arxiv: 2604.21863 · v1 · submitted 2026-04-23 · 🪐 quant-ph · cs.AI· cs.ET· cs.LG

Recognition: unknown

Replay-buffer engineering for noise-robust quantum circuit optimization

Akash Kundu, Sebastian Feld

Authors on Pith no claims yet

Pith reviewed 2026-05-09 22:07 UTC · model grok-4.3

classification 🪐 quant-ph cs.AIcs.ETcs.LG

keywords replay bufferreinforcement learningquantum circuit optimizationnoise robustnesssample efficiencyQASmolecular energy

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The pith

Replay-buffer engineering yields 4-32x efficiency for quantum circuit RL

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

This paper tries to establish that the replay buffer is the key place to intervene in reinforcement learning for quantum circuit optimization. The main innovation is ReaPER+, which anneals its sampling from prioritizing large TD errors at the start to favoring reliable estimates later. This, plus amortizing evaluations and transferring noiseless data to noisy settings, produces large improvements in speed and solution quality. If true, it would mean that quantum circuit design on noisy hardware becomes much more feasible by better managing the data from simulations and experiments.

Core claim

The authors claim that by prioritizing the replay buffer, their ReaPER+ annealed replay rule transitions from TD error-driven prioritization early in training to reliability-aware sampling later, yielding 4-32 times better sample efficiency and more compact circuits in quantum tasks. Combined with amortized curriculum learning that cuts evaluation time by 67.5 percent and a transfer scheme that reuses noiseless trajectories to warm-start noisy training, the approach reduces steps to chemical accuracy by 85-90 percent and energy error by 90 percent on 6 to 12 qubit problems.

What carries the argument

ReaPER+, the annealed replay rule that transitions from TD error-driven prioritization to reliability-aware sampling as value estimates improve.

Load-bearing premise

The reliability-aware sampling and noiseless-to-noisy transfer introduce no hidden biases or need for problem-specific tuning when applied to real quantum hardware with different noise characteristics.

What would settle it

Deploying the ReaPER+ method and transfer scheme on actual quantum hardware and measuring whether the sample efficiency gains and circuit improvements persist without retuning for the specific noise profile.

Figures

Figures reproduced from arXiv: 2604.21863 by Akash Kundu, Sebastian Feld.

**Figure 1.** Figure 1: Overview of replay-buffer engineering for quantum optimization. (Left) Buffer engineering improves experience reuse through replay design and sampling. (Middle) Amortized learning reduces the cost of curriculum RL-based quantum architecture search by performing expensive quantum-classical updates only every m steps. (Right) Noise-aware transfer warm-starts the RL-training in noisy environment by reusing tr… view at source ↗

**Figure 2.** Figure 2: 1-qubit compiling of Haar-random target unitaries with RX, RY, RZ(±π/128) gates. (Left) Success probability and mean fidelity at tolerances 0.99, 0.999, and 0.9999, where ReaPER+ performs best overall. (Right) mean circuit length with std. dev. error bars versus tolerance; although all methods require deeper circuits at higher accuracy and exhibit a similar growth rate with tightening tolerance, ReaPER+ … view at source ↗

**Figure 3.** Figure 3: Replay-buffer design controls circuit compactness in QAS. For 6-BEH2 and 8-H2O, ReaPER+ variants yield the lowest total, CNOT, and rotation gate counts compared to PER and uniform replay (mean ± std over seeds). ω=0 recovers PER; ω=1 gives fully reliability-adjusted replay. ReaPER (ω = 0.4) ReaPER+ PER Vanilla 0 50 100 150 Total gate/CNOT/ROT count 6-BeH2 ReaPER+ ReaPER (ω = 0.6) PER Vanilla 8-H2O Total ga… view at source ↗

**Figure 4.** Figure 4: Efficiency and performance on 12-qubit H2O. (Left) OptCRLQAS reduces wall-clock time per episode by 67.5% over CRLQAS [19]. (Right) ReaPER achieves the lowest minimum energy error and fastest convergence across all replay baselines. CRLQAS OptCRLQAS 0 100 200 300 400 Avg. time per episode (s) 67.5% lower time Method Min err. ↓ Gates ↓ CNOT ↓ Steps ↓ ReaPER 1.7 × 10−2 196 109 1.6 × 104 ReaPER+ 2.3 × 10−2 24… view at source ↗

**Figure 5.** Figure 5: Weighted transfer matrix for BEH2 under noiseless and noisy transfer. Buffer transfer reduces steps to chemical accuracy by 47-58% and improves final energy by up to 90.2% across all noise settings, yielding composite scores of 19.2-35.8%. The strongest score (35.8%) is driven by the largest energy improvement at p2=0.001. ∆steps ∆ROT ∆CNOT ∆err Score Noiseless p2=0.001 p2=0.005 p1=0.001, p2=0.005 53.0% -… view at source ↗

