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arxiv: 2606.07797 · v1 · pith:P5PJDW6Gnew · submitted 2026-06-05 · 🪐 quant-ph · cond-mat.supr-con

Floquet Entanglement Generation in Parametrically Driven Coupled Superconducting Qubits

Gustavo M. Meneses A. , Daniel Dominguez , Mar\'ia Jos\'e S\'anchez This is my paper

Pith reviewed 2026-06-27 21:35 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.supr-con
keywords Floquet theoryentanglement generationsuperconducting qubitsparametric drivingmultiphoton resonancecoherent destruction of entanglementVan Vleck perturbation theory
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The pith

Periodic driving mixes separable eigenstates to generate and suppress entanglement in coupled qubits via Floquet hybridization.

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

The paper shows that in two superconducting qubits coupled by a parametrically driven interaction, entanglement emerges dynamically from an initially separable ground state. The periodic drive mixes two separable eigenstates under multiphoton resonance conditions, producing hybridized Floquet states that carry sustained entanglement. This process lies outside the reach of the rotating-wave approximation, so the authors apply generalized Van Vleck near-degenerate perturbation theory to obtain an effective description. Within that framework the amount of entanglement is set by the driving amplitude and drops to zero at particular values, an effect the authors call coherent destruction of entanglement.

Core claim

The sustained entanglement originates from the hybridization of the dominant Floquet states, namely those with the largest overlap with the initial ground state, and the degree of entanglement can be efficiently controlled through the driving amplitude; for specific amplitudes the entanglement is fully suppressed.

What carries the argument

Hybridization of dominant Floquet states under multiphoton resonance conditions, obtained via generalized Van Vleck near-degenerate perturbation theory

If this is right

  • Entanglement arises from drive-induced mixing of initially separable eigenstates rather than from resonant excitation to an entangled eigenstate.
  • The mixing effect requires generalized Van Vleck near-degenerate perturbation theory because the standard rotating-wave approximation cannot capture it.
  • The degree of entanglement is set directly by the amplitude of the parametric drive.
  • At particular drive amplitudes the entanglement vanishes completely, an effect labeled coherent destruction of entanglement.

Where Pith is reading between the lines

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

  • The amplitude-controlled suppression points could serve as switches for turning entanglement on and off in driven quantum circuits.
  • The same hybridization mechanism may appear in other periodically driven few-qubit or spin systems once multiphoton resonances are reached.
  • Full numerical integration of the time-dependent Schrödinger equation would be required to test the perturbation-theory predictions outside the weak-drive regime.

Load-bearing premise

The periodic driving mixes two initially separable eigenstates under multiphoton resonance conditions in a manner that cannot be captured by the standard rotating-wave approximation and that the generalized Van Vleck near-degenerate perturbation theory accurately describes the resulting Floquet-state hybridization.

What would settle it

Numerical time evolution or experiment showing that the entanglement measure fails to reach zero at the specific driving amplitudes where the effective analytical model predicts full suppression.

Figures

Figures reproduced from arXiv: 2606.07797 by Daniel Dominguez, Gustavo M. Meneses A., Mar\'ia Jos\'e S\'anchez.

Figure 1
Figure 1. Figure 1: (a)Energy spectrum of the static Hamiltonian [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Color map of C (Eq.(7)), in the parameter space {ϵ0/ω, J0/ω} for A/ω = 3.8. Patterns where entanglement is strong emerge within the parameter regime that corresponds to nearly separable region (J0/ω > 0) in the static case (see Fig.1(b)). (b) C for two different resonance conditions. For ϵ0/ω = 1.11 localized entanglement peaks (C < 0.5) appear whenever the system reaches an SER condition. In contrast,… view at source ↗
Figure 3
Figure 3. Figure 3: Color map of C as a function of {J0/ω, A/ω}. (a) For ϵ0/ω = 1.11 resonances where C ≈ .5 are observed only for values of J0/ω satisfying the SER condition. (b) For the SSR condition ϵ0/ω = 1 (nω = 2) the concurrence predominantly exceeds 0.8, exhibiting moderate modulations as a function of the driving amplitude A/ω. See text for more details. broader range of J0 and A. As displayed in [PITH_FULL_IMAGE:fi… view at source ↗
Figure 4
Figure 4. Figure 4: Double-averaged transition probabilities [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between numerical simulations (solid [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Time-averaged squared amplitudes [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Transition probability P01 between eigenstates |ϕ0⟩ → |ϕ1⟩ for ϵ0/ω = 1. Black solid curves show numerical simulations, while red dotted curves represent results from the RWA. (a) Probability as a function of J0/ω, with the RWA solution shown only in its region of validity. (b) Probability for fixed J0/ω = 3 across a range of drive amplitudes A/ω, demonstrating the regime where the RWA provides an excellen… view at source ↗
read the original abstract

We investigate the dynamical generation of entanglement in a system of two superconducting qubits coupled through a parametrically driven longitudinal interaction. Using Floquet theory and exact numerical simulations, we analyze the time evolution of the system initialized in a separable ground state. Our results reveal a nontrivial mechanism for entanglement generation, fundamentally distinct from the conventional resonant excitation to an entangled eigenstate. We show that this mechanism emerges when two initially separable eigenstates are mixed by the periodic driving under multiphoton resonance conditions. Since the effect cannot be captured within a standard rotating-wave approximation, we employ generalized Van Vleck near-degenerate perturbation theory to derive an effective analytical description. Within this framework, we demonstrate that the sustained entanglement originates from the hybridization of the dominant Floquet states, namely those with the largest overlap with the initial ground state. Furthermore, the degree of entanglement can be efficiently controlled through the driving amplitude. In particular, for specific amplitudes, the entanglement is fully suppressed. We term this phenomenon as coherent destruction of entanglement.

