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arxiv: 2605.17604 · v2 · pith:EXICBJOYnew · submitted 2026-05-17 · 🪐 quant-ph · cond-mat.dis-nn

Schedule-dependent basin occupation in a programmable quantum annealer

Luis Lozano This is my paper

Pith reviewed 2026-05-21 07:48 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nn
keywords quantum annealingreverse annealingD-Wavebasin occupationparallel temperingsimulated quantum annealingIsing instancesMarkov chain probe
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The pith

Cycled reverse annealing produces subsystem correlations that bracket between parallel tempering and path-integral simulated quantum annealing on D-Wave devices.

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

This paper examines how different annealing schedules affect which solution basins a programmable quantum annealer settles into for mixed-frustration Ising problems. By cycling the reverse annealing protocol many times without reinitializing the state, the authors track late-time autocorrelation in subsystems and compare it to two classical reference methods at the device's effective temperature. They find that the quantum device's behavior consistently falls between a localized classical sampler and a delocalized quantum-inspired one across all tested schedules and hardware versions. This suggests that reverse annealing can be tuned to control basin occupation in an instance-specific way rather than providing a blanket quantum boost. The work also shows that simple landscape features cannot linearly predict how sensitive the occupation is to schedule changes.

Core claim

On a mixed-frustration 12-qubit Ising instance run on two D-Wave generations, the late-time subsystem autocorrelation under cycled reverse annealing sits strictly between two equilibrium reference processes at the device-calibrated effective temperature: localized parallel tempering, and delocalized equilibrated path-integral simulated quantum annealing at a fixed Advantage2 pause-point transverse-field scale. The bracket holds on all three tested schedules and at both hardware calibrations. Among twenty random training instances, schedule shape modulates basin occupation on six of the thirteen multi-basin instances, with dominant-configuration shifts of up to 38 percentage points.

What carries the argument

The cycled reverse-anneal protocol (reinitialize_state=False, 50 cycles per submission) used as a Markov-chain probe of the device's pause-point dynamics, together with a parallel-tempering falsification framework that supplies bias-corrected bootstrap 95% confidence intervals.

If this is right

  • The bracketing result revises an earlier two-pause-enhancement claim.
  • Reverse-anneal schedules function as instance-specific basin-occupation probes.
  • Schedule shape can shift the dominant configuration by as much as 38 percentage points on multi-basin instances.
  • A pre-registered linear predictor from landscape moments fails to forecast schedule sensitivity on held-out instances.
  • The mismatch direction is reproduced on a native-graph control instance without minor embedding.

Where Pith is reading between the lines

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

  • The protocol could be applied to larger problem sizes to test whether the bracketing between classical references persists or reveals new regimes.
  • Schedule dependence might be leveraged to steer optimization toward specific solution clusters in practical quantum annealing applications.
  • Comparing to other simulation methods beyond parallel tempering and path-integral annealing could clarify what aspects of the device's dynamics are being captured.
  • Extending the analysis to instances with known ground-state degeneracies might quantify how accurately the device samples the intended distribution.

Load-bearing premise

The cycled reverse-anneal protocol functions as an unbiased Markov-chain probe of the device's pause-point dynamics without significant artifacts from cycling, hardware noise, or the reinitialization setting.

What would settle it

Finding that on a new mixed-frustration instance or schedule the late-time autocorrelation under cycled reverse annealing falls outside the 95% confidence interval bracket between the localized parallel tempering and the delocalized path-integral simulated quantum annealing references, or that the interval overlaps one of the references.

Figures

Figures reproduced from arXiv: 2605.17604 by Luis Lozano.

