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REVIEW 4 major objections 3 minor 14 references

Observable Estimation in the Absence of Classical Verification

T0 review · 4 major / 3 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read This paper claims that quantum estimates of observables can be judged credible without any classical ground truth, by testing the noise assumptions behind error mitigation on the target circuit itself.

desk verdict Real validation framework for unbenchmarkable quantum estimates; the most-credible claim is conditional but honestly argued and worth a serious referee. read the letter →

arxiv 2607.25998 v1 pith:IFZPLMHU submitted 2026-07-28 quant-ph

Samantha V. Barron , Bradley Mitchell , Vinay Tripathi , Francesco Grieco , Ilan Rosen , Francesca Pietracaprina , Davide Materia , Alireza Seif
show 40 more authors
Darvin Wanisch Ramón L. Panadés-Barrueta Ewout van den Berg Jay-U Chung Andrew Eddins Sam Ferracin Guillermo García-Pérez John Goold Luke C. G. Govia Holger Haas Ian Hincks Jesse C. Hoke Zoë Holmes Su-un Lee Youngseok Kim Swarnadeep Majumder Sabrina Maniscalco Simone Montangero Daniel Puzzuoli Tomaž Prosen James Raftery Ricardo Rivera Cardoso Max Rossmannek Manuel Rudolph Brendan Saxberg Liran Shirizly Karthik Siva Joshua Skanes-Norman Ilaria Siloi Kevin C Smith Boris Sokolov Maika Takita Yanting Teng Mao Tian Tan Joseph Tindall Zoltán Zimborás Matteo A.C. Rossi Minh C. Tran Sergei N. Filippov Abhinav Kandala
This is my paper
classification quant-ph PACS 03.67.-a
keywords operatorLoschmidtechoquantumerrormitigationglobalrescalingprobabilisticcancellationPauli-Lindbladnoisemodelsemi-scramblingdynamicsverificationnoise-modelvalidation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks how to trust a quantum computer's estimate of an observable when no classical method can verify it. It answers by proposing a hierarchy of tests that interrogate the assumptions of error-mitigation heuristics directly on the target circuit, rather than on classically simulable stand-ins. Applied to a 56-qubit operator Loschmidt echo experiment, these tests support the claim that the rescaled quantum estimate is the most credible among several leading classical heuristics, which disagree sharply in the intermediate regime. The paper further shows how probabilistic error cancellation, with a carefully validated noise model, can attach quantitative error bounds to such estimates, converting the question "is the quantum answer right?" into "is the noise model right?"

What carries the argument

The central object is the operator Loschmidt echo Sδ = 2^{-n} Tr(U†OU Vδ† U†OU Vδ), an overlap between an evolved observable and its perturbed echo; unlike the state echo, it decays only polynomially with perturbation support, so it survives hardware noise. The first mechanism is global rescaling: noise is assumed to attenuate the echo by a factor α independent of probe strength δ, estimated from the δ=0 signal and divided out. The second is probabilistic error cancellation with a sparse Pauli–Lindblad noise model, which replaces the assumption with a validated noise model and provides confidence intervals.

What would settle it

Measure the L=6 echo at two probe strengths (δ=0 and δ=0.3) while deliberately adding a known coherent error common to both, such as a fixed single-qubit over-rotation in every CZ layer. If the ratio of the two decay factors changes as the injected error grows, the attenuation factor is δ-dependent and the rescaled curve is biased.

Watch

Extended reading notes

Core claim

Central claim: for the 56-qubit operator Loschmidt echo at depth L=6, the globally rescaled quantum measurement is the most credible estimate among all methods tested. Without any exact classical benchmark, the authors show the rescaling tracks converged classical results at shallow depths, is stable under deliberate noise changes (gate duration, a second processor, synthetic noise), and obeys the assumed δ-independence of the noise attenuation factor. A separate arm, probabilistic error cancellation with a validated sparse Pauli–Lindblad noise model, adds error bounds and agrees with classical results where available. Trust follows from noise-model validation, not classical agreement.

Load-bearing premise

The rescaling estimate rests on the assumption that hardware noise attenuates the echo signal by a factor that does not depend on the probe strength δ; this is tested directly only at shallow depths, while at L=6 it is inferred from cross-device consistency.

