Three recent experimental studies of D-Wave annealers each report an unexplained effective-temperature phenomenon: fitted inverse temperatures whose dependence on annealing time is left empirical, with sampling quality degrading at a critical frustration point [Pelofske, PRR 8, 033280 (2026)]; a coupling-independent temperature offset t-bar in [0.2,0.4] that violates the assumed T_eff ∝ 1/J scaling [Grattan et al., arXiv:2512.03162]; and hardware inverse temperatures a "consistent" factor of 5–7 above closed-system theory, attributed to uncontrollable hardware effects [Kim et al., PRE 113, 035302 (2026)]. We show that a single account, built from the diabatic effective-temperature relation of Gyhm et al. evaluated on the vendor's published fast-anneal schedules and one thermal bath, organizes all three. First, on real schedules the coherent inverse temperature is nearly linear in annealing time — not ∝ sqrt(t_a) as for linearly vanishing drivers — because the transverse field decays exponentially and dies by s ≈ 0.6; exact statevector simulation confirms the first-order integral to 0.4–4.2% in its validity window. Second, a units identity, beta_cyclic(t_a) = beta_correct(t_a/2pi), resolves the factor of 5–7: the published theoretical reference curves in this lane are quantitatively consistent with schedule data evaluated in cyclic rather than angular frequency units. The foundational paper's own schedule evaluations carry the rescale: its earlier single evaluation, beta ≈ 0.54 at 5 ns, equals our correct-convention value at t_a/2pi (0.539), and all 24 of its current tabulated beta and c_2 values that we can recompute from vendor schedule tables are reproduced at t_a/2pi to within 0.11%; a free-rescale fit to Kim et al.'s published simulation curve gives r = 6.40, with 2pi = 6.283 inside the fit's shallow region; what remains after the correction is consistent with open-system cooling. Third, the coupling-independent offset is a residual-excitation floor read through a domain-wall thermometer, t-bar ≈ 2/ln(1/rho): the implied kink densities (9e-5 to 4e-3) overlap published kink measurements, the excitation-floor form beats the constant-offset (noise) model on AIC for all four reported machines, and the logarithm compresses two and a half decades of rho into the narrow observed band, explaining its apparent universality. In the coherent nanosecond regime the closed-system law is an upper envelope on hardware inverse temperature; the shortfall is a candidate in-situ decoherence diagnostic, machine-resolved, and at the one matched cell where both machines are coherent the measured cross-machine ratio (2.63) agrees with the parameter-free prediction at the few-percent level. All hypotheses, tolerances, and kill criteria were registered before data extraction; failed and undecidable gates are reported alongside the successes. No quantum-advantage claim is made. AI use and validation: This work was produced in close collaboration with AI research assistants, directed by the author, who set the research direction, the standards of evidence, and all decisions about what is claimed and published. Anthropic's Claude (Fable 5) performed the analysis, simulation, extraction, and drafting; xAI's Grok (via Cursor) provided independent pre-publication review; and Anthropic's Claude Opus 5.5 performed a post-publication adversarial audit of the manuscript against its pinned evidence, with findings and dispositions logged in the project ledger and incorporated in subsequent versions. The registered-verdict protocol is designed so that no result rests on trusting a model's output: hypotheses, tolerances, and kill criteria were committed to the repository before any data was extracted; failed and undecidable gates are reported in the paper; every numeric claim traces to pinned, machine-readable extraction files and analysis code included in this deposit; figure data was extracted from the source PDFs' vector drawing operations rather than read by a model; and verbatim quotes were verified against raw page dumps.
