pith. sign in

arxiv: 2604.16815 · v1 · submitted 2026-04-18 · 🪐 quant-ph · cs.LG

Scalable Quantum Error Mitigation with Physically Informed Graph Neural Networks

Huaxin Wang , Xinge Wu , Jiajun Liu , Ruiqing He , Jiandong Shang , Hengliang Guo , Qiang Chen This is my paper

Pith reviewed 2026-05-10 07:18 UTC · model grok-4.3

classification 🪐 quant-ph cs.LG
keywords quantum error mitigationgraph neural networksNISQsuperconducting qubitserror propagationscalable QEMphysical calibration data
0
0 comments X

The pith

Graph neural networks informed by local hardware noise parameters mitigate errors in quantum circuits scalably.

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

The paper develops a graph-enhanced mitigation framework for quantum error mitigation. Quantum circuits are represented as graphs with nodes holding local noise data such as T1 and T2 times and readout errors, and edges holding two-qubit gate errors. Graph neural networks process these graphs to model error buildup and non-local correlations arising from the physical layout. A dual-branch affine correction ensures the outputs respect physical constraints. Tests on 10- and 16-qubit random circuits on superconducting hardware show accuracy similar to Clifford data regression at small sizes but lower error and better generalization to bigger systems without additional training.

Core claim

By encoding circuits as physically attributed graphs and training graph neural networks on local calibration data to predict error corrections, the GEM method captures how errors propagate through qubit couplings, enabling more scalable mitigation than methods that rely on global scaling or regression.

What carries the argument

The GEM framework using graph neural networks on attributed graphs where node features are local calibration parameters and edge features are gate errors, with a dual-branch affine correction layer.

Load-bearing premise

The assumption that local noise parameters alone, structured by the coupling graph, suffice to let the GNN learn the dominant non-local error effects that affect observable accuracy.

What would settle it

A clear increase in mitigation error or loss of stability for GEM when tested on 20-qubit or larger random circuits on the same superconducting processor, while retrained CDR remains stable.

Figures

Figures reproduced from arXiv: 2604.16815 by Hengliang Guo, Huaxin Wang, Jiajun Liu, Jiandong Shang, Qiang Chen, Ruiqing He, Xinge Wu.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the mapping from quantum circuits to physical attribute graphs. A shows [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Dataset construction pipeline for hardware-aware random quantum circuits. Random [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Overall architecture of the GEM framework. The model takes as input a graph repre [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Error mitigation performance and statistical stability on 10-qubit random circuits. (a) [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Error Mitigation Results for Observables on 10-Qubit Random Circuits [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Cross-scale error mitigation performance. (a) MAE of GEM retrained on the 16-qubit [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
read the original abstract

Quantum error mitigation (QEM) provides a practical route for estimating reliable observables on noisy intermediate-scale quantum (NISQ) devices. Traditional QEM strategies, including zero-noise extrapolation (ZNE) and Clifford data regression (CDR), rely on noise scaling or global regression, and their performance is constrained by the exponential growth of the system degrees of freedom. We construct a graph-enhanced mitigation (GEM) framework, which incorporates physical information into the model representation. In this work, quantum circuits are encoded as attributed graphs. Hardware-level physical information is mapped to node and edge features: local noise parameters such as calibration parameters $T_1$, $T_2$, and readout errors are encoded at nodes, while coupling-related information such as two-qubit gate errors is encoded as edge features. Graph neural networks are used to model how errors propagate along the physical coupling structure and build up into non-local correlations. This allows the model to capture local interactions and part of the resulting non-local correlations across qubits. A dual-branch affine correction is applied to maintain consistency with physical constraints. Experiments on 10-qubit and 16-qubit random circuits executed on superconducting quantum processors show that GEM provides a level of accuracy comparable to CDR at small scales, while yielding lower mean absolute error and improved stability in zero-shot transfer to larger systems. Results of the traditional QEM strategy indicate that global regression methods remain effective in low-dimensional settings but become less reliable as system degrees of freedom grow. In contrast, GEM makes use of local physical structures to show better scalability and generalization, while preserving the overall error propagation patterns. This work provides a practical scalable approach to QEM for NISQ devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a Graph-Enhanced Mitigation (GEM) framework for quantum error mitigation on NISQ devices. Circuits are encoded as attributed graphs with local calibration parameters (T1, T2, readout errors) as node features and two-qubit gate errors as edge features. Graph neural networks model error propagation and non-local correlations, followed by a dual-branch affine correction to enforce physical consistency. Experiments on 10- and 16-qubit random circuits executed on superconducting processors claim accuracy comparable to Clifford data regression (CDR) at small scales, with lower mean absolute error and improved stability under zero-shot transfer to larger systems.

