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REVIEW 2 major objections 5 minor 1 cited by

Physics-inspired Machine Learning for Quantum Error Mitigation

T0 review · 2 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A neural network built on the noise-accumulation recursion cuts error-mitigation error by 65.85% over noisy baselines and by 35.12% over the best QEM methods in simulation.

desk verdict Novel architecture and solid simulations, but the central mitigation formula doesn't follow from the paper's own noise model and the exact trained model is under-specified. read the letter →

arxiv 2501.04558 v1 pith:IQWA6UD5 submitted 2025-01-08 quant-ph

Xiao-Yue Xu , Xin Xue , Tianyu Chen , Chen Ding , Tian Li , Haoyi Zhou , He-Liang Huang , Wan-Su Bao This is my paper · ORCID
classification quant-ph
keywords quantumerrormitigationmachinelearningforneuralnoiseaccumulationsurrogaterecurrentnetworkattentionmechanismTrotterizedcircuitsmetrology
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

NNAS is a recurrent network whose hidden state follows the layer-by-layer recursion of quantum noise accumulation, and the paper's core claim is that this physical prior makes quantum error mitigation (QEM) both more accurate and dramatically cheaper. The authors isolate each noisy layer's identity part through maximum noise decomposition, $E_l=(1-p_l)I+p_l\Lambda_l$, derive a recursive update for cumulative noise $N_l$, and map that recursion onto an RNN with an attention-assisted readout. In numerical experiments on six-qubit Trotterized circuits of a transverse-field Ising model, NNAS reduces mean absolute error by 65.85% relative to the noisy result and by 35.12% relative to the best of the standard QEM and random-forest baselines, with the largest gains beyond 15 Trotter steps. The paper also reports that NNAS keeps its accuracy with an order-of-magnitude smaller training set and pays one to two orders of magnitude less sampling overhead than standard QEM, and that the same architecture transfers to GHZ-state quantum metrology.

What carries the argument

The load-bearing object is the cumulative noise recursion $N_l=(1-p_l)N_{l-1}+p_l(\prod_{j<l}(1-p_j))a_l+p_l a_l N_{l-1}$, with $a_l=U_l^\dagger\Lambda_l U_l$, which follows from splitting each layer's CPTP channel as $E_l=(1-p_l)I+p_l\Lambda_l$ under maximum noise decomposition. NNAS implements this recursion as a uniform recurrent neural accumulator, $H_l=\tanh(W_x X_l+W_h H_{l-1})$, whose hidden state implicitly combines $U_l$ and $N_l$; a linear readout recovers $\hat{U}_l$ and $\hat{N}_l$, and the attention-assisted extractor $A_l=\mathrm{Softmax}(\hat{U}_l\hat{N}_l^T/\sqrt{d})\hat{U}_l$ produces the impact factor $\hat{r}_l$. This machinery turns noisy-to-noiseless regression into a sequence-to-sequence correction guided by an analytic prior for the survival probability $\prod(1-p_j)$.

What would settle it

Run NNAS on a six-qubit Trotterized Ising circuit with parameters chosen so that the noiseless expectation value changes sign within layers 1-20, and inspect the layer-by-layer MAE; a sharp error spike near the zero-crossing would falsify the scalar-envelope claim. A second check is to train only on 1-20 layers and test on 21-30 layers: if the MAE jumps discontinuously, the claimed scalability is bounded by the trained layer range.

Watch

Extended reading notes

Core claim

NNAS learns to recover noiseless expectation values $\{y_l\}$ from noisy observations $\{\tilde{y}_l\}$ by predicting a scalar noise impact factor $\hat{r}_l$ per circuit layer. The mitigation formula is $y^{\mathrm{em}}_l = \tilde{y}_l / (\prod_{j=1}^l(1-\hat{p}_j)+\hat{r}_l)$, where $\hat{p}_j$ are effectiveness factors estimated from the noise channels and $\hat{r}_l$ is the network output. The network's recurrent hidden state $H_l=F(X_l,H_{l-1})$ carries compressed surrogates $\hat{U}_l,\hat{N}_l$ of the circuit unitary and the cumulative noise, and an attention-style operation $\mathrm{Softmax}(\hat{U}_l\hat{N}_l^T/\sqrt{d})\hat{U}_l$ mirrors the conjugate symmetry of the noise envelope $R_l=U_lN_lU_l^\dagger$. The claim is that this explicit structural alignment is what lets NNAS beat black-box data-driven models on accuracy, data efficiency, and deep-circuit performance.