Figure 1
Figure 1. Figure 1: Experimental protocol. (a) Subsystem/environment partition on a representative benchmark instance (seed 42, family B; λ = 0.5, W = 1): four subsystem qubits S (orange) are probed while eight environment qubits E (grey) are clamped to their initial product configuration (arrows). Edges color the longitudinal couplings Jij (blue J < 0, red J > 0), with line width proportional to |Jij |. (b) Schedule-family c… view at source ↗
Figure 2
Figure 2. Figure 2: Instance taxonomy across the twenty training seeds. Rows are the twenty random￾regular family-B seeds, sorted so the most schedule-responsive instances sit at the top and schedule￾static instances at the bottom. (a) Classical local-minimum count nbasins from exhaustive steepest￾descent enumeration of the 212 configurations. All seeds are multi-basin at the full-system level (nbasins ∈ [8, 13]). (b) Ground-… view at source ↗
Figure 3
Figure 3. Figure 3: Representative schedule-dependent subsystem basin-occupation shifts on four of the six responsive seeds. Empirical subsystem distribution PS for four of the six schedule￾responsive seeds identified in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Cycled reverse-anneal dynamics on Advantage2 at βeff = 7.22. Left column: seed 8192, a responsive multi-basin seed where pause depth and duration order the dynamics monotonically. Right column: seed 14029, a PT-unmatched instance ( [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Classical falsification with parallel tempering, path-integral SQA and a five￾embedding sensitivity check. (a) QPU C(49) on Advantage2 at βeff = 7.22 versus the best￾matched parallel-tempering C(49) at the same β, across all eighteen (seed, schedule) combinations in the v3 dataset. Error bars are bootstrap 95% CIs over 30 chains per QPU condition and 15 chains per PT sweep-budget (nsweeps ∈ {10, 50, 200, 1… view at source ↗
Figure 6
Figure 6. Figure 6: Native-graph control on Advantage2 Zephyr with no minor embedding. Three random 12-node connected induced subgraphs of the Advantage2 hardware graph, with the Ising Hamiltonian defined directly on the native physical edges and queried through the bare DWaveSampler (auto scale=False). Markers: QPU C(49) per schedule with bootstrap 95% CIs over 30 chains pooled across three initial states; shaded band: PT en… view at source ↗
read the original abstract

On a mixed-frustration 12-qubit Ising instance run on two D-Wave generations, Advantage2 Zephyr and Advantage_system6.4 Pegasus, the late-time subsystem autocorrelation under cycled reverse annealing sits strictly between two equilibrium reference processes at the device-calibrated effective temperature: localized parallel tempering, and delocalized equilibrated path-integral simulated quantum annealing at a fixed Advantage2 pause-point transverse-field scale. The bracket holds on all three tested schedules and at both hardware calibrations. We obtain this result through two ingredients: a cycled reverse-anneal protocol (reinitialize_state=False, 50 cycles per submission) used as a Markov-chain probe of the device's pause-point dynamics, and a parallel-tempering falsification framework with bias-corrected and accelerated bootstrap 95% confidence intervals. Of eighteen tested (instance, schedule) combinations on Advantage2, three are PT-unmatched and correspond to two distinct Ising instances; an independent native-graph control with no minor embedding on a third mixed-frustration instance reproduces the same direction of mismatch. Among twenty random training instances, schedule shape modulates basin occupation on six of the thirteen multi-basin-in-readout instances, with dominant-configuration shifts of up to 38 percentage points including changes of the dominant configuration. A pre-registered linear predictor of schedule sensitivity from exhaustively computable landscape features fails on ten held-out instances, indicating that schedule sensitivity is not captured by simple linear functions of the tested landscape moments. The bracketing result revises an earlier two-pause-enhancement claim and reframes reverse-anneal schedules as instance-specific basin-occupation probes rather than universal quantum-enhancement knobs.

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 manuscript reports experiments on D-Wave Advantage2 and Advantage_system6.4 devices using mixed-frustration 12-qubit Ising instances. It claims that late-time subsystem autocorrelation under a cycled reverse-annealing protocol (reinitialize_state=False, 50 cycles per submission) lies strictly between the values obtained from localized parallel tempering and from delocalized equilibrated path-integral simulated quantum annealing, both at the device-calibrated effective temperature. The bracket is reported to hold for all three tested schedules and both hardware calibrations. Additional results include schedule-dependent basin occupation shifts (up to 38 percentage points) on six of thirteen multi-basin instances and the failure of a pre-registered linear predictor of schedule sensitivity on ten held-out instances. The work revises an earlier two-pause-enhancement claim.

Significance. If the bracketing result is robust, the paper supplies a concrete falsification test for quantum-enhancement claims in programmable annealers and reframes reverse-annealing schedules as instance-specific basin-occupation probes. Strengths include the use of bias-corrected bootstrap confidence intervals, pre-registration, independent reference simulations, and an explicit revision of a prior claim. The finding that schedule shape modulates dominant configurations on some but not all instances is potentially useful for algorithm design.