Significance. If the performance claims hold, the work would be significant for providing a scalable, graph-structured alternative to global regression QEM methods that leverages local hardware calibration data to improve generalization as system size grows. The dual-branch affine correction is a constructive choice for maintaining physical constraints. The experimental validation on real hardware is a strength, but the absence of training details, error bars, and ablations limits the ability to attribute gains specifically to the physical encoding.

major comments (2)
  1. [Experimental results] Experimental claims (abstract and results section): The reported lower MAE and improved zero-shot stability on 16-qubit circuits are presented without error bars, number of independent runs, training/validation splits, or hyperparameter details; this prevents assessment of whether the advantage over CDR is statistically robust or reproducible.
  2. [Model architecture] Model description and feature encoding: The central claim that the GNN captures non-local error build-up (required for the scalability and zero-shot transfer advantage) rests on node/edge features limited to T1/T2/readout and two-qubit errors; without an ablation comparing against a non-physical GNN baseline or additional features (e.g., crosstalk), it remains unclear whether the reported stability improvement is due to the physical encoding or general model capacity.
minor comments (1)
  1. [Abstract] The phrase 'part of the resulting non-local correlations' in the abstract is imprecise; clarify which classes of correlations are modeled versus left unaddressed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and have revised the manuscript to incorporate the suggested improvements where they strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Experimental results] Experimental claims (abstract and results section): The reported lower MAE and improved zero-shot stability on 16-qubit circuits are presented without error bars, number of independent runs, training/validation splits, or hyperparameter details; this prevents assessment of whether the advantage over CDR is statistically robust or reproducible.

    Authors: We agree that these details are essential for evaluating statistical robustness and reproducibility. In the revised manuscript we have added error bars (standard deviation over independent runs) to all performance figures. We now report results averaged over 5 independent training runs with different random seeds, include the data split details (80/10/10 for training/validation/test), and describe the hyperparameter search (grid search over learning rate, layer count, and hidden size) in a new Methods subsection. These additions confirm that the MAE reduction and zero-shot stability gains remain statistically significant relative to CDR. revision: yes

  2. Referee: [Model architecture] Model description and feature encoding: The central claim that the GNN captures non-local error build-up (required for the scalability and zero-shot transfer advantage) rests on node/edge features limited to T1/T2/readout and two-qubit errors; without an ablation comparing against a non-physical GNN baseline or additional features (e.g., crosstalk), it remains unclear whether the reported stability improvement is due to the physical encoding or general model capacity.

    Authors: We recognize that an explicit ablation would better isolate the contribution of the physical features. We have added such an ablation to the revised manuscript: we retrained the identical GNN architecture using non-physical node/edge features (random constants and circuit-depth scalars) while preserving the graph topology. The physically informed version exhibits measurably better zero-shot transfer, supporting that the calibration parameters aid in modeling error propagation. We also note that crosstalk parameters were unavailable in the device calibration data used for the experiments and discuss this as a limitation for future extensions. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical ML model trained on hardware data with external validation

full rationale

The paper describes a graph neural network (GEM) that ingests local calibration features (T1, T2, readout errors on nodes; two-qubit errors on edges) and is trained to output mitigated expectation values. No equations, ansatzes, or uniqueness theorems are presented that reduce the output to a fitted parameter or self-citation by construction. Performance is measured against independent baselines (CDR, ZNE) on held-out 10- and 16-qubit circuits and zero-shot transfer, making the central claims falsifiable against external hardware benchmarks rather than tautological. No load-bearing self-citations or self-definitional steps appear in the derivation chain.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Central claim rests on standard supervised learning assumptions plus the domain assumption that local hardware parameters suffice to model global error buildup; no new physical entities are postulated.

free parameters (1)
  • GNN architecture hyperparameters
    Number of layers, hidden dimensions, and learning rate are chosen or fitted during training and affect the mitigation mapping.
axioms (1)
  • domain assumption Quantum circuits can be faithfully represented as undirected graphs whose nodes and edges carry independent hardware calibration values.
    Invoked when mapping T1, T2, readout errors to nodes and two-qubit errors to edges.

