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arxiv: 2605.05256 · v2 · submitted 2026-05-06 · 🪐 quant-ph

Recognition: 2 theorem links

· Lean Theorem

Error Mitigation in Dynamic Circuits for Hamiltonian Simulation

Sumeet Shirgure , Siyuan Niu
Authors on Pith no claims yet

Pith reviewed 2026-05-15 06:33 UTC · model grok-4.3

classification 🪐 quant-ph
keywords dynamic quantum circuitserror mitigationdynamical decouplingzero-noise extrapolationHamiltonian simulationIsing modelHeisenberg modelground state estimation
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The pith

Combining dynamical decoupling and zero-noise extrapolation mitigates errors from mid-circuit measurements in dynamic quantum circuits for Hamiltonian simulation.

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

The paper establishes that dynamic quantum circuits, which rely on mid-circuit measurements and classical feed-forward for resource-efficient Hamiltonian simulation, suffer from decoherence and measurement errors during idle periods but can have those errors suppressed by applying dynamical decoupling pulses during waits and zero-noise extrapolation to the results. Experiments on IBM hardware for the Ising and Heisenberg models show this combination yields clearer ground-state energy gaps and more accurate time-evolved states than unmitigated dynamic circuits. A sympathetic reader would care because dynamic circuits are promoted for lowering gate counts in algorithms such as error correction and simulation, yet their practical value hinges on whether the added errors can be controlled without losing the resource advantage.

Core claim

We demonstrate that a combination of DD and ZNE is effective in mitigating the errors introduced during mid-circuit measurements and feed-forward operations, as well as the errors arising from faulty measurements. This approach yields a energy gap improvement of at least 60% in ground state estimation and reduces observed error of time-evolved states by up to 99% for the Ising model and up to 20% for the Heisenberg model.

What carries the argument

Dynamical decoupling (DD) sequences applied during idle windows created by mid-circuit measurements and feed-forward delays, paired with zero-noise extrapolation (ZNE) performed on the noisy measurement outcomes to estimate zero-noise observables.

If this is right

  • Ground-state energy gap estimates improve by at least 60 percent when the combined mitigation is applied to dynamic-circuit variational algorithms.
  • Observed errors in time-evolved states drop by up to 99 percent for the Ising model under the mitigated dynamic circuits.
  • Observed errors in time-evolved states drop by up to 20 percent for the Heisenberg model under the mitigated dynamic circuits.
  • Errors originating from mid-circuit measurements, feed-forward delays, and faulty readouts are simultaneously suppressed.

Where Pith is reading between the lines

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

  • The same DD-plus-ZNE protocol could be tested on dynamic circuits used for quantum error correction to check whether logical error rates decrease.
  • Resource savings claimed for dynamic circuits might only become net-positive once mitigation overhead is included in the total gate count.
  • Hardware-specific tuning of DD pulse timings may be required to maintain the reported gains when moving to different quantum processors.

Load-bearing premise

The measured improvements in energy gaps and error rates arise specifically from the DD and ZNE protocols rather than from unaccounted hardware variations, post-selection effects, or differences in how the baseline dynamic circuits were calibrated.

What would settle it

Re-running the identical dynamic circuits for the Ising and Heisenberg models on the same IBM hardware without DD pulses or ZNE extrapolation and observing no improvement in energy gap accuracy or reduction in state errors would falsify the effectiveness claim.

Figures

Figures reproduced from arXiv: 2605.05256 by Siyuan Niu, Sumeet Shirgure.