**Figure 6.** Figure 6: Weighted transfer matrix for H2O under noiseless and noisy transfer. Step reductions range from 49.8% to 84.8%, and energy improvements reach 46.7% under combined noise (p1=0.001, p2=0.005), yielding the highest score of 28.7%. ∆steps ∆ROT ∆CNOT ∆err Score Noiseless p2=0.001 p1=0.001, p2=0.005 61.1% -25.0% -20.0% 9.8% 20.9% 49.8% -19.3% -19.5% 27.0% 22.2% 84.8% -40.7% -75.7% 46.7% 28.7% Transfer matrix (8 … view at source ↗

**Figure 8.** Figure 8: ReaPER+ progressively concentrates buffer mass toward higher-fidelity transitions (fidelity ≥ 0.95) while retaining broader early-training coverage, consistent with its annealed transition from PER-like exploration to ReaPER-like reliability-aware sampling. PER maintains broader low-fidelity coverage throughout training, while ReaPER shows intermediate concentration behavior. 0 2 4 6 8 ReaPER+ (a) Episode… view at source ↗

**Figure 9.** Figure 9: LunarLander-v3 validation of ReaPER+. (Left) rolling success rate (300-episode window). (Middle) ReaPER+ (blue) reaches a higher success rate faster and maintains a higher asymptotic level than fixed ReaPER (red) and PER (green). (Right) normalized cumulative-return AUC. ReaPER+ accumulates +9% more return over the full training run, confirming improved sample efficiency on a dense-reward classical benchma… view at source ↗

read the original abstract

Deep reinforcement learning (RL) for quantum circuit optimization faces three fundamental bottlenecks: replay buffers that ignore the reliability of temporal-difference (TD) targets, curriculum-based architecture search that triggers a full quantum-classical evaluation at every environment step, and the routine discard of noiseless trajectories when retraining under hardware noise. We address all three by treating the replay buffer as a primary algorithmic lever for quantum optimization. We introduce ReaPER$+$, an annealed replay rule that transitions from TD error-driven prioritization early in training to reliability-aware sampling as value estimates mature, achieving $4-32\times$ gains in sample efficiency over fixed PER, ReaPER, and uniform replay while consistently discovering more compact circuits across quantum compilation and QAS benchmarks; validation on LunarLander-v3 confirms the principle is domain-agnostic. Furthermore we eliminate the quantum-classical evaluation bottleneck in curriculum RL by introducing OptCRLQAS which amortizes expensive evaluations over multiple architectural edits, cutting wall-clock time per episode by up to $67.5\%$ on a 12-qubit optimization problem without degrading solution quality. Finally we introduce a lightweight replay-buffer transfer scheme that warm-starts noisy-setting learning by reusing noiseless trajectories, without network-weight transfer or $\epsilon$-greedy pretraining. This reduces steps to chemical accuracy by up to $85-90\%$ and final energy error by up to $90\%$ over from-scratch baselines on 6-, 8-, and 12-qubit molecular tasks. Together, these results establish that experience storage, sampling, and transfer are decisive levers for scalable, noise-robust quantum circuit optimization.

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.

Desk Editor's Note private letter to a colleague

The paper's three replay-buffer tweaks look like solid engineering fixes that deliver the claimed efficiency gains on the benchmarks shown, with a useful non-quantum check.

read the letter

The main thing here is that the authors focus on the replay buffer as the central lever for RL-based quantum circuit optimization. They add ReaPER+ (an annealed shift from TD-error prioritization to reliability-aware sampling), OptCRLQAS (amortized curriculum search that skips full evaluations on every edit), and a lightweight transfer of noiseless trajectories into noisy training. These are presented as direct responses to three bottlenecks, and the reported numbers—4-32× sample efficiency, 67.5% wall-clock reduction, and 85-90% fewer steps to chemical accuracy on 6-12 qubit molecular tasks—come with a domain-agnostic check on LunarLander-v3. That cross-domain test is useful and keeps the claims from feeling too narrowly tuned. The work builds cleanly on standard PER and curriculum RL without introducing new theoretical machinery, which makes the engineering focus clear and reproducible in principle. The transfer scheme avoids weight copying or pretraining, which is a practical plus for noise-robust settings. Soft spots are limited but real. The quantitative claims rest on empirical comparisons, so the full paper needs to show ablations, statistical tests, and sensitivity to noise profiles; without those the 4-32× range could shrink under different hardware conditions. The reliability-aware sampling step assumes value estimates mature in a way that doesn't create hidden bias, which is reasonable but not automatic on real devices. No circularity or load-bearing fitting appears in the argument. This is for researchers doing RL for quantum compilation, variational algorithms, or noisy hardware tasks. A reader who already works with replay buffers in RL will see concrete levers they can test. It deserves peer review—the ideas are specific, the benchmarks are relevant, and the non-quantum validation gives it a wider audience even if the empirical sections need more detail in revision.