Editorial extensions

If this is right

  • Quantum estimates can be declared credible in regimes where all classical heuristics disagree, provided they pass noise-manipulation consistency tests on the target circuit.
  • The global rescaling estimate costs only one extra measurement at δ=0 and needs no classical simulation, making it a practical validation tool for echo-type signals.
  • PEC-based error bounds shift the burden of proof from reproducing a classical answer to characterizing the hardware noise accurately.
  • The operator Loschmidt echo provides an experimentally accessible probe of operator spreading and backflow at scales where state Loschmidt echoes are unmeasurable.
  • Classical heuristic developers can use the same validation hierarchy, and well-characterized quantum experiments can in turn benchmark novel classical approximations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The validation hierarchy generalizes beyond this observable: any heuristic error-mitigation method could be trusted by showing stability under controlled noise manipulation, even when no classical check exists.
  • If δ-independent attenuation continues to hold at deeper circuits, global rescaling may combine with PEC to produce bounded estimates for a wide class of echo observables, not just the operator Loschmidt echo.
  • A sharp test of the framework would be to apply it to an observable with a known exact value at large depth, such as a conserved quantity, and check whether the stability tests still predict credibility.
  • The paper's logic inverts the usual verification arrow: once quantum estimates are trusted, they become references for classical simulation development, potentially accelerating progress on both sides.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper proposes a validation framework for quantum-computed observables in regimes where no reliable classical benchmark exists. It applies this framework to a 56-qubit semi-scrambling Floquet circuit, measuring an operator Loschmidt echo (OLE) and estimating the signal via a global-rescaling error-mitigation heuristic. The quantum estimate is compared with TN-BP, PP-MC, MPS, TTN, quarter-out Pauli propagation, and a full-scrambling analytical value; the authors claim that at depth L=6 the quantum experiment is the most credible of the methods tested, based on shallow-depth agreement, noise-manipulation stability, and cross-device consistency. A second method, PEC with a validated sparse Pauli-Lindblad noise model, provides error-bounded estimates at L=2 and L=4, with extensions to larger depth only projected.

Significance. If the framework is accepted, it offers a genuinely useful alternative to the circular standard of validating a quantum computation by agreement with a classical calculation. The paper's strengths include an honest and unusually thorough multi-method classical benchmarking campaign, direct tests of the rescaling assumption at shallow depth, cross-device and synthetic-noise manipulations, a meticulous PEC noise-model validation suite (Pauli-ness, sparsity, Markovianity, Cliffordization), and the introduction of the OLE as a hardware-accessible probe of operator dynamics. The manuscript is also commendably candid about the failures and non-convergence of the classical heuristics it considers. However, the strongest claim — that the L=6 quantum estimate is the most credible method — rests on an assumption whose direct verification is limited to depths L≤4.

