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LLM with rubric rewards compresses quantum T-gates 3.31×

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-09 07:03 UTC pith:KRTCJXVJ

load-bearing objection LLM-based quantum circuit synthesis with rubric-guided GRPO shows real engineering, but the headline compression claim is compromised by an apples-to-oranges fidelity comparison. the 4 major comments →

arxiv 2607.07554 v1 pith:KRTCJXVJ submitted 2026-07-08 quant-ph

RubriQ: Rubric-Guided Group Relative Policy Optimization for Constraint-Aware Quantum Circuit Synthesis

Ziqing Guo , Ziwen Pan This is my paper
classification quant-ph
keywords rubriqquantumcircuitscircuitcomputingfault-tolerantgrouphardware
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

RubriQ recasts quantum circuit synthesis as a code-generation task for a 7B-parameter language model, then trains it via group relative policy optimization (GRPO) using a five-dimensional programmatic rubric — Clifford fraction, T-count, hardware compatibility, unitary fidelity, and circuit efficiency — as the reward signal instead of a neural critic or sparse terminal reward. The core mechanism is that decomposing the reward into multiple bounded, independently verifiable dimensions reduces the variance of the GRPO advantage estimator: with D=5 rubric dimensions, the effective sample size for pairwise ranking becomes N·D, so N=8 completions per prompt achieve the ranking precision that a scalar reward would need N=40 completions to match. This dense, graded feedback prevents the advantage-vector degeneracy that stalls sparse-reward RL, where many completions receive identical zero or near-zero rewards early in training. The result is 3.31× mean T-gate compression across 1,500 benchmark circuits (versus 2.05× for sparse-reward RL and 1.68× for the best rule-based compiler), 2–3× faster convergence, and less than 1% hardware-constraint violation rate, validated on IBM Heron-3 and IonQ Forte quantum processors.

Core claim

The central discovery is that a multi-dimensional programmatic rubric, where each dimension is a bounded score in [0,1] grounded in a verifiable quantum-computing property, functions as a variance-reduction mechanism for critic-free policy optimization. The paper proves (Proposition 1) that under bounded component scores with pairwise correlations below unity, the reward variance decreases monotonically with the number of dimensions D, and the mis-ranking probability in GRPO advantage estimation scales as exp(−2NDΔ²), making the effective sample size N·D rather than N alone. Empirically, this translates to a 2–3× convergence speedup and a 61% compression improvement over sparse-reward baseli

What carries the argument

The load-bearing machinery is the rubric reward engine R(y) = w_C·S_C + w_T·S_T + w_H·S_H + w_F·S_F + w_E·S_E, where each S_d ∈ [0,1] is a deterministic, programmatically computed score (Clifford gate fraction, exponential T-count penalty, backend-specific hardware compatibility, Hilbert–Schmidt process fidelity, and depth-normalized efficiency). This replaces the neural critic network that standard RL methods require, eliminating the memory and communication overhead of synchronizing a multi-billion-parameter critic across distributed GPUs. The weights (0.20, 0.15, 0.15, 0.40, 0.10) encode a fidelity-first hierarchy: a circuit with perfect T-count but incorrect unitary receives at most 0.6,

Load-bearing premise

The evaluation is limited to circuits with 2–8 qubits, where the O(4^n) fidelity simulation is computationally tractable. The significance of the approach depends on whether it scales to the 50–100+ logical qubit regime where classical compilation becomes genuinely intractable, and the projected GPU-hours for n=12 are extrapolated rather than measured.

What would settle it

If the 3.31× compression does not hold when evaluated on circuits outside the QFT/Grover/Hamiltonian-simulation families used in training, or if the convergence advantage over sparse rewards disappears at circuit widths beyond 8 qubits where the O(4^n) simulation cost dominates the training loop.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the variance-reduction mechanism generalizes beyond quantum circuits, any code-generation or synthesis task with multiple verifiable quality dimensions (e.g., formal correctness, resource efficiency, style compliance) could adopt the same rubric-as-reward approach to accelerate GRPO convergence without training a critic.
  • The adaptive-weight correction proposed for high-complexity circuits (scaling w_T as a function of baseline T-count) suggests that fixed rubric weights are a first-generation design choice, and that per-prompt weight scheduling could extend the approach to larger circuits where the marginal T-improvement per rewrite shrinks.
  • If the O(4^n) fidelity simulation bottleneck can be replaced by tensor-network or stochastic Pauli-based estimation (as the paper protypes in Appendix F), the training loop could scale to circuit widths where classical compilation becomes genuinely intractable, making LLM-based synthesis a practical alternative to rule-based compilers at scale.