Figure 1
Figure 1. Figure 1: (a) Hardware efficient ansatz with two entangling layers. Each Pauli rotation has a dedicated parameter view at source ↗
Figure 2
Figure 2. Figure 2: Inverse of the entangler needed in the Hardware view at source ↗
Figure 3
Figure 3. Figure 3: 3(a) A "brickwork" circuit for a Trotter step in Heisenberg Hamiltonian simulation. The structure for the Ising view at source ↗
Figure 4
Figure 4. Figure 4: Percentage improvements in energy gap for Heisenberg model ground state estimation. view at source ↗
Figure 5
Figure 5. Figure 5: Percentage improvements in energy gap for Ising model ground state estimation. view at source ↗
Figure 6
Figure 6. Figure 6: Percentage improvements in the energy difference after time evolution for Heisenberg model 6(a) and Ising model 6(b). view at source ↗
read the original abstract

Dynamic quantum circuits integrate mid-circuit measurements and feed-forward operations to enable real-time classical processing and conditional quantum logic. These capabilities are central to key quantum protocols such as quantum error correction, and have recently demonstrated significant potential for reducing quantum resources, including circuit depth and gate count, across a range of applications. However, executing dynamic circuits on real quantum hardware introduces a critical trade-off: while resource requirements decrease, circuit fidelity degrades due to high error rates of mid-circuit measurements, as well as the decoherence errors accumulated during the extended idle periods introduced by both mid-circuit measurements and feed-forward operations. In this paper, we systematically investigate the impact of standard error mitigation techniques on dynamic circuit applications pertaining to Hamiltonian simulation and ground state estimation of physically relevant systems like the Heisenberg model. We explore dynamical decoupling (DD) as a strategy to suppress decoherence and crosstalk errors during idle windows introduced by mid-circuit measurements and feed-forward delays, and also examine error mitigation via zero-noise extrapolation (ZNE). Through experiments conducted on IBM quantum hardware, we benchmark effective combinations of these strategies that maximize the practical benefits of dynamic quantum circuits in these applications. We demonstrate that a combination of DD and ZNE is effective in mitigating the errors introduced during mid-circuit measurements and feed-forward operations, as well as the errors arising from faulty measurements. This approach yields a energy gap improvement of at least 60% in ground state estimation and reduces observed error of time-evolved states by up to 99% for the Ising model and up to 20% for the Heisenberg model.

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 experimentally investigates error mitigation for dynamic quantum circuits in Hamiltonian simulation of Ising and Heisenberg models. It applies dynamical decoupling (DD) during idle windows from mid-circuit measurements and feed-forward, combined with zero-noise extrapolation (ZNE), and reports that this yields at least 60% improvement in energy gap for ground-state estimation plus error reductions up to 99% (Ising) and 20% (Heisenberg) on IBM hardware.

Significance. If the reported gains can be unambiguously attributed to the mitigation protocols, the work would be significant for near-term dynamic-circuit applications, including quantum error correction and resource-efficient simulation. The quantitative improvements are large enough to be practically relevant, and the direct hardware benchmarks constitute a concrete contribution.

major comments (2)
  1. [Results section] Results section (experimental benchmarks): the headline improvements (60% energy-gap gain, 99%/20% error reductions) are presented as direct evidence that DD+ZNE mitigates mid-circuit measurement and idle-time errors, yet the text provides no description of controls ensuring baseline and mitigated circuits were executed under identical conditions (same calibration epoch, randomized interleaving, identical transpilation, matched post-selection). Without these, the differences cannot be confidently assigned to the protocols rather than hardware drift or recalibration.
  2. [Abstract] Abstract and experimental description: the manuscript states clear quantitative gains but omits essential details on shot counts, error-bar methodology, and how faulty mid-circuit measurements were treated in post-processing. These omissions make it impossible to evaluate whether the reported percentages are statistically robust or sensitive to analysis choices.
minor comments (1)
  1. [Abstract] The abstract refers to 'the Ising model' and 'the Heisenberg model' without specifying the number of qubits or the precise Hamiltonian parameters used in the benchmarks; adding these would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We address each of the major comments point by point below and have revised the manuscript accordingly to enhance the description of our experimental procedures and statistical methods.

read point-by-point responses

  1. Referee: [Results section] Results section (experimental benchmarks): the headline improvements (60% energy-gap gain, 99%/20% error reductions) are presented as direct evidence that DD+ZNE mitigates mid-circuit measurement and idle-time errors, yet the text provides no description of controls ensuring baseline and mitigated circuits were executed under identical conditions (same calibration epoch, randomized interleaving, identical transpilation, matched post-selection). Without these, the differences cannot be confidently assigned to the protocols rather than hardware drift or recalibration.