major comments (4)
  1. [Building trust in the quantum estimate, Fig. 2(d)] The L=6 cross-device consistency check is a relative test. It compares decay factors across noise profiles after referencing to ibm_boston, and can therefore only test whether alpha_delta/alpha_0 is the same for the different profiles; it cannot detect a delta-dependent attenuation that is common to all profiles. A concrete mechanism exists: the perturbation V_delta is implemented as RX(delta) gates on 35 qubits, while at delta=0 these gates are absent. Errors in those RX gates (including coherent or angle-dependent errors) enter S~_delta but not S~_0, so alpha_delta/alpha_0 could deviate from 1 by a common factor across all devices and synthetic noise settings. The direct delta-independence test in Fig. 2(b) is performed only at L=3,4. Thus the headline L=6 curve in Fig. 1(e) may carry an unquantified systematic bias, and the statement that the quantum estimate is 'the most credible of
  2. [Building trust in the quantum estimate, Fig. 2(c)] The collapse of the globally rescaled signals under hardware changes and synthetic noise injections is evidence that the attenuation factor is stable with respect to the noise profile, but it is not evidence that the attenuation factor is delta-independent. The text says these manipulations 'provide evidence that the global rescaling captures the dominant effect of noise on the target circuits'; this conflates profile-independence with delta-independence. The caption and main text should distinguish the two, since the delta-independence of alpha is the assumption needed for the global-rescaling estimator S_delta ≈ S~_delta / S~_0.
  3. [Towards estimation with error bounds, Figs. 3(f)-(g)] The PEC error bounds are demonstrated only at L=2 and L=4, where converged TN-BP reference values exist. The L=6 target regime of Fig. 1(e) receives no PEC data; the text only says (App. F) that extending to L=6 would require 'modest reductions to hardware error rates'. Consequently the paper offers no quantitative accuracy statement for its central L=6 observable estimate. This is not a flaw in the PEC methodology, but it should be stated explicitly in the main text that the 'most credible' claim at L=6 is a heuristic, consistency-based claim without a numerical error bound.
  4. [Classical benchmarking, Table I vs. main text] The main text states that at L=4 'TN-BP converges at a modest bond dimension chi=128 (fidelity above 0.97)', but App. B reports f≈0.974 only at chi=768 (Table I), and Fig. 10 suggests the fidelity at chi=128 is substantially lower. This discrepancy matters because Fig. 2(a) uses TN-BP at chi=128 as the ground truth for L=4. Please clarify the fidelity at chi=128 and, if it is not above 0.97, either adjust the shallow-depth claim or use a higher bond dimension for the L=4 reference.
minor comments (3)
  1. [Fig. 2(d), caption and axis definition] Please define precisely what 'decay factor' means when the ideal S_delta is unknown at L=6. Is it the ratio of the unmitigated signal to the globally rescaled ibm_boston reference? Without an explicit definition, the y=x line is ambiguous.
  2. [Eq. (1) and circuit notation] Eq. (1) writes the OLE in terms of a generic U and V_delta, while the experiment uses U = U0^dagger U_eta and V_delta placed in the middle of the echo. The main text introduces this later, but the reader would benefit from a one-line statement after Eq. (1) that the experimental circuit is a specific instance of this definition.
  3. [Appendices B and C] The appendix results would be easier to navigate if each classical method included a one-sentence bottom-line statement in the main text (e.g., 'MPS and TTN fail already at L=3-4'). Most of this information is present in the appendices but is slow to extract.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the quantum estimates are constructed from explicit, tested assumptions and validated against independent classical/exact references.

full rationale

The paper's central estimates are not forced by construction. Global rescaling is an explicit heuristic: ˜S_δ ≈ α S_δ with α estimated at δ=0, and the assumption of δ-independent attenuation is directly tested at L=3,4 against converged TN-BP and probed at L=6 via noise-manipulation stability and cross-device consistency. The cross-device consistency check treats the rescaled ibm_boston signal as a reference and cannot exclude a common δ-dependent bias; the paper itself acknowledges that small-scale tests 'do not directly validate its assumptions on the target circuits.' That is an honest limitation and a correctness risk, not a circular reduction: no equation or fitted parameter equals the claimed prediction by definition. The PEC estimates are learned from independent calibration/cycle-benchmarking data and then validated on Cliffordizations, exact δ=0 signals, and converged TN-BP at L=2,4, which are out-of-sample checks relative to the fitted noise parameters. Self-citations to prior work on sparse Pauli–Lindblad models and global rescaling are supportive but not load-bearing, since the present paper contains its own validations. The manuscript explicitly identifies and avoids the circular standard of judging a quantum computation trustworthy only when it agrees with a classical calculation. No step in the claimed derivation chain reduces to its own input.

Assumptions & free parameters 5 free parameters · 8 assumptions · 1 invented entities

The paper's headline heuristic (global rescaling) is parameter-free: alpha is measured at delta=0 where the ideal signal equals 1 exactly, and the delta-independence assumption is tested rather than fitted. The main fitted quantities are the sparse Pauli-Lindblad noise coefficients, learned from independent calibration circuits and validated out-of-sample (Fig. 3b-f). Invented physical entities: none — the model is a standard Floquet kicked-Ising construction with hand-chosen angles, and the OLE is observable. The dominant domain assumptions are the transfer of heuristics from validated regimes (shallow depth, auxiliary circuits) to the target L=6 circuits, and the claim that noise manipulation perturbs only the noise.

