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arxiv: 2510.05872 · v2 · submitted 2025-10-07 · 🪐 quant-ph

Entanglement dynamics and performance of two-qubit gates for superconducting qubits under non-Markovian effects

Kiyoto Nakamura , Joachim Ankerhold This is my paper

Pith reviewed 2026-05-18 09:29 UTC · model grok-4.3

classification 🪐 quant-ph
keywords entanglement dynamicsnon-Markovian effectssuperconducting qubitstwo-qubit gatesrotating wave approximationdissipative dynamicsquantum computing
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The pith

Non-Markovian qubit-reservoir correlations must be included to accurately describe disentanglement dynamics and two-qubit gate performance in superconducting systems.

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

The paper applies numerically exact simulations to a two-qubit setup in which each superconducting qubit couples to its own reservoir. It tests whether the rotating wave approximation remains valid when tracking how entanglement decays. It follows the build-up and loss of entanglement while a √iSWAP† gate is applied and while memory effects from the reservoirs are active. It also compares different ways to decompose a Hadamard-plus-CNOT sequence under several noise types and qubit parameters. The central finding is that these subtle correlations change the expected dynamics in ways missed by simpler models.

Core claim

Within a numerically exact simulation technique, the dissipative dynamics of a two-qubit architecture is considered in which each qubit couples to its individual noise source. The work examines the validity of the rotating wave approximation for disentanglement, analyzes entanglement generation and destruction during and after a √iSWAP† gate with focus on reservoir memory effects, and evaluates the performance of a Hadamard + CNOT sequence under different decomposition schemes and various noise sources.

What carries the argument

Numerically exact simulation of the reduced dynamics for two qubits each coupled to its own reservoir, used to track non-Markovian memory effects and to test the rotating wave approximation.

If this is right

  • The rotating wave approximation fails to capture key features of disentanglement dynamics for certain qubit parameters and reservoir spectra.
  • Reservoir memory effects modify both the creation and the subsequent decay of entanglement during √iSWAP† gate operation.
  • Different decompositions of the Hadamard + CNOT sequence exhibit distinct fidelity losses when non-Markovian contributions are retained.
  • Accounting for individual-reservoir correlations improves predictions of gate performance across a range of noise strengths.

Where Pith is reading between the lines

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

  • Device calibration routines could be extended to include short-time reservoir correlation measurements to adjust gate timings.
  • The same simulation approach applied to three or more qubits might expose how non-Markovian errors accumulate in larger circuits.
  • Reservoir spectral engineering that suppresses memory effects could be tested as a practical mitigation strategy.

Load-bearing premise

The numerically exact simulation technique accurately captures the full dissipative dynamics of each qubit coupled to its individual reservoir without introducing uncontrolled approximations beyond those explicitly tested.

What would settle it

Direct experimental measurement of concurrence decay or gate fidelity in a superconducting two-qubit device under parameters where the simulations predict clear non-Markovian deviations from rotating-wave or Markovian results; agreement with the simpler models would falsify the necessity of the full correlations.

Figures

Figures reproduced from arXiv: 2510.05872 by Joachim Ankerhold, Kiyoto Nakamura.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the model we consider in this study. The [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Time traces of the concurrence [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Time traces of the concurrence [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Schematic of the sequence of the qubit–qubit coupling strength [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Dynamics of the off-diagonal element [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Time traces of the concurrence [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a), (b) Decomposition schemes of the Hadamard ( [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: displays the time traces of the fidelity under Seq. (a) with the initial state |00⟩⟨00|. Here, those during the first single-qubit gate application [𝑅 𝑦 (−𝜋/2) ⊗ 𝑅 𝑥 (𝜋/2)] and the first idling (with the duration 𝜔𝑞Δ𝑡 = 𝜋/2) in the deep sub￾Ohmic case 𝑠 = 1/8 are depicted. Since no entanglement is generated until the end in [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: displays the time traces of the concurrence of sys￾tems in heterogeneous environments. All the combinations of the spectral exponent, 𝑠𝑗 ∈ {1, 1/2, 1/8}, are depicted. Since the initial state is asymmetric with respect to each qubit, the dynamics with (𝑠1, 𝑠2) = (𝑎, 𝑏) and (𝑏, 𝑎) are different. At the end time of the gate, one finds that the gate performance with the heterogeneous environments is bounded t… view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Time traces of the fidelity during the first gate operation [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
read the original abstract

Within a numerically exact simulation technique, the dissipative dynamics of a two-qubit architecture is considered in which each qubit couples to its individual noise source (reservoir). The goal is to reveal the role of subtle qubit-reservoir correlations including non-Markovian processes as a prerequisite to guide further improvements of quantum computing devices. This paper addresses the following three topics. First, we examine the validity of the rotating wave approximation imposed previously on the qubit-reservoir coupling with respect to the disentanglement dynamics. Second, generation of the entanglement as well as destruction are analyzed by monitoring the reduced dynamics during and after application of a $\sqrt{\mbox{iSWAP}^\dagger}$ gate, also focusing on memory effects caused by reservoirs. Finally, the performance of a Hadamard + CNOT sequence is analyzed for different gate decomposition schemes. In all three cases, various types of noise sources and qubit parameters are considered.

