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arxiv: 2604.18734 · v1 · submitted 2026-04-20 · 🪐 quant-ph

Learning error suppression strategies for dynamic quantum circuits

Christopher Tong , Liran Shirizly , Edward H. Chen , Derek S. Wang , Bibek Pokharel This is my paper

Pith reviewed 2026-05-10 04:32 UTC · model grok-4.3

classification 🪐 quant-ph
keywords dynamical decouplingdynamic quantum circuitserror suppressionrandomized benchmarkingquantum Fourier transformmid-circuit measurementfeedforward
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The pith

Empirically learned dynamical decoupling sequences cut average error rates in dynamic quantum circuits by a factor of three.

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

Dynamic quantum circuits perform unitary gates alongside mid-circuit measurements and classical feedforward, but the added measurement errors and control limits fall outside the reach of standard error-suppression tools. The authors build an empirical learning procedure that tunes dynamical decoupling sequences separately for chosen circuit segments and qubit groups. When these tuned sequences are inserted, randomized benchmarking shows a three-fold drop in average error rates. The same sequences support nontrivial process fidelity for a quantum Fourier transform with measurement on chains of up to 20 qubits and permit a clean QFT right after preparing a 10-qubit entangled state.

Core claim

We introduce an empirical learning framework that optimizes dynamical decoupling sequences for dynamic circuits at the level of circuit subintervals and qubit subregisters. Applying empirically learned DD sequences, we achieve a three-fold reduction in average dynamic circuit error rates as measured via randomized benchmarking. We apply the learned strategies to the dynamic circuit implementation of the quantum Fourier transform with measurement, demonstrating nontrivial process fidelity on connected chains of up to 20 qubits and a high signal-to-noise QFT immediately following the preparation of a 10-qubit entangled state.

What carries the argument

The empirical learning framework that optimizes dynamical decoupling sequences separately on circuit subintervals and qubit subregisters.

If this is right

  • Empirically learned DD sequences systematically outperform theoretically derived sequences for dynamic circuits.
  • Nontrivial process fidelity becomes achievable for QFT+M on connected chains of up to 20 qubits.
  • High signal-to-noise QFT can be executed immediately after preparing a 10-qubit entangled state.
  • The approach applies directly to any quantum algorithm or protocol that requires mid-circuit measurement and feedforward.

Where Pith is reading between the lines

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

  • Subinterval-level optimization may let researchers reuse learned patterns across larger dynamic circuits without retraining every time.
  • Hardware-specific training could become a routine calibration step before running any measurement-based routine on noisy devices.
  • The same learning loop might be applied to other suppression methods beyond DD, such as pulse shaping or spectator-qubit decoupling.

Load-bearing premise

The sequences discovered during training continue to suppress errors on dynamic circuits and noise profiles that were not part of the training data.

What would settle it

Running the learned sequences on a new dynamic circuit or qubit chain outside the training set and observing no error reduction or an increase in error rate would show the claimed improvement does not generalize.

Figures

Figures reproduced from arXiv: 2604.18734 by Bibek Pokharel, Christopher Tong, Derek S. Wang, Edward H. Chen, Liran Shirizly.