free parameters (5)
  • Transverse-field angles (h, b1, b2) = h=pi/8, b1=3pi/16, b2=0.125
    Hand-chosen (App. A2c) to place the model in the semi-scrambling regime where classical methods diverge yet the echo signal survives noise; engineered for the benchmark, not fitted to the target observable.
  • Circuit geometry (VS, VP, VO) = |VS|=11, |VP|=35, |VO|=12
    Scattering, perturbation, and observable supports selected by hand; layout 'chosen and optimized to maximize the overall fidelity' (Quantum experiments section), with the observable on a 'fast loop.'
  • Sparse Pauli-Lindblad noise coefficients = per-gate Pauli error rates (Fig. 3a)
    Learned from cycle-benchmarking calibration circuits, not from the target observables; held fixed for PEC prediction. A legitimate out-of-sample fit that the paper validates, but PEC error bars inherit its accuracy.
  • Classical method truncations (chi, M, rc) = chi<=980; M<=5e8; rc in {5e-2, 1e-2}
    Truncation budgets of the classical benchmarking methods (TN-BP bond dimension, PP-MC cache, quarter-out coefficient threshold). These affect the classical estimates, not the quantum observable, but they set the terms of the 'most credible' comparison.
  • Global rescaling factor alpha ~ S~_0 = measured, not fitted (S~_0 at delta=0)
    Deliberately parameter-free: measured at delta=0 where the ideal signal S0=1 is known exactly; the delta-independence of alpha is the tested assumption, not a fitted constant.
assumptions (8)
  • standard math The OLE estimator (Eq. A6) converges to the operator trace: averaging eigenstate parities implements 2^{-n}O in the M->infinity limit.
    App. A1a; standard ensemble representation of an operator as a signed mixture of density operators; exact in the sampling limit.
  • domain assumption Noise attenuation of the OLE signal is approximately independent of probe strength delta (global rescaling assumption: S~_delta ~ alpha*S_delta).
    Main text 'Quantum experiments'; tested directly at L=3,4 (Fig. 2b) and by cross-device consistency at L=6 (Fig. 2d); cannot be absolutely verified at L=6.
  • domain assumption Device noise is Markovian, stochastic-Pauli, and sparse-local, represented by a sparse Pauli-Lindblad model.
    Main text 'Towards estimation with error bounds'; supported by Pauli-ness (Fig. 3b), sparsity (Fig. 3c), Markovianity with post-selection (Fig. 3d), Cliffordization (Fig. 3e), delta=0 analytics (Fig. 3f).
  • domain assumption The TN-BP fidelity estimator (Eq. B1) is a reliable convergence proxy for choosing trustworthy classical ground truth.
    App. B1a: the paper states the estimator 'is neither exact nor a guaranteed lower bound'; it certifies the L<=4 comparisons that anchor both validation figures (Fig. 2a, Fig. 3g).
  • domain assumption Off-diagonal OTOC contributions are negligible for the PP-MC diagonal approximation.
    App. C1b; supported by BP numerics at L=3 (Fig. 16), assumed to hold at L=6 where BP no longer converges.
  • standard math S_delta ~ 1 - delta^2*C/2 with higher-order moments resummed (OLE-OTOC expansion).
    App. A1c, Eq. (A10); commutator expansion; the paper retains moments up to order 2m~16-20 where needed (App. C5).
  • domain assumption The noise channel is stable over the ~45-minute recharacterization interval.
    App. E7; supported indirectly by successful PEC recovery at delta=0 (Fig. 3f) and by electrode-bias modulation [17].
  • domain assumption Noise manipulation (gate duration, device, synthetic Pauli insertion) modifies only the noise, leaving the ideal signal unchanged.
    Underpins Fig. 2c-d reproducibility evidence; if coherent transient errors (App. E3) change with gate duration, the ideal OLE could differ across settings.
invented entities (1)
  • Operator Loschmidt echo (OLE) as a hardware-implemented probe independent evidence
    purpose: Measurable overlap of an evolved operator with its perturbed echo; the central observable that remains resolvable on noisy hardware at scale.
    The OLE is directly measurable — that is its falsifiable handle — but it is a constructed observable, not a new physical entity. The quantity itself predates this paper (refs [40,41] per App. A1); the contribution is the 56-qubit ensemble-based implementation.