Three recent experimental studies of D-Wave annealers each report an unexplained effective-temperature phenomenon: fitted inverse temperatures whose dependence on annealing time is left empirical, with sampling quality degrading at a critical frustration point [Pelofske, PRR 8, 033280 (2026)]; a coupling-independent temperature offset t-bar in [0.2,0.4] that violates the assumed T_eff ∝ 1/J scaling [Grattan et al., arXiv:2512.03162]; and hardware inverse temperatures a "consistent" factor of 5–7 above closed-system theory, attributed to uncontrollable hardware effects [Kim et al., PRE 113, 035302 (2026)]. We show that a single account, built from the diabatic effective-temperature relation of Gyhm et al. evaluated on the vendor's published fast-anneal schedules and one thermal bath, organizes all three. First, on real schedules the coherent inverse temperature is nearly linear in annealing time — not ∝ sqrt(t_a) as for linearly vanishing drivers — because the transverse field decays exponentially and dies by s ≈ 0.6; exact statevector simulation confirms the first-order integral to 0.4–4.2% in its validity window. Second, a units identity, beta_cyclic(t_a) = beta_correct(t_a/2pi), resolves the factor of 5–7: the published theoretical reference curves in this lane are quantitatively consistent with schedule data evaluated in cyclic rather than angular frequency units. The foundational paper's own schedule evaluations carry the rescale: its earlier single evaluation, beta ≈ 0.54 at 5 ns, equals our correct-convention value at t_a/2pi (0.539), and all 24 of its current tabulated beta and c_2 values that we can recompute from vendor schedule tables are reproduced at t_a/2pi to within 0.11%; a free-rescale fit to Kim et al.'s published simulation curve gives r = 6.40, with 2pi = 6.283 inside the fit's shallow region; what remains after the correction is consistent with open-system cooling. Third, the coupling-independent offset is a residual-excitation floor read through a domain-wall thermometer, t-bar ≈ 2/ln(1/rho): the implied kink densities (9e-5 to 4e-3) overlap published kink measurements, the excitation-floor form beats the constant-offset (noise) model on AIC for all four reported machines, and the logarithm compresses two and a half decades of rho into the narrow observed band, explaining its apparent universality. In the coherent nanosecond regime the closed-system law is an upper envelope on hardware inverse temperature; the shortfall is a candidate in-situ decoherence diagnostic, machine-resolved, and at the one matched cell where both machines are coherent the measured cross-machine ratio (2.63) agrees with the parameter-free prediction at the few-percent level. All hypotheses, tolerances, and kill criteria were registered before data extraction; failed and undecidable gates are reported alongside the successes. No quantum-advantage claim is made. AI use and validation: This work was produced in close collaboration with AI research assistants, directed by the author, who set the research direction, the standards of evidence, and all decisions about what is claimed and published. Anthropic's Claude (Fable 5) performed the analysis, simulation, extraction, and drafting; xAI's Grok (via Cursor) provided independent pre-publication review; and Anthropic's Claude Opus 5.5 performed a post-publication adversarial audit of the manuscript against its pinned evidence, with findings and dispositions logged in the project ledger and incorporated in subsequent versions. The registered-verdict protocol is designed so that no result rests on trusting a model's output: hypotheses, tolerances, and kill criteria were committed to the repository before any data was extracted; failed and undecidable gates are reported in the paper; every numeric claim traces to pinned, machine-readable extraction files and analysis code included in this deposit; figure data was extracted from the source PDFs' vector drawing operations rather than read by a model; and verbatim quotes were verified against raw page dumps.
A recent experiment [Le and Pelofske, arXiv:2512.19685] estimated the density of states and partition function of a 25-spin ±J Ising instance by reading raw energy histograms of D-Wave annealer samples, and highlighted a striking unexplained observation: the fastest anneals (8ns, within the coherent timescale of the device) gave the best estimates, reaching a log-relative error of 7.6 × 10−6. We show that no anomaly remains once two known ingredients are combined. First, a diabatic anneal is approximately a Boltzmann sampler whose inverse temperature βe is set by the annealing rate [Gyhm et al., arXiv:2409.18126]; we verify this in exact closed-system simulations at the experimental size n = 25, across two schedules, to sub-percent accuracy in the fast regime, and we measure the sampled ensembles to be uniform within energy shells to high precision, validating the energy-only description. Second, the raw-histogram estimator is unbiased only for a flat sampler: its bias is exactly φ(β + βe) − φ(βe) − φ(β), with φ(x) = ln⟨e−xE⟩unif, which grows linearly in βe while low-energy enrichment buys no compensating variance reduction for a Gaussian-like bulk. The fastest anneals are therefore accurate because they are nearly flat samplers sitting on the shot-noise floor; slow or strongly coupled anneals degrade exactly as observed; the interior optima in the reported cumulative sweeps are the bias–variance crossover of histogram pooling; and the headline 7.6 × 10−6 is consistent with the order statistics of a grid search over shot-noise-limited cells. The same analysis yields a free upgrade: because the schedule predicts each cell’s temperature, multi-histogram reweighting (WHAM) applies with rate-derived weights, converting the anneal-time ladder into a temperature ladder, removing the pooling bias by up to three orders of magnitude in our simulations, and extending accurate estimation toward temperatures where flat sampling fails. We state what the closed-system account does not explain as concrete, falsifiable predictions for reanalysis of the hardware data. AI use and validation: This work was produced in close collaboration with an AI research assistant (Anthropic's Claude, Fable 5), directed by the author, who set the research direction, the standards of evidence, and all decisions about what is claimed and published. The model performed analysis, simulation, and drafting under a registered protocol: hypotheses, tolerances, and kill criteria were committed to the repository before the experiments were run; validation scripts and their outputs are included in this deposit; and all results are reproducible from the code and data archived here.