Figure 1
Figure 1. Figure 1: (left) A general dynamic circuit consists of repeated layers where some subset of “measured” qubits receive [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Two distinct sequences (teal and purple) are independently optimized for the depicted DD motif. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) We optimize DD strategies for the QFT+M circuit with an initial choice of 30 device qubits in a 1D [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: EPL for each qubit on which the DC-RB blocks (top) [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Through implementation of empirical learning, we observe persistent nontrivial [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) The family of states {|Ψm⟩} is constructed by a fan-out preparation of the Z-basis GHZ state, followed by a Hadamard transform to generate the X-basis GHZ state, then a Rz(π) rotation on qubit m. (b) As the fan-out GHZ state preparation requires an adjacent set of device qubits, error suppression is necessary to address both always-on and measurement-induced correlated errors. We perform the QFT+M on t… view at source ↗
Figure 7
Figure 7. Figure 7: (a) We optimize DD strategies for the QFT+M circuit with an initial choice of 30 device qubits in a 1D [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: GADD learning utilities for each individual in the genetic algorithm population at each iteration for each of [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: MCM-RB results on the first set of parallelized qubit registers, [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Results of MCM-RB experiments performed on the second set of parallelized qubit registers, [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Raw counts measured over 10000 shots of the experiment described in Sec. [PITH_FULL_IMAGE:figures/full_fig_p028_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: 1-norm similarity (Eqn. A1) between each experimental data series (GADD, XpXm, and no DD) and the theoretical prediction; a value of 1 occurs if and only if the distributions are exactly the same, while a completely uniform distribution will achieve a value of near 0 [PITH_FULL_IMAGE:figures/full_fig_p028_13.png] view at source ↗
read the original abstract

Dynamic quantum circuits integrate unitary evolution with mid-circuit measurement and feedforward, enabling conditional operations essential for efficient quantum algorithms and foundational for fault-tolerant quantum computation. However, such operations introduce measurement-induced errors and control constraints that are not addressed by conventional error-suppression techniques. Here, we introduce an empirical learning framework that optimizes dynamical decoupling (DD) sequences for dynamic circuits at the level of circuit subintervals and qubit subregisters. Applying empirically learned DD sequences, we achieve a three-fold reduction in average dynamic circuit error rates as measured via randomized benchmarking. We apply the learned strategies to the dynamic circuit implementation of the quantum Fourier transform with measurement (QFT+M), demonstrating nontrivial process fidelity on connected chains of up to 20 qubits. Applying the resulting enhancement, we perform a high signal-to-noise QFT immediately following the preparation of a 10-qubit entangled state. Our results demonstrate that empirically optimized DD systematically outperforms theoretically derived sequences for dynamic circuits, establishing it as an efficient approach for error suppression in dynamic quantum circuits, with direct relevance to applications requiring measurement and feedback such as quantum error correction.

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 / 2 minor

Summary. The manuscript introduces an empirical learning framework to optimize dynamical decoupling (DD) sequences for dynamic quantum circuits that incorporate mid-circuit measurements and feedforward operations. It reports achieving a three-fold reduction in average dynamic circuit error rates as measured by randomized benchmarking, applies the learned sequences to a dynamic implementation of the quantum Fourier transform with measurement (QFT+M) on chains of up to 20 qubits with nontrivial process fidelity, and demonstrates a high signal-to-noise QFT immediately after preparing a 10-qubit entangled state. The central claim is that empirically optimized DD systematically outperforms theoretically derived sequences for such circuits.

Significance. If the central experimental claims hold under scrutiny, the work is significant for practical error suppression in dynamic quantum circuits, which are foundational for quantum error correction and measurement-based algorithms. Credit is due for the data-driven approach that outperforms analytic DD sequences, the use of independent validation metrics (randomized benchmarking and process fidelity) rather than circular self-validation, and the hardware demonstration on up to 20 qubits with a concrete application to post-entanglement QFT. These elements provide a reproducible experimental template that could be directly tested on other devices.

major comments (2)
  1. [Results section] Results section (around the randomized benchmarking experiments): the reported three-fold reduction in average error rates lacks accompanying error bars, number of shots or circuit repetitions, and any statistical significance test. This is load-bearing for the headline claim, as hardware noise variability could render the factor non-robust without these details.
  2. [Learning framework and experimental validation sections] Learning framework and experimental validation sections: no held-out test circuits, cross-validation across distinct dynamic-circuit topologies (e.g., different measurement/feedforward patterns), or transfer experiments to a second device are reported. This directly affects the claim that the learned sequences constitute a general strategy rather than an instance-specific fit to the training subintervals, qubit registers, and hardware noise profile.
minor comments (2)
  1. [Abstract] The abstract states 'three-fold reduction' without specifying the baseline (standard DD or no DD) or the exact metric averaging procedure; a brief clarification would improve readability.
  2. [Learning framework] Notation for subinterval and subregister partitioning in the learning framework could be made more explicit with a small diagram or equation defining the optimization objective.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and have made revisions to strengthen the statistical reporting while clarifying the scope of our claims.

read point-by-point responses

  1. Referee: [Results section] Results section (around the randomized benchmarking experiments): the reported three-fold reduction in average error rates lacks accompanying error bars, number of shots or circuit repetitions, and any statistical significance test. This is load-bearing for the headline claim, as hardware noise variability could render the factor non-robust without these details.

