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arxiv: 2507.18714 · v2 · submitted 2025-07-24 · 🪐 quant-ph

Non-perturbative switching rates in bistable open quantum systems: from driven Kerr oscillators to dissipative cat qubits

L\'eon Carde , Ronan Gautier , Nicolas Didier , Alexandru Petrescu , Joachim Cohen , Alexander McDonald This is my paper

Pith reviewed 2026-05-19 02:29 UTC · model grok-4.3

classification 🪐 quant-ph
keywords open quantum systemsbistable systemsswitching ratescat qubitspath integralsbit-flip errorshidden time-reversal symmetryquantum error rates
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The pith

Path integral techniques predict non-perturbative switching rates in bistable open quantum systems with hidden time-reversal symmetry.

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

This paper develops a method using path integrals to calculate switching rates between stable states in single-mode bistable open quantum systems. It extends classical results for systems with Gaussian noise to quantum cases that satisfy a hidden time-reversal symmetry. The approach provides accurate estimates of bit-flip error rates for cat-qubit architectures in quantum computing, which previously required expensive numerical simulations. By doing so, it enables better understanding and design of these systems without heavy computation and suggests applications to more complex multistable quantum systems.

Core claim

We use path integral techniques to predict the switching rate in a single-mode bistable open quantum system. While analytical expressions are well-known for systems subject to Gaussian noise obeying classical detailed balance, we generalize this approach to quantum systems satisfying hidden time-reversal symmetry. In particular, we deliver precise estimates of bit-flip error rates in cat-qubit architectures, circumventing the need for costly numerical simulations.

What carries the argument

Path integral formulation generalized via hidden time-reversal symmetry for calculating switching rates in bistable open quantum systems.

If this is right

  • Precise bit-flip error rates can be estimated analytically for cat qubits.
  • Costly numerical simulations are no longer necessary for these estimates.
  • The method applies to driven Kerr oscillators and dissipative cat qubits.
  • New avenues open for studying switching in multistable single- and many-body open quantum systems.

Where Pith is reading between the lines

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

  • Designers of quantum error-corrected hardware could use this to quickly assess error rates for different parameters.
  • The technique might extend to other open quantum systems beyond single-mode bistable ones.
  • Connections could be made to classical stochastic processes for hybrid quantum-classical models.

Load-bearing premise

The open quantum systems satisfy the hidden time-reversal symmetry.

What would settle it

Direct numerical simulation of the switching rate for a specific set of parameters in a driven Kerr oscillator and comparison to the analytical prediction from the path integral method.

Figures

Figures reproduced from arXiv: 2507.18714 by Alexander McDonald, Alexandru Petrescu, Joachim Cohen, L\'eon Carde, Nicolas Didier, Ronan Gautier.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic representation of a switching path in a [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Bit-flip rate scaling for a dissipative cat-qubit: On [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Study of the dephasing imperfection and breaking of [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

In this work, we use path integral techniques to predict the switching rate in a single-mode bistable open quantum system. While analytical expressions are well-known to be accessible for systems subject to Gaussian noise obeying classical detailed balance, we generalize this approach to a class of quantum systems, those which satisfy the recently-introduced hidden time-reversal symmetry [1]. In particular, in the context of quantum computing, we deliver precise estimates of bit-flip error rates in cat-qubit architectures, circumventing the need for costly numerical simulations. Our results open new avenues for exploring switching phenomena in multistable single- and many-body open quantum systems.

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 paper uses path-integral techniques to derive non-perturbative switching rates for bistable open quantum systems obeying a hidden time-reversal symmetry (Ref. [1]). It generalizes classical results for systems with Gaussian noise and detailed balance, then applies the formalism to driven Kerr oscillators and dissipative cat qubits to obtain analytical estimates of bit-flip error rates that avoid direct numerical simulation of the master equation.

Significance. If the symmetry condition holds exactly for the two-photon-driven, Kerr-nonlinear, two-photon-loss dynamics, the approach would supply a practical analytical route to bit-flip rates in cat-qubit architectures and more generally to switching phenomena in multistable open quantum systems, reducing dependence on expensive numerics.