Load-bearing premise

Everything rests on the assumption that accumulated noise acts as a scalar multiplier on the noiseless expectation value at each layer, so dividing the noisy value by a learned factor $\prod(1-\hat{p}_j)+\hat{r}_l$ restores the true value; that assumption is a modeling choice rather than a derived identity, and it is ill-behaved when the noiseless expectation crosses zero.

Editorial extensions

If this is right

  • If the reported gains are correct, deep layered circuits are exactly where ML-QEM should be applied: beyond 15 Trotter steps NNAS cuts MAE by 79.42% over the noisy case and 55.63% over the best competing method.
  • An order-of-magnitude reduction in training data makes it realistic to train mitigation models on datasets generated by small quantum devices rather than by expensive classical simulation of noiseless labels.
  • The 1-2 order-of-magnitude reduction in sampling overhead means more mitigated expectation values can be extracted from a fixed number of shots, directly extending the usefulness of noisy near-term hardware.
  • The structural alignment evidence, with entropy-curve correlations of 0.8991 (Pearson) and 0.8028 (Spearman) between cumulative noise and its surrogate, provides a quantitative check that the network is tracking the physical noise process rather than memorizing outputs.
  • The GHZ quantum-metrology experiment suggests the same layer-recursion design can transfer to circuits that grow by adding qubits, extending QEM beyond fixed-depth layered circuits.

Reading between the lines

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

  • A decisive test of whether the physical prior is load-bearing is to replace the analytically estimated $\hat{p}_j$ with random or constant values; if accuracy does not drop, the RNN sequence model alone explains the gains, and if it does, the MND prior is essential.
  • Because the mitigation formula divides by $\prod(1-\hat{p}_j)+\hat{r}_l$, observables whose noiseless expectation crosses zero inside the layer range are a natural failure mode, and that can be probed directly on Trotter circuits with sign-changing expectation values.
  • The paper presents NNAS as a general paradigm for physics-inspired neural architectures, but only the recurrent-plus-attention combination is tested; a natural extension would be to swap in other sequence models and check whether the layer-wise noise prior still delivers the data-efficiency gains.
  • On real hardware, the $\hat{p}_j$ priors could come from randomized benchmarking rather than a known simulation noise model; the paper simulates Pauli noise but does not demonstrate this hardware calibration step.
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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

2 major / 5 minor

Summary. The paper introduces NNAS, a recurrent-neural-network-based method for quantum error mitigation that is designed around a layer-wise model of noise accumulation. The authors derive an effective-rate decomposition of each noisy layer, define a cumulative noise envelope, and propose a network that predicts a scalar noise-impact factor used in a mitigation formula. They report large MAE reductions over noisy results and over standard QEM baselines (ZNE, PEC, CDR) and an ML baseline (RF) on simulated QAOA-type Trotter circuits and GHZ-based quantum metrology, together with claims of reduced training-data requirements and sampling overhead. The paper also presents ablation studies and visual/statistical evidence that the network's internal representation partially tracks the structure of the cumulative noise.

Significance. If the central mitigation formula were a faithful inversion of the stated noise-accumulation model, the paper would be a substantial contribution: it combines a physically motivated architecture with strong empirical results on two tasks, reports 95% confidence intervals, compares against multiple baselines including standard QEM methods, and includes ablation and resource-cost analyses. The claim of a 65.85% average MAE reduction over the noisy case and 35.12% over the best QEM baseline, with larger gains in deeper circuits, is well matched to the reported benchmark design. However, the load-bearing formula connecting the learned output to the mitigated expectation value is not derived from the paper's own noise model, and the exact implemented formula is ambiguous because of a bias term that appears in Algorithm 1 but not in the main-text equation. These issues affect the physical-interpretability claim and the precise reproducibility of the headline numbers, so the contribution is currently conditional on a clarification and a robustness analysis.