    Authors: We agree that explicit error bars, details on the number of shots and circuit repetitions, and statistical significance testing are necessary to substantiate the reported three-fold reduction. In the revised manuscript, we have added bootstrapped error bars to the randomized benchmarking plots, specified that each circuit was executed with 1024 shots and averaged over 50 independent repetitions, and included a paired t-test confirming statistical significance (p < 0.01) for the improvement over theoretical sequences. revision: yes

  2. Referee: [Learning framework and experimental validation sections] Learning framework and experimental validation sections: no held-out test circuits, cross-validation across distinct dynamic-circuit topologies (e.g., different measurement/feedforward patterns), or transfer experiments to a second device are reported. This directly affects the claim that the learned sequences constitute a general strategy rather than an instance-specific fit to the training subintervals, qubit registers, and hardware noise profile.

    Authors: We acknowledge that the original manuscript does not report held-out test circuits, cross-validation on varied topologies, or transfer to a second device. This stems from hardware access constraints and the computational cost of exhaustive validation. The framework is modular by design, optimizing at the subinterval and subregister level, and we demonstrate consistent gains across chain lengths up to 20 qubits. In the revision, we have added explicit discussion of these limitations, tempered the generality claim to focus on the tested dynamic circuit classes, and highlighted the modular structure as a basis for future transfer. We maintain that the results establish the value of the empirical approach for the demonstrated cases. revision: partial

standing simulated objections not resolved
  • The absence of held-out test circuits, cross-validation across distinct dynamic-circuit topologies, and transfer experiments to a second device, which cannot be addressed without additional hardware access and resources.

Circularity Check

0 steps flagged

No significant circularity; empirical results validated by independent benchmarks

full rationale

The paper describes an empirical learning framework that optimizes DD sequences on training data and then measures performance gains via randomized benchmarking and process fidelity on applied circuits (including QFT+M). These validation metrics are separate experimental protocols that do not reduce to the optimization inputs or fitted parameters by construction. No self-definitional equations, fitted inputs relabeled as predictions, load-bearing self-citations, or ansatzes smuggled via prior work appear in the derivation. The central claim rests on external hardware measurements rather than internal redefinition, satisfying the criteria for a self-contained result against independent benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests primarily on empirical fitting of DD sequences to experimental data rather than first-principles derivation, introducing learned parameters that are hardware-specific and not independently derived.

free parameters (1)
  • Learned DD sequence parameters
    Timings and pulse patterns are optimized empirically from hardware data to minimize observed error rates in dynamic circuit subintervals.
axioms (1)
  • domain assumption Dynamical decoupling sequences can be empirically optimized to suppress measurement-induced errors in dynamic circuits
    The framework assumes DD remains effective when applied to circuits with mid-circuit measurements and that learning will discover superior sequences compared to theoretical designs.

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Forward citations

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    Combining dynamical decoupling and zero-noise extrapolation mitigates errors in dynamic circuits for Hamiltonian simulation, improving ground-state fidelity by at least 60% and cutting time-evolution errors by up to 9...

  2. Error Mitigation in Dynamic Circuits for Hamiltonian Simulation

    quant-ph 2026-05 unverdicted novelty 4.0

    Combining dynamical decoupling and zero-noise extrapolation on real quantum hardware improves energy gap estimates by at least 60% and reduces time-evolution errors by up to 99% for the Ising model in dynamic circuit ...

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