major comments (2)
  1. [Methods/Results] Protocol description (Methods/Results): The central bracketing claim requires that the 50-cycle reverse-anneal protocol with reinitialize_state=False functions as an unbiased Markov-chain probe of pause-point dynamics. No explicit diagnostic for cross-cycle correlations, persistent hardware memory, or incomplete thermalization at the pause point is reported. On the mixed-frustration instances where PT mismatch is observed, such artifacts could shift the measured autocorrelation outside the reported bracket or introduce schedule-dependent bias unrelated to equilibrium dynamics.
  2. [Results] Reference simulations (Results): The strict bracketing is asserted relative to localized PT and delocalized PI-SQA at a fixed Advantage2 pause-point transverse-field scale. The manuscript does not provide a direct quantitative comparison (e.g., overlap or distance metrics) between the hardware-calibrated effective temperature and the simulation parameters used for the two reference processes, leaving open whether the bracket is an artifact of simulation assumptions rather than a physical constraint.
minor comments (2)
  1. [Abstract] Abstract: The sentence 'Of eighteen tested (instance, schedule) combinations on Advantage2, three are PT-unmatched...' would benefit from an explicit table or supplementary listing of which instances and schedules produce the mismatch.
  2. [Main text] Notation: The term 'subsystem autocorrelation' is used without a precise definition or equation in the main text; a short clarifying equation or reference to the supplementary material would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and outline planned revisions to strengthen the presentation of the cycled reverse-annealing protocol and the reference simulations.

read point-by-point responses

  1. Referee: [Methods/Results] Protocol description (Methods/Results): The central bracketing claim requires that the 50-cycle reverse-anneal protocol with reinitialize_state=False functions as an unbiased Markov-chain probe of pause-point dynamics. No explicit diagnostic for cross-cycle correlations, persistent hardware memory, or incomplete thermalization at the pause point is reported. On the mixed-frustration instances where PT mismatch is observed, such artifacts could shift the measured autocorrelation outside the reported bracket or introduce schedule-dependent bias unrelated to equilibrium dynamics.

    Authors: We agree that explicit diagnostics for cross-cycle correlations and potential hardware memory effects would strengthen the Markov-chain interpretation. In the revised manuscript we will add a dedicated subsection with autocorrelation analysis across cycles (computed from the existing dataset) and checks for persistent state memory by comparing early- versus late-cycle statistics. These additions will quantify the decay of correlations and support that 50 cycles suffice to probe pause-point equilibrium dynamics without introducing schedule-dependent artifacts beyond those already bounded by the bootstrap intervals. revision: yes

  2. Referee: [Results] Reference simulations (Results): The strict bracketing is asserted relative to localized PT and delocalized PI-SQA at a fixed Advantage2 pause-point transverse-field scale. The manuscript does not provide a direct quantitative comparison (e.g., overlap or distance metrics) between the hardware-calibrated effective temperature and the simulation parameters used for the two reference processes, leaving open whether the bracket is an artifact of simulation assumptions rather than a physical constraint.

    Authors: The PT and PI-SQA simulations are performed at the device-calibrated effective temperature reported in the Methods. To provide the requested quantitative comparison we will add, in the revision, explicit overlap metrics (e.g., total variation distance and temperature-sensitivity sweeps) between the calibrated hardware temperature distribution and the simulation parameters, together with a brief sensitivity analysis showing that the observed bracketing remains intact within the calibration uncertainty. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental bracketing is grounded in hardware data and independent simulations.

full rationale

The paper's central claim is an empirical observation: late-time subsystem autocorrelation from a cycled reverse-anneal protocol on D-Wave hardware lies between two independent equilibrium references (localized PT and delocalized PI-SQA) at device-calibrated temperature. This is tested across schedules and instances with bias-corrected bootstrap CIs, plus a native-graph control and held-out instances where a pre-registered linear predictor fails. No derivation reduces a result to its own inputs by construction, no fitted parameter is relabeled as a prediction, and the noted revision of an earlier claim is not load-bearing for the current bracketing result. Hardware runs and external simulations supply independent grounding.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on device-calibrated temperature matching and standard simulation references; no new particles or forces introduced.

free parameters (1)
  • device-calibrated effective temperature
    Used to scale the equilibrium reference processes for direct comparison to hardware results.
axioms (2)
  • domain assumption Parallel tempering and path-integral simulated quantum annealing at fixed transverse-field scale constitute accurate equilibrium references for the device's effective temperature.
    Invoked to establish the bracketing bounds for hardware autocorrelation.
  • domain assumption Cycled reverse annealing with reinitialize_state=False serves as a faithful Markov-chain probe of pause-point dynamics.
    Underlies the experimental protocol and interpretation of late-time autocorrelation.

pith-pipeline@v0.9.0 · 5821 in / 1561 out tokens · 54645 ms · 2026-05-21T07:48:30.475116+00:00 · methodology

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