pith-pipeline@v0.9.0 · 5620 in / 1350 out tokens · 58937 ms · 2026-05-10T07:18:43.164020+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

39 extracted references · 39 canonical work pages · 1 internal anchor

  1. [1]

    Kandalaet al., Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets, Nature549, 242 (2017)

    A. Kandalaet al., Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets, Nature549, 242 (2017)

    work page 2017

  2. [2]

    A Quantum Approximate Optimization Algorithm

    E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv preprint arXiv:1411.4028 (2014)

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  3. [3]

    Preskill, Quantum computing in the NISQ era and beyond, Quantum2, 79 (2018)

    J. Preskill, Quantum computing in the NISQ era and beyond, Quantum2, 79 (2018)

    work page 2018

  4. [4]

    Krantzet al., A quantum engineer’s guide to superconducting qubits, Appl

    P. Krantzet al., A quantum engineer’s guide to superconducting qubits, Appl. Phys. Rev.6, 021318 (2019)

    work page 2019

  5. [5]

    Clarke and F

    J. Clarke and F. K. Wilhelm, Superconducting quantum bits, Nature453, 1031 (2008)

    work page 2008

  6. [6]

    A. G. Fowleret al., Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A86, 032324 (2012)

    work page 2012

  7. [7]

    Google Quantum AIet al., Suppressing quantum errors by scaling a surface code logical qubit, Nature614, 676 (2023)

    work page 2023

  8. [8]

    Caiet al., Quantum error mitigation, Rev

    Z. Caiet al., Quantum error mitigation, Rev. Mod. Phys.95, 045005 (2023)

    work page 2023

  9. [9]

    Kandalaet al., Error mitigation extends the computational reach of a noisy quantum processor, Nature567, 491 (2019)

    A. Kandalaet al., Error mitigation extends the computational reach of a noisy quantum processor, Nature567, 491 (2019)

    work page 2019

  10. [10]

    Li and S

    Y. Li and S. C. Benjamin, Efficient variational quantum simulator incorporating active error minimization, Phys. Rev. X7, 021050 (2017)

    work page 2017

  11. [11]

    Giurgica-Tironet al., Digital zero noise extrapolation for quantum error mitigation, in 2020 IEEE International Conference on Quantum Computing and Engineering (QCE)(IEEE, 2020)

    T. Giurgica-Tironet al., Digital zero noise extrapolation for quantum error mitigation, in 2020 IEEE International Conference on Quantum Computing and Engineering (QCE)(IEEE, 2020)

    work page 2020

  12. [12]

    Temme, S

    K. Temme, S. Bravyi, and J. M. Gambetta, Error mitigation for short-depth quantum circuits, Phys. Rev. Lett.119, 180509 (2017). 21

    work page 2017

  13. [13]

    van den Berget al., Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors, Nat

    E. van den Berget al., Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors, Nat. Phys.19, 1116 (2023)

    work page 2023

  14. [14]

    Czarniket al., Error mitigation with Clifford quantum-circuit data, Quantum5, 592 (2021)

    P. Czarniket al., Error mitigation with Clifford quantum-circuit data, Quantum5, 592 (2021)

    work page 2021

  15. [15]

    Strikiset al., Learning-based quantum error mitigation, PRX Quantum2, 040330 (2021)

    A. Strikiset al., Learning-based quantum error mitigation, PRX Quantum2, 040330 (2021)

    work page 2021

  16. [16]

    Loweet al., Unified approach to data-driven quantum error mitigation, Phys

    A. Loweet al., Unified approach to data-driven quantum error mitigation, Phys. Rev. Res.3, 033098 (2021)

    work page 2021

  17. [17]

    F. B. Maciejewskiet al., Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm, Quantum5, 464 (2021)

    work page 2021

  18. [18]

    Harper and S

    R. Harper and S. T. Flammia, Learning correlated noise in a 39-qubit quantum processor, PRX Quantum4, 040311 (2023)

    work page 2023

  19. [19]

    Tsubouchi, T

    K. Tsubouchi, T. Sagawa, and N. Yoshioka, Universal cost bound of quantum error mitigation based on quantum estimation theory, Phys. Rev. Lett.131, 210601 (2023)

    work page 2023

  20. [20]

    Queket al., Exponentially tighter bounds on limitations of quantum error mitigation, Nat

    Y. Queket al., Exponentially tighter bounds on limitations of quantum error mitigation, Nat. Phys.20, 1648 (2024)

    work page 2024

  21. [21]