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 / 2 minor

Summary. The paper examines the dissipative dynamics of a two-qubit superconducting architecture in which each qubit couples independently to its own reservoir. Using a numerically exact simulation technique, it investigates three topics: (i) the validity of the rotating-wave approximation for disentanglement dynamics, (ii) entanglement generation and destruction during and after a √iSWAP† gate with emphasis on reservoir memory effects, and (iii) the performance of Hadamard+CNOT sequences under different gate decompositions, considering various noise sources and qubit parameters.

Significance. If the numerical method is shown to be free of uncontrolled truncations and the reported differences between non-Markovian and Markovian/RWA cases are robust, the results would usefully quantify when subtle qubit-reservoir correlations must be retained for accurate modeling of entanglement decay and two-qubit gate fidelity in superconducting platforms. The concrete focus on experimentally relevant gates adds practical value for device characterization.

major comments (2)
  1. [Abstract] Abstract and opening paragraph: the assertion that a 'numerically exact simulation technique' is employed is central to the claim that non-Markovian correlations must be included. However, no explicit validation against known limits (Markovian limit, weak-coupling analytic results, or convergence with respect to bath discretization/memory cutoff) is described, nor are quantitative error bars or sensitivity tests provided. Without these, it is impossible to confirm that the reported concurrence decay rates or gate infidelities exceed any numerical artifacts.
  2. [Abstract] The three topics listed in the abstract each rely on the fidelity of the reduced dynamics. A direct comparison of concurrence or gate fidelity with and without the rotating-wave approximation (or with varying non-Markovian memory depth) should be presented with explicit numerical differences and statistical uncertainties to establish that the non-Markovian corrections are load-bearing rather than marginal.
minor comments (2)
  1. Notation for the √iSWAP† gate and the precise definition of the two-qubit Hamiltonian should be stated explicitly in the main text rather than only in the abstract.
  2. Figure captions (if present) should include the specific parameter values (coupling strengths, cutoff frequencies, temperature) used for each curve to allow reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We have revised the paper to include additional validations and direct comparisons as suggested. Our point-by-point responses are as follows.

read point-by-point responses

  1. Referee: [Abstract] Abstract and opening paragraph: the assertion that a 'numerically exact simulation technique' is employed is central to the claim that non-Markovian correlations must be included. However, no explicit validation against known limits (Markovian limit, weak-coupling analytic results, or convergence with respect to bath discretization/memory cutoff) is described, nor are quantitative error bars or sensitivity tests provided. Without these, it is impossible to confirm that the reported concurrence decay rates or gate infidelities exceed any numerical artifacts.

    Authors: We acknowledge the need for explicit validation to support the 'numerically exact' claim. In the revised manuscript, we have included a dedicated paragraph in the Methods section describing the convergence tests with respect to bath discretization and memory cutoff. We also compare our results to the Markovian limit obtained from the Lindblad equation and to weak-coupling analytics where applicable. Error estimates derived from the truncation parameters are now provided, demonstrating that the differences in concurrence decay and gate fidelities are well above numerical uncertainties. revision: yes

  2. Referee: [Abstract] The three topics listed in the abstract each rely on the fidelity of the reduced dynamics. A direct comparison of concurrence or gate fidelity with and without the rotating-wave approximation (or with varying non-Markovian memory depth) should be presented with explicit numerical differences and statistical uncertainties to establish that the non-Markovian corrections are load-bearing rather than marginal.

    Authors: We agree that presenting direct comparisons with quantitative differences is essential. We have updated the figures corresponding to the three topics to include comparisons with and without the rotating-wave approximation, as well as results for varying memory depths. Explicit percentage differences in key quantities (e.g., concurrence at specific times or gate infidelities) are now reported in the text and captions. Sensitivity to parameters serves as a proxy for uncertainties, shown via shaded areas in plots. These revisions confirm that non-Markovian effects lead to noticeable changes in the dynamics. revision: yes

Circularity Check

0 steps flagged

No circularity: forward numerical simulation of non-Markovian open-system dynamics

full rationale

The paper applies a numerically exact simulation technique to compute reduced dynamics, concurrence, and gate fidelities for a two-qubit system with independent reservoirs. All reported results on RWA validity, entanglement generation/destruction under √iSWAP† and Hadamard+CNOT, and memory effects follow directly from these computations across varied noise models and parameters. No equations reduce outputs to inputs by construction, no predictions are statistically forced by prior fits within the same run, and any methodological citations are not load-bearing for the central claims. The derivation chain is self-contained and externally verifiable through the described numerics.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central analysis rests on the assumption that each qubit is coupled to an independent reservoir whose correlations can be treated by a numerically exact method whose concrete realization is not specified in the abstract; no free parameters or new entities are named.

axioms (2)
  • domain assumption Each qubit couples to its own individual noise source (reservoir).
    Stated in the first sentence of the abstract as the architecture under study.
  • domain assumption A numerically exact simulation technique exists that can capture the full non-Markovian dynamics without further uncontrolled approximations.
    Invoked when the authors state they use such a technique to examine the listed topics.

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Reference graph

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