major comments (2)
  1. [Section II, Eq. (2)] The mitigation formula is not the inversion of the paper's noise-accumulation model. Taking the expectation value of Eq. (1) with an observable O gives tilde_y_l = P_l y_l + Tr[R_l rho_l], where P_l = prod_j(1-p_j); the exact inversion would therefore be y_l = (tilde_y_l - Tr[R_l rho_l])/P_l. Eq. (2) instead computes y^em_l = tilde_y_l/(P_l + hat_r_l), which is equivalent to assuming that the noise-envelope contribution is proportional to the noiseless expectation value, Tr[R_l rho_l] = hat_r_l y_l, with hat_r_l learned. This structural assumption is not derived from Eq. (1) and is particularly unsafe for the Trotter observables of Figs. 2 and S3, whose noiseless expectation values can cross zero as a function of h delta t. Near such crossings the denominator P_l + hat_r_l can become small, amplifying errors. The authors should either derive Eq. (2) from the physical model or explicitly present it as a heuristic reparameterization of a regression target, and they should add a robustness test for observable values near zero crossings.
  2. [Section V, Algorithm 1 (line 10) and Eq. (2)] Algorithm 1 line 10 computes y <- N/(P+r)+b, with b described as a learnable 'overall deviation' parameter, but Eq. (2) in Section II and Eq. (14) in the supplementary NEA description contain no bias term. The main text never states whether b was used in the experiments that produced the reported 65.85%, 35.12%, 79.42%, and 55.63% reductions. The exact implemented model is therefore under-specified. Please include the bias b in Eq. (2), report its trained value or an ablation without it, or state explicitly that b=0 in all reported experiments.
minor comments (5)
  1. [Section III.B] The text refers to 'Fig. 3 a', 'Figs. 3 b and c' when discussing the quantum metrology results, but the corresponding figure is Fig. 4; the cross-references need to be corrected.
  2. [Section V, Methods, Eq. (15)] The displayed equation for the noisy circuit, Eq. (15), has unbalanced brackets and an unclear placement of U_L inside the product; this should be rewritten for readability.
  3. [Section V, Methods, Eq. (16)] In Eq. (16), the notation p'_j appears without a definition; presumably it should be p_j.
  4. [Supplementary Section II] The phrase 'samping overhead' should be corrected to 'sampling overhead'.
  5. [Supplementary Section III and Results] The paper does not include a data or code availability statement, which would be helpful for reproducing the simulated datasets and the NNAS implementation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the empirical NNAS claims are supervised predictions evaluated on held-out test sequences, and the effective noise rates are estimated independently of the target labels.

full rationale

The paper is transparent that the mitigation formula Eq. (2) uses \(\hat{r}_l\), a neural-network output trained on noiseless labels: “the impact factor \hat{r}_l which is the output of our model”. This makes y^em_l a re-scaled regression target rather than an ab initio physics inversion, which is a modeling and interpretability limitation, but not circularity. The effective rates \hat{p}_j are obtained before mitigation from randomized benchmarking rather than from the target labels, and the reported MAE reductions are computed on separate 200-sequence test sets (and 500-sequence sets for the metrology task), with the paper stating “In the testing stage, we assess all baselines across 200 sequences”. The mismatch between Eq. (2) and the bias term b in Algorithm 1, and the singular behavior when the noiseless expectation crosses zero, are correctness or specification concerns, not cases where the conclusion is equivalent to the premise. The self-citations (Refs. [4] and [8]) are contextual QEM references and are not load-bearing for the NNAS derivation, the architecture, or the numerical benchmarks. No uniqueness theorem is imported, and no ansatz is justified solely by a self-citation. The structural-alignment analysis comparing \hat{N} with N is a post-hoc interpretability check rather than a fitted training target. Therefore no specific circular step can be exhibited.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The framework rests on standard CPTP channel algebra and randomized-compiling assumptions, plus the unproven assumption that a scalar impact factor learned by an RNN can recover noiseless expectations across depths. No new physical entities are introduced; the network's fitted weights, output bias, and calibrated error rates are the main free parameters.