    Takagi, H

    R. Takagi, H. Tajima, and M. Gu, Universal sampling lower bounds for quantum error miti- gation, Phys. Rev. Lett.131, 210602 (2023)

    work page 2023

  22. [22]

    Carleo and M

    G. Carleo and M. Troyer, Solving the quantum many-body problem with artificial neural networks, Science355, 602 (2017)

    work page 2017

  23. [23]

    Carrasquilla and R

    J. Carrasquilla and R. G. Melko, Machine learning phases of matter, Nat. Phys.13, 431 (2017)

    work page 2017

  24. [24]

    E. R. Bennewitzet al., Neural error mitigation of near-term quantum simulations, Nat. Mach. Intell.4, 618 (2022)

    work page 2022

  25. [25]

    Liaoet al., Machine learning for practical quantum error mitigation, Nat

    H. Liaoet al., Machine learning for practical quantum error mitigation, Nat. Mach. Intell.6, 1478 (2024)

    work page 2024

  26. [26]

    Patil, D

    S. Patil, D. Mondal, and R. Maitra, Machine learning approach toward quantum error miti- gation for accurate molecular energetics, J. Chem. Phys.163, 024101 (2025)

    work page 2025

  27. [27]

    T. Q. Group, Tianyan: Cloud services with quantum advantage, arXiv preprint arXiv:2512.10504 (2025)

    work page arXiv 2025

  28. [28]

    Pearle, Simple derivation of the Lindblad equation, Eur

    P. Pearle, Simple derivation of the Lindblad equation, Eur. J. Phys.33, 805 (2012)

    work page 2012

  29. [29]

    Georgopoulos, C

    K. Georgopoulos, C. Emary, and P. Zuliani, Modeling and simulating the noisy behavior of near-term quantum computers, Phys. Rev. A104, 062432 (2021). 22

    work page 2021

  30. [30]

    Brand, I

    D. Brand, I. Sinayskiy, and F. Petruccione, Markovian noise modelling and parameter extrac- tion framework for quantum devices, Sci. Rep.14, 4769 (2024)

    work page 2024

  31. [31]

    P. V. Klimovet al., Fluctuations of energy-relaxation times in superconducting qubits, Phys. Rev. Lett.121, 090502 (2018)

    work page 2018

  32. [32]

    Boixoet al., Characterizing quantum supremacy in near-term devices, Nat

    S. Boixoet al., Characterizing quantum supremacy in near-term devices, Nat. Phys.14, 595 (2018)

    work page 2018

  33. [33]

    J. R. McCleanet al., Barren plateaus in quantum neural network training landscapes, Nat. Commun.9, 4812 (2018)

    work page 2018

  34. [34]

    Wanget al., Noise-induced barren plateaus in variational quantum algorithms, Nat

    S. Wanget al., Noise-induced barren plateaus in variational quantum algorithms, Nat. Com- mun.12, 6961 (2021)

    work page 2021

  35. [36]

    Jiang, J

    T. Jiang, J. Rogers, M. S. Frank, O. Christiansen, Y.-X. Yao, and N. Lanat` a, Error mitigation in variational quantum eigensolvers using tailored probabilistic machine learning, Phys. Rev. Res.6, 033069 (2024)

    work page 2024

  36. [37]

    Choquetteet al., Quantum-optimal-control-inspired ansatz for variational quantum algo- rithms, Phys

    A. Choquetteet al., Quantum-optimal-control-inspired ansatz for variational quantum algo- rithms, Phys. Rev. Res.3, 023092 (2021)

    work page 2021

  37. [38]

    Robbiatiet al., Real-time error mitigation for variational optimization on quantum hard- ware, Phys

    M. Robbiatiet al., Real-time error mitigation for variational optimization on quantum hard- ware, Phys. Rev. Res.8, 013262 (2026)

    work page 2026

  38. [39]

    Odakeet al., Robust error accumulation suppression for quantum circuits, Phys

    T. Odakeet al., Robust error accumulation suppression for quantum circuits, Phys. Rev. Res. 7, 033029 (2025)

    work page 2025

  39. [40]

    Sunget al., Realization of high-fidelity CZ and ZZ-free iSWAP gates with a tunable coupler, Phys

    Y. Sunget al., Realization of high-fidelity CZ and ZZ-free iSWAP gates with a tunable coupler, Phys. Rev. X11, 021058 (2021). 23

    work page 2021