Reverse annealing initializes a programmable quantum annealer in a chosen classical state, reintroduces quantum fluctuations down to a pause point, and returns to readout; repeated cycles form a configurable dissipative dynamics whose schedule knobs are routinely treated as a temperature. On mixed-frustration 12-qubit Ising instances on two D-Wave generations (Advantage2 and Advantage_system6.4), we measure schedule-driven redistribution of the subsystem readout and calibrate each schedule's effective scales, using exhaustive enumeration of the 212 configurations, a locked analysis plan with a prior-knowledge disclosure, and regenerated classical reference families. First, schedule shape redistributes basin occupation: 11 of 20 random instances respond to a single-pause-to-two-pause change (15 of 20 for long-hold; block permutation, FDR-controlled), with shifts up to 38 percentage points and changes of dominant-configuration identity. Second, the single-qubit probe temperature does not transfer to the many-body problem: moment-matched inverse temperatures span 0.63-9.1 against a probe value of 7.22, and pause depth and duration each shift the scale on most instances (19/20 and 15/20). Third, no observation requires more than the tested classical families: with update budgets extended below one sweep per cycle, all 33 (device, instance, schedule) cells are reproduced within the tested family (minimum intersection-union p=0.76), and schedule-aware spin-vector Monte Carlo brings the late-window statistics within semiclassical reach. A pre-registered linear predictor fails on held-out instances, and an earlier pilot's two-pause enhancement claim is contradicted (Fisher p=0.0013). Reverse-anneal schedules are instance-specific basin-occupation controls whose effective scales must be calibrated per instance and schedule; nothing here licenses a quantum-mechanistic reading.
Quantum annealers are emerging as programmable, dynamical experimental platforms for probing strongly correlated spin systems. Yet key thermal assumptions, chiefly a Gibbs-distributed output ensemble, remain unverified in the large-scale regime. Here, we experimentally and quantitatively assess Gibbs sampling fidelity across system sizes spanning over three orders of magnitude. We explore a wide parameter space of coupling strengths, system sizes, annealing times, and D-wave hardware architectures. We find that the naively assumed scaling law for the effective temperature requires a non-negligible, coupling-independent offset that is robust across machines and parameter regimes, quantifying residual non-thermal effects that still conform to an effective Gibbs description. These non-idealities are further reflected in a systematic discrepancy between the physical temperature inferred from the sampled ensemble and the nominal cryogenic temperature of the device. Our results systematically assess the viability of quantum annealers as experimental platforms for probing classical thermodynamics, correct previous assumptions, and provide a physically grounded thermometry framework to benchmark these machines for future thermodynamic experiments.
For a region of a free-fermion ground state the entanglement Hamiltonian K_A = log[(1 - C_A) C_A^-1] splits into a part proportional to the identity and a trace-free remainder. The identity part shifts every level rigidly, so every observable built from level differences is blind to it. This paper is about that part. It is not a bulk quantity. The block carries one ladder per entangling cut, the trace is the difference of the two cut-phase charges, and on the exactly dimerised chain with a single cut carrying the whole charge it has the closed form 2 artanh(v / sqrt(v^2 + t^2)), derived in one line and measured to 10^-11. In exact arithmetic the trace is a definite number: zero to thirty-three digits when the two cut phases agree, and 0.786153199019314523 when they do not. The apparent divergence reported in earlier work was double-precision truncation of a finite sum, and is retired here. Along the two lines through the Rice-Mele plane where the half-line entanglement Hamiltonian is known in closed form, it is proportional to the Bisognano-Wichmann deformation T = (1/2){X, H} with no additive constant, and the ladder spacing and phase are fixed by the literature. Between those lines the commuting operator survives, measured at 10^-13 against controls that fail at 1.5 and 29, but