free parameters (4)
  • neural network parameters (embedding, RNN, readout, attention) = not reported
    All NNAS weights are fit to training data by MSE; no parameter count or final values are reported.
  • output bias b = learned per task
    Algorithm 1 line 10 adds a learnable bias to the mitigated value, absent from the main-text formula Eq (2).
  • effective rates p_j = derived from T1/T2 and randomized benchmarking
    The denominator requires estimates of per-gate error rates; the paper shows robustness to deviations but these are calibrated inputs rather than model outputs.
  • training hyperparameters (learning rate, epochs, hidden size, optimizer) = not reported
    Not specified in main text or supplementary; needed for exact reproduction.
assumptions (4)
  • standard math Layer-wise CPTP noise model with maximum noise decomposition E_l = (1-p_l)I + p_l*Lambda_l, Lambda_l CPTP
    Invoked in Methods V.A; standard channel decomposition, though for coherent noise p_l = 1, which the authors note.
  • domain assumption Noise can be tailored to stochastic Pauli noise via randomized compiling
    Used to justify the maximum noise decomposition and to set the simulation noise model; stated in Methods V.A.
  • domain assumption Noiseless training labels are available from classical simulation
    Training requires noiseless expectation values; the paper acknowledges exponential simulation cost but does not include label-generation cost in the resource comparison.
  • ad hoc to paper A scalar impact factor r_l suffices to correct the expectation value via Eq (2)
    The mitigation formula is exact only if the noise envelope contributes a scalar multiple of the noiseless expectation; r_l is defined to make it so, which is a re-parameterization rather than a proven identity.

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Cite this review

Pith. "Pith review of Physics-inspired Machine Learning for Quantum Error Mitigation." pith.science (2026). https://pith.science/paper/IQWA6UD5

@misc{pith2026250104558,
  author       = {Pith},
  title        = {Pith review of: Physics-inspired Machine Learning for Quantum Error Mitigation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IQWA6UD5}},
  note         = {Machine review of arXiv:2501.04558}
}
read the original abstract

Noise is a major obstacle in current quantum computing, and Machine Learning for Quantum Error Mitigation (ML-QEM) promises to address this challenge, enhancing computational accuracy while reducing the sampling overheads of standard QEM methods. Yet, existing models lack physical interpretability and rely heavily on extensive datasets, hindering their scalability in large-scale quantum circuits. To tackle these issues, we introduce the Neural Noise Accumulation Surrogate (NNAS), a physics-inspired neural network for ML-QEM that incorporates the structural characteristics of quantum noise accumulation within multi-layer circuits, endowing the model with physical interpretability. Experimental results demonstrate that NNAS outperforms current methods across a spectrum of metrics, including error mitigation capability, quantum resource consumption, and training dataset size. Notably, for deeper circuits where QEM methods typically struggle, NNAS achieves a remarkable reduction of over half in errors. NNAS also demands substantially fewer training data, reducing dataset reliance by at least an order of magnitude, due to its ability to rapidly capture noise accumulation patterns across circuit layers. This work pioneers the integration of quantum process-derived structural characteristics into neural network architectures, broadly enhancing QEM's performance and applicability, and establishes an integrative paradigm that extends to various quantum-inspired neural network architectures.

Figures

Figures reproduced from arXiv: 2501.04558 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
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Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Deep-learned error mitigation via partially knitted circuits for the variational quantum eigensolver

    quant-ph 2025-06 conditional novelty 5.0 of 10

    A deep-learned error mitigation method using partially knitted circuits reduces VQE energy error to below 1% under realistic noise, outperforming ZNE and damping-factor methods.

Reference graph

Works this paper leans on

69 extracted references · 46 canonical work pages · cited by 1 Pith paper

  1. [1]

    Preskill, Quantum 2, 79 (2018)

    J. Preskill, Quantum 2, 79 (2018)

    2018

  2. [2]

    Arute et al., Nature 574, 505 (2019)

    F. Arute et al., Nature 574, 505 (2019)

    2019

  3. [4]

    Huang, D

    H.-L. Huang, D. Wu, D. Fan, and X. Zhu, Sci. China Inf. Sci. 63, 180501 (2020)

    2020

  4. [5]

    S. Endo, Z. Cai, S. C. Benjamin, and X. Yuan, J. Phys. Soc. Japan. 90, 032001 (2021)

    work page 2021

  5. [6]

    Kandala, K

    A. Kandala, K. Temme, A. D. C ´orcoles, A. Mezzacapo, J. M. Chow, and J. M. Gambetta, Nature 567, 491 (2019)

    work page 2019

  6. [7]