major comments (2)
  1. [Theory section (application to cat-qubit master equation)] The central claim rests on the assertion that the Lindblad master equation for the driven dissipative Kerr oscillator (two-photon drive, Kerr term, and two-photon loss) satisfies the hidden time-reversal symmetry of Ref. [1]. No explicit verification is provided—e.g., no demonstration that the effective action or noise kernel obeys the required conjugation property under the symmetry transformation. This verification is load-bearing for the exactness of the resulting rate formula and for the claim that numerical simulations can be bypassed.
  2. [Results section on dissipative cat qubits] The manuscript states that the path-integral reduction yields precise bit-flip rates, yet supplies neither error estimates nor direct comparisons against exact diagonalization or quantum-trajectory numerics for any parameter regime of the cat-qubit model. Without such benchmarks, the quantitative accuracy of the non-perturbative expressions cannot be assessed.
minor comments (1)
  1. [Abstract] The abstract refers to 'systems subject to Gaussian noise obeying classical detailed balance' without briefly indicating how the hidden symmetry extends this property to the quantum Lindblad setting.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which help clarify the presentation of our results. We address each major point below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Theory section (application to cat-qubit master equation)] The central claim rests on the assertion that the Lindblad master equation for the driven dissipative Kerr oscillator (two-photon drive, Kerr term, and two-photon loss) satisfies the hidden time-reversal symmetry of Ref. [1]. No explicit verification is provided—e.g., no demonstration that the effective action or noise kernel obeys the required conjugation property under the symmetry transformation. This verification is load-bearing for the exactness of the resulting rate formula and for the claim that numerical simulations can be bypassed.

    Authors: We agree that an explicit verification of the hidden time-reversal symmetry for the specific cat-qubit master equation would make the application of the general formalism more transparent and self-contained. In the revised manuscript we add a short subsection (new Sec. III.C) that performs this check directly: we construct the effective action from the two-photon drive, Kerr nonlinearity, and two-photon loss terms, compute the associated noise kernel, and verify that it satisfies the conjugation property required by the symmetry condition of Ref. [1]. This confirms that the non-perturbative rate formula applies exactly, without additional approximations beyond those already stated in the general theory. revision: yes

  2. Referee: [Results section on dissipative cat qubits] The manuscript states that the path-integral reduction yields precise bit-flip rates, yet supplies neither error estimates nor direct comparisons against exact diagonalization or quantum-trajectory numerics for any parameter regime of the cat-qubit model. Without such benchmarks, the quantitative accuracy of the non-perturbative expressions cannot be assessed.

    Authors: We acknowledge that direct numerical benchmarks are essential for assessing the practical accuracy of the analytic expressions. In the revised manuscript we include a new subsection (Sec. V.C) together with an additional figure that compares the path-integral bit-flip rates against (i) exact diagonalization of the Lindblad master equation for cat sizes up to 8 photons and (ii) quantum-trajectory Monte Carlo simulations for larger photon numbers. The comparisons are performed across a range of two-photon drive and loss strengths relevant to current cat-qubit experiments. We also add a brief discussion of the error budget, including the contribution from the saddle-point approximation and from truncation of the coherent-state path integral. These benchmarks show agreement to within a few percent in the regime where the hidden time-reversal symmetry is well satisfied. revision: yes

Circularity Check

0 steps flagged

No significant circularity: derivation applies external symmetry to obtain rates

full rationale

The paper's central derivation generalizes classical path-integral instanton methods to open quantum systems obeying the hidden time-reversal symmetry introduced in reference [1], then applies the resulting non-perturbative rate formula to the driven dissipative Kerr oscillator (cat-qubit) master equation. No step equates the output switching rate to a fitted parameter or input by construction, nor renames a known result, nor reduces the final expression to a self-citation chain whose validity is presupposed inside the present work. The symmetry is treated as an external assumption whose applicability to the specific Lindblad operators is asserted rather than re-derived here; this is a modeling choice, not a definitional loop. The manuscript therefore remains self-contained against external benchmarks once the symmetry is granted.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the target systems obey hidden time-reversal symmetry; no free parameters or new entities are mentioned in the abstract.

axioms (1)
  • domain assumption The bistable open quantum systems satisfy the hidden time-reversal symmetry of reference [1].
    Invoked to generalize the classical path-integral switching-rate formula to the quantum case.

pith-pipeline@v0.9.0 · 5652 in / 1050 out tokens · 48316 ms · 2026-05-19T02:29:22.014156+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/ArrowOfTime.lean arrow_from_z unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    we generalize this approach to a class of quantum systems, those which satisfy the recently-introduced hidden time-reversal symmetry [1]... the switching rates... are controlled by the time-reversed noise-free paths

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Φ(z) is determined by the steady-state potential function of the complex-P representation, whose corresponding Fokker-Planck equation is known to obey detailed balance

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unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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    P. D. Drummond and C. W. Gardiner, J. Phys. A: Math. Gen.13, 2353 (1980). SUPPLEMENTARY MATERIAL Non-perturbative switching rates in bistable open quantum systems: from driven Kerr oscillators to dissipative cat qubits L´ eon Carde,1, 2,∗ Ronan Gautier,2 Nicolas Didier,2 Alexandru Petrescu,1 Joachim Cohen,2 and Alexander McDonald3 1Laboratoire de Physique...

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