    Authors: We agree that a clear description of the experimental controls is crucial for confidently attributing the improvements to DD and ZNE. In our experiments, the baseline and mitigated circuits were executed during the same calibration epoch on the IBM quantum hardware. The different circuit variants were randomly interleaved during execution to mitigate the effects of temporal drift. Identical transpilation parameters were applied to all circuits, and post-selection was performed using the same criteria for all variants. We have now included a dedicated paragraph in the Results section detailing these controls to address this concern. revision: yes

  2. Referee: [Abstract] Abstract and experimental description: the manuscript states clear quantitative gains but omits essential details on shot counts, error-bar methodology, and how faulty mid-circuit measurements were treated in post-processing. These omissions make it impossible to evaluate whether the reported percentages are statistically robust or sensitive to analysis choices.

    Authors: We acknowledge that the abstract and main text omitted key details on the experimental statistics and post-processing. We have revised the manuscript to specify the shot counts employed, the methodology used to compute error bars, and how faulty mid-circuit measurements were handled through post-processing. These details have been added to the experimental description section, enabling readers to assess the robustness of the quantitative gains reported. revision: yes

Circularity Check

0 steps flagged

No circularity; results are direct experimental benchmarks with no derivation chain

full rationale

The paper reports empirical results from IBM hardware experiments applying DD and ZNE to dynamic circuits for Ising and Heisenberg Hamiltonian simulation and ground-state estimation. No equations, fitted parameters, predictions, or uniqueness theorems are presented that could reduce to self-definition, self-citation, or ansatz smuggling. The claimed improvements (60% energy-gap gain, up to 99%/20% error reduction) are stated as measured outcomes, not derived quantities. The central claim therefore remains externally falsifiable via hardware replication and does not contain any load-bearing circular step.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work is purely experimental and introduces no new free parameters, axioms beyond standard quantum error models, or invented entities.

axioms (1)
  • domain assumption Standard models of decoherence, crosstalk, and measurement errors on superconducting qubits during idle periods and mid-circuit operations.
    Invoked to justify why DD suppresses idle-time errors and why ZNE can extrapolate measurement outcomes.

pith-pipeline@v0.9.0 · 5572 in / 1273 out tokens · 39414 ms · 2026-05-15T06:33:42.005439+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We explore dynamical decoupling (DD) as a strategy to suppress decoherence and crosstalk errors during idle windows introduced by mid-circuit measurements and feed-forward delays, and also examine error mitigation via zero-noise extrapolation (ZNE). ... yields a energy gap improvement of at least 60% in ground state estimation and reduces observed error of time-evolved states by up to 99% for the Ising model and up to 20% for the Heisenberg model.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Dynamical Decoupling (DD) ... utilizes sequences of periodic pulses to average out unwanted environmental noise

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages · 2 internal anchors

  1. [1]

    Faisal Alam and Bryan K Clark. 2024. Learning dynamic quantum circuits for efficient state preparation.arXiv preprint arXiv:2410.09030(2024)

    work page arXiv 2024

  2. [2]

    Elisa Bäumer, David Sutter, and Stefan Woerner. 2025. Approximate Quan- tum Fourier Transform in Logarithmic Depth on a Line.arXiv preprint arXiv:2504.20832(2025)

    work page arXiv 2025

  3. [3]