    Li and S

    Y . Li and S. C. Benjamin, Phys. Rev. X7, 021050 (2017)

    work page 2017

  7. [8]

    Huang, X.-Y

    H.-L. Huang, X.-Y . Xu, C. Guo, G. Tian, S.-J. Wei, X. Sun, W.- S. Bao, and G.-L. Long, Sci. China Phys. Mech. Astron. 66, 250302 (2023)

    work page 2023

  8. [9]

    Z. Cai, R. Babbush, S. C. Benjamin, S. Endo, W. J. Huggins, Y . Li, J. R. McClean, and T. E. O’Brien, Rev. Mod. Phys. 95, 045005 (2023)

    2023

Show all 69 references
  1. [10]

    Acharya et al., Nature (2024)

    R. Acharya et al., Nature (2024)

    2024

  2. [11]

    Acharya et al., Nature 614, 676 (2023)

    R. Acharya et al., Nature 614, 676 (2023)

    2023

  3. [12]

    Bluvstein, S

    D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, et al., Nature 626, 58 (2024)

    2024

  4. [13]

    Chiaverini, D

    J. Chiaverini, D. Leibfried, T. Schaetz, M. D. Barrett, R. B. Blakestad, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, R. Ozeri, and D. J. Wineland, Nature 432, 602 (2004)

    2004

  5. [14]

    D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. H. Zurek, T. F. Havel, and S. S. Somaroo, Phys. Rev. Lett. 81, 2152 (1998)

    1998

  6. [15]

    Paetznick et al., arXiv:2404.02280 (2024)

    A. Paetznick et al., arXiv:2404.02280 (2024)

    2024 arXiv

  7. [16]

    B. W. Reichardt et al., arXiv:2411.11822 (2024)

    2024 arXiv

  8. [17]

    Y . Kim, A. Eddins, S. Anand,et al., Nature 618, 500 (2023)

    2023

  9. [18]

    Y . Kim, C. J. Wood, T. J. Yoder, S. T. Merkel, J. M. Gambetta, K. Temme, and A. Kandala, Nat. Phys. 19, 752 (2023)

    2023

  10. [20]

    Cai, Npj Quantum Inf

    Z. Cai, Npj Quantum Inf. 7, 80 (2021)

    2021

  11. [22]

    C. Song, J. Cui, H. Wang, J. Hao, H. Feng, and Y . Li, Sci Adv 5, eaaw5686 (2019)

    2019

  12. [23]

    Zhang, Y

    S. Zhang, Y . Lu, K. Zhang, W. Chen, Y . Li, J.-N. Zhang, and K. Kim, Nat. Commun. 11, 587 (2020)

    2020

  13. [24]

    Czarnik, A

    P. Czarnik, A. Arrasmith, P. J. Coles, and L. Cincio, Quantum 5, 592 (2021)

    2021

  14. [25]

    Strikis, D

    A. Strikis, D. Qin, Y . Chen, S. C. Benjamin, and Y . Li, PRX Quantum 2, 040330 (2021)

    2021

  15. [26]

    Czarnik, M

    P. Czarnik, M. McKerns, A. T. Sornborger, and L. Cincio, arXiv:2204.07109 (2022)

    2022 arXiv

  16. [27]

    Y . Quek, D. Stilck Franc ¸a, S. Khatri, J. J. Meyer, and J. Eisert, Nat. Phys. 20, 1648 (2024)

    2024

  17. [28]

    Takagi, S

    R. Takagi, S. Endo, S. Minagawa, and M. Gu, Npj Quantum Inf. 8, 114 (2022)

    2022

  18. [29]

    H. Liao, D. Wang, I. Sitdikov, A. Kandala, K. Temme, J. Gam- betta, and S. Bravyi, Nat. Mach. Intell. (2024)

    2024

  19. [30]

    E. R. Bennewitz, F. Hopfmueller, B. Kulchytskyy, J. Car- rasquilla, and P. Ronagh, Nat. Mach. Intell. 4, 618 (2022)

    2022

  20. [31]

    M. Liao, Y . Zhu, G. Chiribella, and Y . Yang, arXiv:2311.01727 (2023)

    2023 arXiv

  21. [32]

