67. [67]

    Chatterjee, S

    A. Chatterjee, S. N. Shevchenko, S. Barraud, R. M. Otxoa, F. Nori, J. J. L. Morton, and M. F. Gonzalez- Zalba, A silicon-based single-electron interferometer cou- pled to a fermionic sea, Phys. Rev. B97, 045405 (2018)

    2018

  68. [68]

    A. L. Gramajo, D. Domínguez, and M. J. Sánchez, Am- plitude tuning of steady-state entanglement in strongly driven coupled qubits, Phys. Rev. A98, 042337 (2018)

    2018

  69. [69]

    A. A. Zvyagin, Modulation of the longitudinal pump- ing in quantum spin systems, Phys. Rev. B101, 174408 (2020)

    2020

  70. [70]

    A. A. Zvyagin and G. A. Zvyagina, Manifestation of crossovers in low-temperature characteristics of the trig- onal rare-earth paramagnet, Low Temp. Phys.52, 290 (2026)

    2026

  71. [71]

    J. Li, K. Chalapat, and G. S. Paraoanu, Entanglement of superconducting qubits via microwave fields: Classical and quantum regimes, Phys. Rev. B78, 064503 (2008)

    2008

  72. [72]

    C. W. Gardiner and P. Zoller,Quantum noise, 3rd ed., Springer complexity (Springer, Berlin, 2010)

    2010

  73. [73]

    Pearle, Simple derivation of the Lindblad equation, Eur

    P. Pearle, Simple derivation of the Lindblad equation, Eur. J. Phys.33, 805 (2012)

    2012

  74. [74]

    Haroche and J.-M

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

    2006

  75. [75]

    Simon, Holonomy, the quantum adiabatic theorem, and Berry’s phase, Phys

    B. Simon, Holonomy, the quantum adiabatic theorem, and Berry’s phase, Phys. Rev. Lett.51, 2167 (1983)

    1983