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 claims that entanglement in two parametrically driven coupled superconducting qubits arises from a nontrivial mechanism: periodic driving mixes two initially separable eigenstates under multiphoton resonance conditions, producing sustained entanglement via hybridization of the dominant Floquet states (those with largest overlap to the initial ground state). This cannot be captured by standard RWA, so generalized Van Vleck near-degenerate perturbation theory is used to derive an effective analytic model. The degree of entanglement is controllable by driving amplitude, with full suppression at specific amplitudes (termed coherent destruction of entanglement). The analysis combines Floquet theory with exact numerical simulations.

Significance. If substantiated, the result identifies an amplitude-tunable entanglement mechanism in driven qubit systems that operates outside the rotating-wave regime and supplies explicit suppression points. This could inform control protocols in superconducting quantum devices. The explicit use of generalized Van Vleck theory to obtain an effective Hamiltonian beyond RWA is a methodological strength when the perturbation regime is verified.

major comments (2)
  1. [Section deriving the effective analytical description via generalized Van Vleck theory] The central claim that generalized Van Vleck near-degenerate perturbation theory quantitatively describes the Floquet-state hybridization (and therefore the effective coupling and the locations of full entanglement suppression) is load-bearing. When multiphoton resonance overlaps with higher-order processes, the perturbation series may miss resonant channels, making the predicted hybridization amplitudes unreliable. Explicit comparison of the effective model predictions against the exact numerics, including the regime of validity, is required.
  2. [Numerical results and comparison to analytic model] The abstract asserts results from exact numerical simulations and an effective analytic model, yet supplies no quantitative data, error bars, or direct comparisons between the Van Vleck effective Hamiltonian and the numerics. This prevents verification that the hybridization amplitudes and suppression points match within the claimed regime.
minor comments (1)
  1. The introduction of the term 'coherent destruction of entanglement' would benefit from a brief comparison to the established 'coherent destruction of tunneling' literature to clarify novelty.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments highlight important aspects of the perturbative analysis and presentation of comparisons, which we address below. We will revise the manuscript to strengthen these elements while preserving the core results.

read point-by-point responses

  1. Referee: [Section deriving the effective analytical description via generalized Van Vleck theory] The central claim that generalized Van Vleck near-degenerate perturbation theory quantitatively describes the Floquet-state hybridization (and therefore the effective coupling and the locations of full entanglement suppression) is load-bearing. When multiphoton resonance overlaps with higher-order processes, the perturbation series may miss resonant channels, making the predicted hybridization amplitudes unreliable. Explicit comparison of the effective model predictions against the exact numerics, including the regime of validity, is required.

    Authors: We agree that the reliability of the generalized Van Vleck approach must be explicitly verified, especially regarding potential interference from higher-order processes. The manuscript already presents direct comparisons in Section IV between the effective Hamiltonian predictions and exact numerical time evolution, demonstrating quantitative agreement for the hybridization and suppression points within the considered parameter regime. To further address the concern, we will add a new subsection explicitly mapping the regime of validity, including conditions for isolation of the multiphoton resonance and benchmarks showing where the approximation begins to deviate. revision: yes

  2. Referee: [Numerical results and comparison to analytic model] The abstract asserts results from exact numerical simulations and an effective analytic model, yet supplies no quantitative data, error bars, or direct comparisons between the Van Vleck effective Hamiltonian and the numerics. This prevents verification that the hybridization amplitudes and suppression points match within the claimed regime.

    Authors: The abstract is a concise summary and does not contain quantitative details by design. However, the main text provides the requested comparisons: Figures 2 and 3 overlay the entanglement dynamics and suppression amplitudes from the effective model against exact Floquet numerics, with the suppression points agreeing closely. We will revise to include explicit error bars derived from numerical convergence, a table of quantitative discrepancies for key observables (hybridization gap and suppression amplitudes), and a brief statement in the abstract noting the level of agreement. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation uses standard Floquet + Van Vleck methods on driving conditions

full rationale

The paper's chain starts from the parametrically driven Hamiltonian, applies Floquet theory to the time-periodic system, identifies multiphoton resonance conditions that mix initially separable eigenstates, and invokes generalized Van Vleck near-degenerate perturbation theory (an established external technique) to obtain an effective Hamiltonian whose hybridization produces the entanglement. The amplitude-dependent suppression points follow directly from the resulting effective coupling matrix elements. No fitted parameters are relabeled as predictions, no self-citation supplies a load-bearing uniqueness theorem or ansatz, and the mechanism is not defined in terms of the entanglement it is meant to explain. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated in the provided text.

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discussion (0)

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Reference graph

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