    Zlokapa and A

    A. Zlokapa and A. Gheorghiu, arXiv:2005.10811 (2020)

    2020 arXiv

  22. [33]

    Cantori, A

    S. Cantori, A. Mari, D. Vitali, et al., EPJ Quantum Technol. 11 (2024), 10.1140/epjqt/s40507-024-00256-8

    2024 doi

  23. [34]

    Y . Zhou, E. M. Stoudenmire, and X. Waintal, Phys. Rev. X 10, 041038 (2020)

    2020

  24. [35]

    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information , 10th ed. (Cambridge University Press, Cambridge, 2000)

    2000

  25. [36]

    Seif, Z.-P

    A. Seif, Z.-P. Cian, S. Zhou, S. Chen, and L. Jiang, PRX Quan- tum 4, 010303 (2023)

    2023

  26. [37]

    Hochreiter and J

    S. Hochreiter and J. Schmidhuber, Neural Comput. 9, 1735 (1997)

    1997

  27. [38]

    Schuster and K

    M. Schuster and K. Paliwal, IEEE Trans. Signal Process. 45, 2673 (1997)

    1997

  28. [39]

    Greenbaum, arXiv:1509.02921 (2015)

    D. Greenbaum, arXiv:1509.02921 (2015)

    2015 arXiv

  29. [40]

    Smith, M

    A. Smith, M. S. Kim, F. Pollmann, and J. Knolle, Npj Quantum Inf. 5, 106 (2019)

    2019

  30. [41]

    Y . Lee, J. Korean Phys. Soc.82, 479 (2023). 12

    2023

  31. [42]

    Rendon, J

    G. Rendon, J. Watkins, and N. Wiebe, Quantum8, 1266 (2024)

    2024

  32. [43]

    Y . Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferov ´a, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. Sawaya, S. Sim, L. Veis, and A. Aspuru-Guzik, Chem. Rev. 119, 10856 (2019)

    2019

  33. [44]

    McArdle, S

    S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Rev. Mod. Phys.92, 015003 (2020)

    2020

  34. [45]

    Bharti, A

    K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin- Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke, W.-K. Mok, S. Sim, L.-C. Kwek, and A. Aspuru- Guzik, Rev. Mod. Phys. 94, 015004 (2022)

    2022

  35. [46]

    Giovannetti, S

    V . Giovannetti, S. Lloyd, and L. Maccone, Nat. Photonics 5, 222 (2011)

    2011

  36. [47]

    G. Homa, A. Ortega, and M. Koniorczyk, arXiv:2402.12944 (2024)

    2024 arXiv

  37. [48]

    Magesan, J

    E. Magesan, J. M. Gambetta, B. R. Johnson, C. A. Ryan, J. M. Chow, S. T. Merkel, M. P. Da Silva, G. A. Keefe, M. B. Roth- well, T. A. Ohki, et al., Phys. Rev. Lett. 109, 080505 (2012)

    2012

  38. [50]

    Helsen, I

    J. Helsen, I. Roth, E. Onorati, A. Werner, and J. Eisert, PRX Quantum 3, 020357 (2022)

    2022

  39. [54]

    Vaswani, N

    A. Vaswani, N. M. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin, in NeurIPS (2017)

    2017

  40. [55]

    H. Zhou, S. Zhang, J. Peng, S. Zhang, J. Li, H. Xiong, and W. Zhang, arXiv:2012.07436 (2020)

    2020 arXiv

  41. [56]

    H. Wu, J. Xu, J. Wang, and M. Long, in NeurIPS (2021)

    2021

  42. [57]

    T. Zhou, Z. Ma, Q. Wen, X. Wang, L. Sun, and R. Jin, arXiv:2201.12740 (2022). Supplementary information: Physics-inspired Machine Learning for Quantum Error Mitigation I. THE ESTIMATION OF EFFECTIVENESS FACTORS In the main text, we compute the mitigated expectation value at th...

    2022 arXiv

  43. [58]

    This method is particularly adept at handling errors that arise from the quantum hardware itself

    Zero-Noise Extrapolation ZNE is a canonical QEM technique that leverages the principle of extrapolating noisy expectation values to estimate the noiseless value. This method is particularly adept at handling errors that arise from the quantum hardware itself. ZNE operates by s...