    Elisa Bäumer, Vinay Tripathi, Alireza Seif, Daniel Lidar, and Derek S Wang. 2024. Quantum Fourier transform using dynamic circuits.Physical review letters133, 15 (2024), 150602. 6 Error Mitigation in Dynamic Circuits for Hamiltonian Simulation

    work page 2024

  4. [4]

    Elisa Bäumer, Vinay Tripathi, Derek S Wang, Patrick Rall, Edward H Chen, Swarnadeep Majumder, Alireza Seif, and Zlatko K Minev. 2024. Efficient long- range entanglement using dynamic circuits.PRX Quantum5, 3 (2024), 030339

    work page 2024

  5. [5]

    Elisa Bäumer and Stefan Woerner. 2025. Measurement-based long-range entan- gling gates in constant depth.Physical Review Research7, 2 (2025), 023120

    work page 2025

  6. [6]

    Todd A Brun. 2019. Quantum error correction.arXiv preprint arXiv:1910.03672 (2019)

    work page arXiv 2019

  7. [7]

    Harry Buhrman, Marten Folkertsma, Bruno Loff, and Niels MP Neumann. 2024. State preparation by shallow circuits using feed forward.Quantum8 (2024), 1552

    work page 2024

  8. [8]

    Almudena Carrera Vazquez, Caroline Tornow, Diego Ristè, Stefan Woerner, Maika Takita, and Daniel J Egger. 2024. Combining quantum processors with real-time classical communication.Nature636, 8041 (2024), 75–79

    work page 2024

  9. [9]

    Marco Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, et al. 2021. Variational quantum algorithms.Nature Reviews Physics3, 9 (2021), 625–644

    work page 2021

  10. [10]

    Andrew M Childs, Yuan Su, Minh C Tran, Nathan Wiebe, and Shuchen Zhu

    work page

  11. [11]

    Theory of trotter error with commutator scaling.Physical Review X11, 1 (2021), 011020

    work page 2021

  12. [12]

    Roland C Farrell, Nikita A Zemlevskiy, Marc Illa, and John Preskill. 2025. Digital quantum simulations of scattering in quantum field theories using W states. arXiv preprint arXiv:2505.03111(2025)

    work page arXiv 2025

  13. [13]

    Tudor Giurgica-Tiron, Yousef Hindy, Ryan LaRose, Andrea Mari, and William J Zeng. 2020. Digital zero noise extrapolation for quantum error mitigation. In 2020 IEEE international conference on quantum computing and engineering (QCE). IEEE, 306–316

    work page 2020

  14. [14]

    Daniel Gottesman and Isaac L Chuang. 1999. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature402, 6760 (1999), 390–393

    work page 1999

  15. [15]

    Riddhi S Gupta, Ewout Van Den Berg, Maika Takita, Diego Riste, Kristan Temme, and Abhinav Kandala. 2024. Probabilistic error cancellation for dynamic quantum circuits.Physical Review A109, 6 (2024), 062617

    work page 2024

  16. [16]

    Daniel Hothem, Jordan Hines, Charles Baldwin, Dan Gresh, Robin Blume-Kohout, and Timothy Proctor. 2025. Measuring error rates of mid-circuit measurements. Nature Communications16, 1 (2025), 5761

    work page 2025

  17. [17]

    Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M Chow, and Jay M Gambetta. 2017. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets.nature549, 7671 (2017), 242–246

    work page 2017

  18. [18]

    Jin Ming Koh, Dax Enshan Koh, and Jayne Thompson. 2026. Readout error mitigation for mid-circuit measurements and feedforward.PRX Quantum7, 1 (2026), 010317

    work page 2026

  19. [19]

    Daniel A Lidar. 2014. Review of Decoherence-Free Subspaces, Noiseless Subsys- tems, and Dynamical Decoupling.Quantum information and computation for chemistry(2014), 295–354

    work page 2014

  20. [20]