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Cite this review

Pith. "Pith review of Observable Estimation in the Absence of Classical Verification." pith.science (2026). https://pith.science/paper/IFZPLMHU

@misc{pith2026260725998,
  author       = {Pith},
  title        = {Pith review of: Observable Estimation in the Absence of Classical Verification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IFZPLMHU}},
  note         = {Machine review of arXiv:2607.25998}
}
read the original abstract

The predictive success of quantum mechanics underpins many areas of modern science, even as the exact simulation of large, interacting quantum systems remains beyond the reach of classical computation. This success has been enabled by the remarkable advancement of scalable numerical approximation methods, which often demonstrate practical accuracy despite the absence of formal guarantees. As quantum simulation pushes into regimes where these approximations struggle, a fundamental challenge arises: How can quantum outcomes be trusted when reliable classical benchmarks are unavailable? Here, we establish a framework for the independent validation of quantum estimates in this setting and present evidence that they provide the most credible result among several considered methods, in the absence of an immediately accessible ground-truth solution. We apply our framework to the semi-scrambling dynamics of a physical model that strains several leading classical simulation methods yet remains experimentally accessible, in part through our introduction of the \textit{operator Loschmidt echo}. We systematically design a series of experiments using quantum heuristics that, taken together, test the underlying assumptions and provide strong confidence in the observable estimates obtained from the quantum computer. We then show how this framework can be extended to place accuracy bounds on quantum estimates via careful characterization and manipulation of the device noise, transforming the problem of validating the observable estimation to validating the noise model. These results establish a route towards trusted quantum computation for scientific discovery, independent of classical verification.