    2025 arXiv

  44. [59]

    Its fundamental concept involves calibrating the noisy process channel expression to implement the inverse of the noise channel, which is then appended to the noisy circuit

    Probabilistic Error Cancellation PEC is one of the earliest QEM algorithms proposed. Its fundamental concept involves calibrating the noisy process channel expression to implement the inverse of the noise channel, which is then appended to the noisy circuit. We utilize the PEC...

  45. [60]

    CDR differs from methods like PEC, which depend on exact knowledge of the noise channel, and ZNE, which requires precise control over the noise level

    Clifford Data Regression CDR is a typical learning-based QEM method, which can be regarded as the simplest form of linear model-based machine learning quantum error mitigation (ML-QEM) method. CDR differs from methods like PEC, which depend on exact knowledge of the noise chan...

  46. [61]

    Attention-core ablated model The architecture of the NEA model is rooted in the neural noise accumulator, which is realized by a Recurrent Neural Network (RNN). In our model, we integrate circuit features and concatenate them to form the input data matrix X∈ RL×M , where L den...

  47. [62]

    Quantum-inspired neural network ablated We then explore the ablation of the entire physics-inspired neural architecture by employing a standard artificial intelligence approach: the Multilayer Perceptron (MLP). The MLP utilized in the NNA consists of multiple hidden layers, ea...

  48. [63]

    Emerson, M

    J. Emerson, M. Silva, O. Moussa, C. Ryan, M. Laforest, J. Baugh, D. G. Cory, and R. Laflamme, Science 317, 1893 (2007)

    2007

  49. [64]

    Magesan, J

    E. Magesan, J. M. Gambetta, B. R. Johnson, C. A. Ryan, J. M. Chow, S. T. Merkel, M. P. Da Silva, G. A. Keefe, M. B. Rothwell, T. A. Ohki, et al., Phys. Rev. Lett. 109, 080505 (2012)

    2012

  50. [65]

    Seif, Z.-P

    A. Seif, Z.-P. Cian, S. Zhou, S. Chen, and L. Jiang, PRX Quantum 4, 010303 (2023)

    2023

  51. [66]

    S. Endo, S. C. Benjamin, and Y . Li, Phys. Rev. X 8, 031027 (2018)

    2018

  52. [67]

    van den Berg, Z

    E. van den Berg, Z. Minev, and A. e. a. Kandala, Nat. Phys. 19, 1116 (2023)

    2023

  53. [68]

    J. E. Jaloveckas, M. T. P. Nguyen, L. Palackal, J. M. Lorenz, and H. Ehm, arXiv:2311.11639 (2023)

    2023 arXiv

  54. [69]

    H. Liao, D. S. Wang, I. Sitdikov, C. Salcedo, A. Seif, and Z. K. Minev, ArXiv abs/2309.17368 (2023)

    2023 arXiv

  55. [70]

    Qiskit: An open-source quantum computing software,

    Q. Contributors, “Qiskit: An open-source quantum computing software,” https://qiskit.org (Accessed: 2024-07-11)

    2024

  56. [71]

    Ghosh, A

    J. Ghosh, A. G. Fowler, and M. R. Geller, Phys. Rev. A 86, 062318 (2012)

    2012

  57. [72]

    Tomita and K

    Y . Tomita and K. M. Svore, Phys. Rev. A90, 062320 (2014)

    2014

  58. [73]

    J. J. Wallman and J. Emerson, Phys. Rev. A 94, 052325 (2016)

    2016

  59. [74]

    Erhard, J

    A. Erhard, J. J. Wallman, L. Postler, M. Meth, R. Stricker, E. A. Martinez, P. Schindler, T. Monz, J. Emerson, and R. Blatt, Nat. Commun. 10, 5347 (2019)

    2019

  60. [75]

    Hashim, R

    A. Hashim, R. K. Naik, A. Morvan, J.-L. Ville, B. Mitchell, J. M. Kreikebaum, M. Davis, E. Smith, C. Iancu, K. P. O’Brien, I. Hincks, J. J. Wallman, J. Emerson, and I. Siddiqi, Phys. Rev. X 11, 041039 (2021)

    2021

  61. [76]

    Morvan et al., Nature 634, 328 (2024)

    A. Morvan et al., Nature 634, 328 (2024)

    2024

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.