    Siyuan Niu, Efekan Kokcu, Anupam Mitra, Aaron Szasz, Akel Hashim, Justin Kalloor, Wibe Albert de Jong, Costin Iancu, and Ed Younis. 2024. AC/DC: Automated Compilation for Dynamic Circuits. arXiv:2412.07969 [quant-ph] https://arxiv.org/abs/2412.07969

    work page arXiv 2024

  21. [21]

    Siyuan Niu and Aida Todri-Sanial. 2022. Effects of dynamical decoupling and pulse-level optimizations on ibm quantum computers.IEEE Transactions on Quantum Engineering3 (2022), 1–10

    work page 2022

  22. [22]

    Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien. 2014. A variational eigenvalue solver on a photonic quantum processor.Nature communications5, 1 (2014), 4213

    work page 2014

  23. [23]

    Lukas Postler, Sascha Heu𝛽en, Ivan Pogorelov, Manuel Rispler, Thomas Feld- ker, Michael Meth, Christian D Marciniak, Roman Stricker, Martin Ringbauer, Rainer Blatt, et al. 2022. Demonstration of fault-tolerant universal quantum gate operations.Nature605, 7911 (2022), 675–680

    work page 2022

  24. [24]

    Joschka Roffe. 2019. Quantum error correction: an introductory guide.Contem- porary Physics60, 3 (2019), 226–245

    work page 2019

  25. [25]

    Sumeet Shirgure, Efekan Kökcü, Anupam Mitra, Wibe Albert de Jong, Costin Iancu, and Siyuan Niu. 2026. Characterizing and Benchmarking Dynamic Quan- tum Circuits. arXiv:2604.03360 [quant-ph] https://arxiv.org/abs/2604.03360

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  26. [26]

    Kevin C Smith, Eleanor Crane, Nathan Wiebe, and SM Girvin. 2023. Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements.PRX Quantum4, 2 (2023), 020315

    work page 2023

  27. [27]

    Kevin C Smith, Abid Khan, Bryan K Clark, Steven M Girvin, and Tzu-Chieh Wei. 2024. Constant-depth preparation of matrix product states with adaptive quantum circuits.PRX Quantum5, 3 (2024), 030344

    work page 2024

  28. [28]

    Alexandre M Souza, Gonzalo A Alvarez, and Dieter Suter. 2011. Robust dynamical decoupling for quantum computing and quantum memory.Physical review letters 106, 24 (2011), 240501

    work page 2011

  29. [29]

    Kristan Temme, Sergey Bravyi, and Jay M Gambetta. 2017. Error mitigation for short-depth quantum circuits.Physical review letters119, 18 (2017), 180509

    work page 2017

  30. [30]

    Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H Booth, et al. 2022. The variational quantum eigensolver: a review of methods and best practices. Physics Reports986 (2022), 1–128

    work page 2022

  31. [31]

    Christopher Tong, Liran Shirizly, Edward H Chen, Derek S Wang, and Bibek Pokharel. 2026. Learning error suppression strategies for dynamic quantum circuits.arXiv preprint arXiv:2604.18734(2026)

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  32. [32]

    Hale F Trotter. 1959. On the product of semi-groups of operators.Proc. Amer. Math. Soc.10, 4 (1959), 545–551

    work page 1959

  33. [33]

    Lorenza Viola and Seth Lloyd. 1998. Dynamical suppression of decoherence in two-state quantum systems.Physical Review A58, 4 (1998), 2733

    work page 1998

  34. [34]

    Hyeonjun Yeo, Ha Eum Kim, IlKwon Sohn, and Kabgyun Jeong. 2025. Reduc- ing circuit depth in quantum state preparation for quantum simulation using measurements and feedforward.Physical Review Applied23, 5 (2025), 054066

    work page 2025

  35. [35]

    Wei Zi, Junhong Nie, and Xiaoming Sun. 2025. Constant-depth quantum circuits for arbitrary quantum state preparation via measurement and feedback.arXiv preprint arXiv:2503.16208(2025). 7

    work page arXiv 2025