Figures

Figures reproduced from arXiv: 2607.25998 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Quantum circuits to compute the OLE signal, i.e. the overlap between an observable and its echoed version. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. (d). These hardware-level and controlled noise manipulations provide evidence that the global rescal￾ing captures the dominant effect of noise on the target circuits. Towards estimation with error bounds: The val￾idation of global rescaling’s assumptions provides con￾fidence in its estimate, which is now the most credible among the methods considered. Yet, this estimate lacks a quantitative statement of its accuracy… view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (34 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. BP simulation results compared to the experimental data from [PITH_FULL_IMAGE:figures/full_fig_p022_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Panel (a): infidelity as a function of inverse [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. OLE signal as a function of inverse bond dimension 1 [PITH_FULL_IMAGE:figures/full_fig_p023_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. MPS simulations of the circuit under different qubit orderings. We show the four qubit orderings considered, overlaid [PITH_FULL_IMAGE:figures/full_fig_p027_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. MPS results compared to BP and the experimental values for the circuits with 2,3,4 and 6 Floquet layers respectively [PITH_FULL_IMAGE:figures/full_fig_p029_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Convergence of the MPS method for the three best orderings, spectral (panel (a)), RCM (panel (b)), and ann-opt [PITH_FULL_IMAGE:figures/full_fig_p030_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Comparison of annealing-optimized orderings ann-opt and ann-opt-g for the TTN ansatz with BP and experimental [PITH_FULL_IMAGE:figures/full_fig_p030_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. In this picture we numerically demonstrate with TN simulations that the contribution of off diagonal terms to the [PITH_FULL_IMAGE:figures/full_fig_p034_16.png]
Figure 17
Figure 17. Figure 17: FIG. 17. Convergence of the hybrid PP-MC signal [PITH_FULL_IMAGE:figures/full_fig_p045_17.png]
Figure 18
Figure 18. Figure 18: FIG. 18. Per-sample OTOC ( [PITH_FULL_IMAGE:figures/full_fig_p046_18.png]
Figure 19
Figure 19. Figure 19: FIG. 19. Quarter-out unitary expansion, normalization comparison. (a) OTOC versus [PITH_FULL_IMAGE:figures/full_fig_p046_19.png]
Figure 20
Figure 20. Figure 20: FIG. 20. Truncation dependence of the quarter-out expansion at sc = 0 [PITH_FULL_IMAGE:figures/full_fig_p047_20.png]
Figure 21
Figure 21. Figure 21: FIG. 21. OLE signal [PITH_FULL_IMAGE:figures/full_fig_p048_21.png]
Figure 22
Figure 22. Figure 22: FIG. 22. Collection of all methods used to compute the OLE signal for the [PITH_FULL_IMAGE:figures/full_fig_p049_22.png]
Figure 23
Figure 23. Figure 23: FIG. 23. The 56 qubits of [PITH_FULL_IMAGE:figures/full_fig_p051_23.png]
Figure 24
Figure 24. Figure 24: FIG. 24. Cumulative distribution functions of the coherence times of the 56 qubit sections on (a) [PITH_FULL_IMAGE:figures/full_fig_p051_24.png]
Figure 25
Figure 25. Figure 25: FIG. 25. Cumulative distribution function of CZ gate errors due to pulse transients as a function of delay time between CZ [PITH_FULL_IMAGE:figures/full_fig_p052_25.png]
Figure 26
Figure 26. Figure 26: FIG. 26 [PITH_FULL_IMAGE:figures/full_fig_p053_26.png]
Figure 27
Figure 27. Figure 27: FIG. 27. (a) The unmitigated signal of the weight-12 observable at [PITH_FULL_IMAGE:figures/full_fig_p053_27.png]
Figure 28
Figure 28. Figure 28: FIG. 28. Histograms of model agreement for stabilizers for the Cliffordization circuits for [PITH_FULL_IMAGE:figures/full_fig_p055_28.png]
Figure 29
Figure 29. Figure 29: FIG. 29. PEC Experiment execution workflow. Data is repeatedly collected in “super-batches”, which comprise of a noise [PITH_FULL_IMAGE:figures/full_fig_p056_29.png]
Figure 30
Figure 30. Figure 30: FIG. 30. Left panels: Noise learning traces over the course of an example experiment. Different colors correspond to different [PITH_FULL_IMAGE:figures/full_fig_p056_30.png]
Figure 31
Figure 31. Figure 31: FIG. 31. Model Agreement and PEC stability. (a) Model agreement for the [PITH_FULL_IMAGE:figures/full_fig_p057_31.png]
Figure 32
Figure 32. Figure 32: FIG. 32. Shaded lightcone (SLC) for PEC. (a) The SLC of a representative weight-one observable shown at several CZ layers [PITH_FULL_IMAGE:figures/full_fig_p058_32.png]
Figure 33
Figure 33. Figure 33: FIG. 33. (a) Projected quantum-processor runtime for PEC without SLC to reach a target standard error on the OLE [PITH_FULL_IMAGE:figures/full_fig_p059_33.png]
Figure 34
Figure 34. Figure 34: FIG. 34. Propagation of statistical fluctuation and bias from the noise model to error bounds on the PEC mitigated estimates [PITH_FULL_IMAGE:figures/full_fig_p060_34.png]
Figure 35
Figure 35. Figure 35: FIG. 35. A histogram of the bootstrapped standard deviations due to shot noise of the largest 50% of the learned rates. The [PITH_FULL_IMAGE:figures/full_fig_p060_35.png]
Figure 36
Figure 36. Figure 36: FIG. 36. Sub-lattice variants of the full 56-qubit OLE circuit. Gray circles indicate qubits that remain in the sub-lattices. [PITH_FULL_IMAGE:figures/full_fig_p061_36.png]
Figure 37
Figure 37. Figure 37: FIG. 37. Difference in the globally rescaled signal at [PITH_FULL_IMAGE:figures/full_fig_p062_37.png]

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Reference graph

Works this paper leans on

14 extracted references

  1. [1]

    thepair-diagonalapproximation ofb 2 P [Eq. (C67)], which retains only them=a,n=bcontributions and lets each pair (a, b) contribute independently, reducing the cost from quartic to quadratic and, crucially, letting 45 1 0.12 0.14 0.16 0.18 0.20OLE signal S( = 0.3) (a) 5M 50M 250M500M cache size M 10 20 30 truncation order 2kmax 1.5 1.0 0.5 0.0 0.5 1.0 1.5 ...

  2. [2]

    cores/job

    theapproximate self-normalizationN approx = P a |ca|2 2 =∥ ˜U∥ 4, obtained by applying the same pair- diagonal truncation to the normN( ˜U †O ˜U) = P P b2 P [Eq. (C64)]. Since the physical (normalized) estimator divides the raw pair sum by this normalization, ˆC approx 2,diag of App. C 3, and likewise every higher momentC 2m that entersS δ, the choice ofN...