the proportionality does not: the level map acquires an intercept b that is zero to 3 x 10^-9 on both lines and of order 10^-1 in the interior, and is identical whether the region has one entangling cut or two. That intercept is the measured failure of exact Bisognano-Wichmann proportionality. At first order in the staggering v the intercept is derived rather than fitted. The symbol's determinant is det(z - P) = z(z - 1) independently of momentum, so the factorisation is canonical everywhere; its logarithm is affine in an involution R = H/E with R^2 = I; the abelian Szego-type boundary functional is identically even in v and therefore cannot carry an odd intercept; and the first-order piece follows from the chiral zero mode of the dimerised chain, whose amplitudes are (-r)^j C(2j,j) 4^-j in closed form. The result is b/v = 2(E' - K')/(1 - r^2) + K', K' = K(1 - r^2), E' = E(1 - r^2), r = t1/t2, whose expansion in the modulus u is, in exact rationals, h(u)/(pi/8) = 1 - (5/8) u^2 - (9/64) u^4 - (65/1024) u^6 - (595/16384) u^8 - ... So pi/8, -5/8 and -9/64 are consequences rather than recognitions, and the natural elliptic candidate [9E - K]/16 - pi/8 is excluded by 7.7 percent on the first coefficient it does not get to choose. The closed form agrees with direct measurement extrapolated to v -> 0 by two to three orders better than the fitted series it replaces; a previously reported u^6 coefficient of -0.0648 is corrected here to -65/1024 and identified as truncation. The trace-free half is treated in parallel. A Clausius relation with a single temperature holds exactly when that half is proportional to the region's own Hamiltonian. At a ground state it never is, and the measured temperature is zero, which is correct rather than a failure. In a thermal state the same instrument returns 1/beta to five significant figures, and the boundary of the region where it does so collapses onto two dimensionless ratios. Two further results are included. The offset vanishes when the two cuts sit at the same phase in the unit cell, without requiring chirality, time reversal, inversion or cleanliness, and a mirror-symmetrised disordered chain gives a larger offset than its unsymmetrised control, which rules reflection out as the mechanism. And in two dimensions the offset is exactly additive along the boundary for a transverse coupling proportional to the identity in sublattice space, for a reason short enough to state, with a derived crossing past which additivity fails and a sigma_z coupling that breaks it smoothly. Every claim carries one of four grades: [T] proven here, [V] computationally verified with stated controls and a stated failure mode, [C] imported from the cited literature, [H] interpretation. The two exact lines, the commuting deformation, the boundary-locality of the entanglement spectrum, and the first law of entanglement entropy are not this work's and are used as given. Sixteen retired claims, including two withdrawn from earlier versions of this manuscript, are listed with the measurement that killed each. Files in this deposit: the_offset_belongs_to_the_boundary_v8_submission.pdf — 35 pages, gate output verbatim, script listings supplied separately. the_offset_belongs_to_the_boundary_v8_complete.pdf — 59 pages, identical body with all scripts printed inline. offset_v8_scripts.zip — 23 files. Every number quoted in the paper is printed by one of them; the two gate files reproduce their stored output byte for byte. KEYWORDS entanglement Hamiltonian; entanglement spectrum; modular Hamiltonian; Bisognano-Wichmann; Rice-Mele model; SSH model; free fermions; boundary charge; cut-phase charge; corner transfer matrix; Toeplitz operators; Wiener-Hopf factorisation; Szego-Widom asymptotics; algebraic Heun operator; complete elliptic integrals; entanglement first law; area law; Landau-Widom counting function ADDITIONAL NOTES Supersedes earlier versions of this manuscript. Two claims present in versions 1 to 3 are withdrawn and recorded in the kill list: that the incommensurate offset has no value, and that the offset is one quantum. Both were double-precision truncation of a finite sum. The u^6 coefficient of the shape function reported in the companion results ledger is likewise superseded by the derived value. Computational verification, gating and drafting assistance by an AI collaborator (Claude, Anthropic). Every gate is independently re-runnable from the ancillary scripts.