Referee Report

2 major / 3 minor

Summary. The manuscript introduces three replay-buffer-centric improvements for deep RL applied to quantum circuit optimization: ReaPER+, an annealed prioritization scheme transitioning from TD-error to reliability-aware sampling; OptCRLQAS, which amortizes expensive quantum-classical evaluations across multiple architecture edits in curriculum search; and a lightweight buffer-transfer method that reuses noiseless trajectories to warm-start learning under hardware noise. It reports 4-32× sample-efficiency gains over fixed PER/ReaPER/uniform baselines, up to 67.5% wall-clock reduction, and 85-90% fewer steps to chemical accuracy with up to 90% lower final energy error on 6-12 qubit molecular tasks, plus domain-agnostic validation on LunarLander-v3.

Significance. If the empirical gains are robust, the work demonstrates that targeted engineering of experience storage, sampling, and transfer can materially reduce the number of costly quantum evaluations required for RL-based circuit design and compilation, addressing a practical bottleneck for scaling to noisy hardware. The non-quantum validation and explicit separation of the three levers strengthen the case that these are generalizable algorithmic improvements rather than problem-specific tweaks.

major comments (2)

[Results (molecular tasks)] Results section (molecular tasks): the reported 85-90% reductions in steps to chemical accuracy and 90% error reduction are presented as aggregate maxima without per-instance tables, number of independent seeds, or statistical significance tests against the from-scratch baselines; this makes it impossible to judge whether the central claim of consistent superiority holds across the 6-, 8-, and 12-qubit instances.
[Method (ReaPER+)] ReaPER+ description: the precise functional form of the reliability-aware sampling weight (and the annealing schedule that transitions from TD-error prioritization) is not given as an equation or algorithm box, so the claimed 4-32× efficiency gains cannot be reproduced or ablated from the text alone.

minor comments (3)

[Abstract] The abstract is unusually long and contains quantitative claims that would be better summarized with a single headline number per contribution; the detailed percentages can move to the introduction or results.
[Figures] Figure captions for the benchmark plots should explicitly state the number of runs and error-bar convention (e.g., standard error or min/max).
[Method (OptCRLQAS)] The OptCRLQAS amortization is described at a high level; a small pseudocode block or complexity table comparing per-episode quantum calls before and after would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. The two major comments highlight important issues of statistical rigor in the results and reproducibility of the ReaPER+ method. We address each point below and have revised the manuscript accordingly to strengthen the presentation.

read point-by-point responses

Referee: [Results (molecular tasks)] Results section (molecular tasks): the reported 85-90% reductions in steps to chemical accuracy and 90% error reduction are presented as aggregate maxima without per-instance tables, number of independent seeds, or statistical significance tests against the from-scratch baselines; this makes it impossible to judge whether the central claim of consistent superiority holds across the 6-, 8-, and 12-qubit instances.

Authors: We agree that aggregate maxima alone do not allow readers to assess consistency across qubit sizes. In the revised manuscript we have added a new table that breaks down the steps-to-accuracy and final-energy-error metrics for each of the 6-, 8-, and 12-qubit molecular instances separately. The table reports means and standard deviations computed over five independent random seeds, together with the results of paired t-tests against the corresponding from-scratch baselines. These additions make the consistency of the reported gains directly verifiable. revision: yes
Referee: [Method (ReaPER+)] ReaPER+ description: the precise functional form of the reliability-aware sampling weight (and the annealing schedule that transitions from TD-error prioritization) is not given as an equation or algorithm box, so the claimed 4-32× efficiency gains cannot be reproduced or ablated from the text alone.

Authors: We accept that the absence of an explicit equation and algorithm box prevents independent reproduction and ablation. The revised manuscript now contains a new equation that defines the reliability-aware sampling weight as a convex combination of normalized TD-error and a reliability score based on value-estimate variance, together with the precise linear annealing schedule that transitions from pure TD-error prioritization to the reliability-aware regime. We have also inserted an algorithm box that fully specifies the ReaPER+ sampling procedure, enabling direct implementation and controlled ablation studies. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on empirical benchmarks

full rationale

The manuscript introduces three engineering components (ReaPER+ annealed replay, OptCRLQAS amortization, and noiseless-to-noisy buffer transfer) and reports measured performance gains on quantum compilation, QAS, molecular VQE tasks, and LunarLander-v3. These are presented as experimental outcomes rather than any derivation chain, first-principles prediction, or fitted quantity renamed as a result. No equations, uniqueness theorems, or self-citations are invoked as load-bearing premises that reduce the central claims to their own inputs by construction. The argument is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based on abstract only; no explicit free parameters, invented entities, or non-standard axioms are described beyond the usual deep RL assumptions of Markovian environments and temporal-difference learning.

axioms (1)

domain assumption Quantum circuit optimization can be formulated as a Markov decision process with reliable TD targets under both noiseless and noisy settings
Implicit in the use of replay buffers and curriculum search for circuit design.

pith-pipeline@v0.9.0 · 5594 in / 1345 out tokens · 42317 ms · 2026-05-09T22:07:07.731990+00:00 · methodology

discussion (0)

Reference graph

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