  3. [3]

    The labelquarter-outrefers to how the operator propagation is initialized at the seam between the two halvesU 0 andU † η of the evolution

    Unitary ‘quarter-out’ propagation We now consider an alternative propagation strategy based on expanding the unitaryU=U † 0 Uη itself into Pauli strings rather than sequentially propagating Pauli operators. The labelquarter-outrefers to how the operator propagation is initialized at the seam between the two halvesU 0 andU † η of the evolution. At a high l...

  4. [4]

    In addition to previously discussed methods, we have systematically explored other variants that led to less promising results

    Summary of Pauli propagation variants explored Table V collects the Pauli-propagation variants we examined, organized along two largely independent axes: how the operator expansion is approximated, and which operator is evolved through the circuit. In addition to previously discussed methods, we have systematically explored other variants that led to less...

  5. [5]

    C 2) and the quarter-out unitary expansion (App

    Additional numerical studies of Pauli propagation methods We now report the numerical performance of the two adopted Pauli-propagation variants, hybrid PP-MC (App. C 2) and the quarter-out unitary expansion (App. C 3), on the target semi-scrambling OLE circuits, and compare them against theibm bostonhardware data. Unless stated otherwise, all results are ...

  6. [6]

    Both devices are Heron (R3) architectures comprising 156 fixed- frequency transmon qubits arranged in a heavy-hexagonal connectivity

    Superconducting Quantum Hardware Experiments were performed onibm bostonandibm pittsburgh, which are superconducting quantum processors available through the IBM Quantum Platform. Both devices are Heron (R3) architectures comprising 156 fixed- frequency transmon qubits arranged in a heavy-hexagonal connectivity. Qubit coherence times are shown in Fig. 24....

  7. [7]

    Therefore, the CZ gates were calibrated with identical pulse duration and parallelized using the three sets of matching batches of gates [4]

    Two-Qubit Gate Calibrations The OLE circuit consists of repetitions of three unique layers of CZ gates. Therefore, the CZ gates were calibrated with identical pulse duration and parallelized using the three sets of matching batches of gates [4]. Calibration included optimization of theZZ,IZ, andZIrotation angles effectuated by the gate pulse, as determine...

  8. [8]

    Figure 25 demonstrates transient gate errors as a function of delay times between CZ gates

    Gate T ransient Errors Pulse transients due to signal distortions in flux control lines may impart coherent errors to CZ gates and are a source of non-Markovianity that is particularly a challenge for noise learning and PEC. Figure 25 demonstrates transient gate errors as a function of delay times between CZ gates. This implies that the noise model learne...

Show all 14 references
  1. [9]

    Noise stabilization For PEC experiments, drift in the landscape of two-level system defects (TLS) between noise model learning and target-circuit execution could cause changes in the noise channel and therefore invalidation of the learned model. To stabilize the noise channel,...

  2. [10]

    node-based

    Post-selection of non-Markovian leakage errors Error mitigation protocols often rely on having a representative model of the device noise that is informed by an experimental noise learning step. An efficient Pauli noise-learning protocol based on the sparse Pauli-Lindblad nois...

  3. [11]

    Recall that the OLE circuits are decomposed into CZ, R Z(2h), and RX (2b) whereh=π/8 andb∈ {b 1, b2, b1 −η}

    Cliffordizations In our experiments, we useCliffordizationsof our target circuit to calibrate and validate the noise models [112]. Recall that the OLE circuits are decomposed into CZ, R Z(2h), and RX (2b) whereh=π/8 andb∈ {b 1, b2, b1 −η}. A Cliffordization of the OLE circuit ...

  4. [12]

    Model Fit Observables

    Maintaining an Accurate Noise Model In the idealized limit where the learned noise model coincides with the true device noise, probabilistic error cancellation (PEC) yields unbiased expectation values with rigorous error bounds [14]. In practice, however, device noise may have...

  5. [13]

    Current rates

    Shaded lightcones Standard PEC [14, 15] inverts every error channel in the circuit, including channels that commute with the observable and therefore leave its expectation value unchanged. Mitigating these channels wastes sampling overhead. The Shaded Lightcone (SLC) [31, 119]...

    2000

  6. [14]

    39q” “44q 0

    Error propagation As mentioned earlier, if noise learning were exact, the error of a PEC-mitigated estimate would be purely statistical. In practice the learned ratesλ P carry both statistical uncertainty, from the finite number of cycle-benchmarking shots, and systematic erro...

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.