CORRECTION NOTICE (v5, 2026-09-06). The central result of v1-v4 is WITHDRAWN. This record has not been peer reviewed. Issued 2026-09-06 by the author (v5 of this record). This notice was added to the archived record; the manuscript itself is unaltered. This record has not been peer reviewed. What is wrong The force exponent reported here as alpha = 3.92 +/- 0.16 is an artifact of the fitting procedure, not a property of the data. The fit was unweighted least squares in linear space applied to a steeply falling profile, which places 95.8 percent of its objective on the single point at the shortest retained separation. Re-fitting the same data with nothing discarded, changing only the error model, gives 2.82 (relative-error weighting) or 2.89 (log-space regression). Across fifteen combinations of standard estimator and fit window the exponent spans 2.53 to 3.92, and the value published here is the largest of them. What the data show instead, and how firmly The retraction is certain. The replacement is not. On the open 24-site chain the same data give alpha = 2.6 +/- 0.2, where the interval is the spread of a plateau in the local logarithmic slope over six consecutive separations, not a statistical error (the bootstrap error on the published fit to the same data is 0.63); the plateau value was reproduced at 2.5921 by a separately written implementation run on the same recorded state (SIM-2026-073). This is a single geometry at a single size. On a 24-site periodic ring, analysed with chord distance as pre-registered, two probes that are both energy-density-like (Delta = 1) give 1.83 and 2.37 against a CFT two-point value of 2 (SIM-2026-074): one size, not converged, disagreeing with each other by 29 percent, and not attributable to a single operator channel. No corrected exponent is established. The exchange channel is an open question. Treat 2.6 +/- 0.2 as the provisional open-chain value, not as a result. Also withdrawn or voided alpha = 3.92 +/- 0.16 (24 sites) and alpha = 3.97 +/- 0.15 (16 sites, exact) from stress-tensor exchange. Was: headline result and its first corroboration. Now: withdrawn. Why: the same estimator artifact: both move in lockstep under it (3.92 to 2.56, 3.97 to 2.75 on dropping the contact point), because they share one observable, one fit window and one fitting routine. scalar exchange (alpha = 2) excluded. Was: stated as excluded at about 12 sigma. Now: withdrawn. Why: the 12 sigma used the covariance error 0.16; at the bootstrap error 0.63 computed before release the exclusion is about 2.2 sigma, and under any window starting at separation 3 the point estimate itself falls to about 2.56. alpha = 4 is universal; alpha = 4.00 at Ising, tricritical Ising and Potts. Was: confirmed at three classes. Now: withdrawn; the operator towers at all three classes stand. Why: the exponent was measured only at Ising and inherited by the other two; the towers are spectra, not forces. third independent evaluation alpha = 4.07 (chi = 3 MERA), and with it the statement that this was the first holographic force measurement from an optimized tensor network state. Was: supporting evidence and a priority claim. Now: both withdrawn. Why: the profile changes sign inside its own fit window and cannot be a fixed-sign power law; the priority claim rests on that evaluation alone and was never gated against prior work. the discriminating test: stress tensor (Z_j Z_j+1) versus spin primary (X_j). Was: registered killer test. Now: void. Why: at the critical point these are one operator, related by exact Kramers-Wannier self-duality. Measured on the periodic ring: identical expectation values to 1e-15 and identical force profiles to 1e-13 at 14 sites, 2.4e-9 at 24 sites (SIM-2026-074). Open boundaries break the duality, which is why the open-chain run of this test (SIM-2026-073) showed a spurious difference between the two arms. The test compared the energy density to itself. Neither label was correct: Z_j Z_j+1 is the energy density, not the stress tensor; X_j is its dual, not the spin primary. transport time T = (pi/2) l_AdS to 1.2 percent as a geometric prediction. Was: confirmed. Now: measurement stands (T = 2.239 at N = 16); geometric reading not established. Why: l_AdS cancels in the cited derivation, which also gives pi rather than the pi/2 the manuscript compares against; the chi = 3 estimate of l_AdS gives a 57 percent miss; the transport driver never applies a MERA. The true spin primary Z_j was never in the design, and the direct replacement test is blocked: Z_j is odd under the Z2 symmetry, so the energy-difference observable used throughout this work subtracts across symmetry sectors and is undefined for it. A replacement test using two Z2-even probes has been pre-registered (PREREGISTRATION-T.md, committed before its driver) and run; its result is deliberately not part of this correction and will appear in a later version. Not previously reported The published fit has a reduced chi-squared of 6.008 on 9 degrees of freedom, and a bootstrap standard deviation of 0.63 rather than the quoted 0.16. Both were computed before release and omitted. What is unaffected Of the claims in this record: the two-phase optimization method, the chi = 3 criticality threshold, the exact-diagonalization gates, the measured OPE coefficient C_sigma-sigma-epsilon = 0.50 +/- 0.03 against the exact 1/2, and the conformal towers at all three classes. Not part of this record, mentioned only because they are sometimes read together with it: the later C_TTT stress-tensor self-coupling measurements (SIM-2026-067/068/069, dated after this record) and the matched off-critical ring control (SIM-2026-074) are unaffected by this correction and make no claim about the force exponent. How the error was found and what this record contains The error was found by the author's own internal adversarial audit, not by a reviewer; the journal submission it was found after is closed, and no review of this work has taken place. Files in this record: the full re-analysis (SIM-2026-072.json, driver, figure), the pre-registered chain test (SIM-2026-073.json) and ring test (SIM-2026-074.json) with both pre-registrations as committed before the runs, the runnable drivers with their shared module and the negative test suite for their validation gates, and the error register (ERRATA.md). Concept DOI 10.5281/zenodo.19660302 always resolves to the current version. The abstract of the original manuscript follows unchanged, for the record. Every claim in it about the force exponent should be read against the correction above. We report results from classical simulation of critical spin chains that establish quantitative physical content in the MERA-AdS correspondence. First, the interaction energy between boundary-primary excitations follows a power law F(dr) ~ dr^(-alpha) with three consistent evaluations yielding alpha = 3.92 +/- 0.16 (24q), 3.97 +/- 0.15 (16q), and 4.07 +/- 0.18 (16q chi=3 MERA), all consistent with stress-tensor exchange (alpha = 2*Delta_T = 4) and inconsistent with scalar exchange (alpha = 2); the exponent is explained by the Ising CFT fusion rule eps x eps = [1]. Because Delta_T = 2 is fixed by conformal symmetry in every unitary 2D CFT, alpha = 4 is universal: we confirm this at two further fixed points - the tricritical Ising model (c = 7/10), where a scale-invariant MERA recovers the full M(4,5) primary spectrum (Delta_sigma = 0.092, Delta_eps = 0.204, Delta_T = 1.999), and the three-state Potts model (c = 4/5), where a Z3-symmetric MERA at chi = 12 recovers Delta_sigma = 0.134, Delta_eps = 0.805, Delta_T = 2.001 - giving alpha = 4.00 at all three universality classes. Second, the holographic transport time matches the AdS_3 null geodesic prediction T = (pi/2) l_AdS to 1.2% at N = 16 sites on a time-grid-converged measurement, with the residual shrinking from 2.8% at N = 12. Third, we introduce a two-phase optimization method (ALM + Z2 projection) for Z2-symmetric MERA ground states at 24 qubits. Fourth, extending the MERA bond dimension from chi=2 to chi=3 overcomes the expressibility barrier, achieving 0.15% energy error at 16 qubits and enabling the first holographic force measurement from an optimized tensor network state. The OPE coefficient is also measured directly from the fixed-point tensors: C_sigma-sigma-eps = 0.50 +/- 0.03 against the exact Ising value 1/2. A hardware path is designed for Quantinuum Helios (57 CNOTs, 0.57% logical error). Version 4 changes (relative to v3): Transport: N=16 residual restated as the time-grid-converged value of -1.21% (dt = 1e-3), with -2.78% at N=12 showing the finite-size trend; the 0.72% figure in v3 was an artifact of the dt = 0.05 integration grid and is now labeled as such. The N=24 transport point carries a new reliability caveat (double-lobe trace structure). The l_AdS comparison table is recomputed against the converged transport time (best fit 1.425, deviation 1.21%). Effective-mass derivation rewritten in a consistent AdS3 convention m^2 l^2 = Delta(Delta-2); m_eff = 0.693 = 1/l_AdS follows from Delta = 1 exactly. NEW: universality section extended to a third fixed point - a Z3-symmetric MERA at chi = 12 recovers the three-state Potts (c = 4/5) tower, giving alpha = 4.00 at all three universality classes (c = 1/2, 7/10, 4/5). NEW: the OPE coefficient C_sigma-sigma-eps = 0.50 +/- 0.03 measured directly from the fixed-point tensors, with C_sigma-sigma-sigma = 0 at machine precision as the Z2 structural check. Supplemental table row SIM-007 annotated (record lost; script preserved); data availability expanded; Zenodo DOI added to the front matter.
Understanding the physical nature of the D-Wave annealers remains a subject of active investigation. In this study, we analyze the sampling behavior of these systems and explore whether their results can be replicated using quantum and Markovian models. Employing the standard and the fast annealing protocols, we observe that the D-Wave annealers sample states with frequencies matching the Gibbs distribution for sufficiently long annealing times. Using Bloch equation simulations for single-qubit problems and Lindblad and Markovian master equations for two-qubit systems, we compare experimental data with theoretical predictions. Our results provide insights into the role of quantum mechanics in these devices.