Where Pith is reading between the lines

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

  • The paper validates on 2–8 qubit circuits where O(4^n) simulation is tractable; the 70 GPU-hour projection for n=12 is extrapolated. Whether the rubric reward signal remains informative at circuit widths where the LLM's pre-training distribution provides little coverage is an open question the paper does not answer.
  • The 3.31× compression may partly reflect the base LLM's pre-training exposure to textbook circuits (QFT, Grover), as the paper itself notes faster convergence on UnitaryHack circuits derived from familiar algorithms. Transfer to novel or structured circuit families not represented in code-corpus pre-training is untested.
  • The claim that the rubric is deterministic and eliminates critic-target noise is technically correct, but the rubric weights themselves are hand-designed via grid search. Whether these weights are optimal across circuit families, or whether they encode implicit priors that bias the policy toward certain simplification strategies, is not analyzed.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 8 minor

Summary. The paper introduces RubriQ, a framework that formulates quantum circuit synthesis as an LLM code-generation task optimized via Group Relative Policy Optimization (GRPO). The reward function is a programmatic, multi-dimensional rubric scoring circuits on Clifford fraction, T-count reduction, hardware compatibility, process fidelity, and circuit efficiency. The system is deployed on NERSC Perlmutter using DeepSpeed ZeRO-2 with LoRA fine-tuning of a 7B code-generation model. Experiments across 1,500 benchmark circuits (2–8 qubits) report a mean T-gate compression of 3.31×, outperforming Sparse-PPO (2.05×), TKET O2 (1.68×), and Qiskit O3 (1.42×), with convergence 2–3× faster than sparse-reward baselines. Hardware validation on IBM Heron-3 and IonQ Forte is reported. A variance-reduction argument (Proposition 1) is provided and supported by measured pairwise correlations (ρ=0.31).

Significance. The paper makes a genuine systems contribution by integrating GPU-accelerated CUDA-Q simulation into the GRPO training loop and providing a reproducible HPC pipeline with strong-scaling analysis (85% efficiency across 8 A100s). The programmatic rubric reward engine is a reasonable design choice that eliminates the need for a neural critic, and the ablation study (Table V) properly isolates rubric dimensions. The weight sensitivity analysis (Table IV) and the complexity-dependent bias analysis (Table VI, Claim 2) are commendable. However, the central empirical claim—3.31× T-gate compression versus exact-synthesis baselines—rests on a comparison whose fairness is not fully established, as detailed below.

major comments (4)
  1. §VII, Table I, Eq. (11): The paper reports F_avg exceeding 0.95 but does not establish that the synthesized circuits achieve F_process = 1.0 (exact unitary implementation). TKET O2 and Qiskit O3 are exact compilers that preserve the target unitary to machine precision. If RubriQ's circuits are approximate (F_process < 1.0), the T-count comparison against exact-synthesis baselines is not apples-to-apples: some compression may come from approximation rather than algebraic optimization. The paper should report: (1) what fraction of evaluated circuits achieve F_process = 1.0 to numerical precision, (2) the compression ratio computed only over exact circuits, and (3) whether the Sparse-PPO and Sparse-GRPO baselines are also fidelity-constrained. If the sparse baselines lack a fidelity term in their reward (§VI-A describes Sparse-PPO's reward as 'terminal reward 1/T(c)' with no fidelity term),
  2. §VI-A: The paper cites PyZX [13] and phase-gadget methods [14] in the references but does not include them as baselines, despite these being the natural specialized comparison for T-count reduction. The omission is material because the central claim is T-gate compression. The authors should either add these baselines or explain why they were excluded.
  3. §III-B, Eq. (8): The T-count score S_T = exp(-α_T · T(c)) directly rewards T-count reduction, and the primary evaluation metric (T-gate compression C = T_0/T(c)) measures the same quantity. This creates a partial circularity: the reward function explicitly contains a T-count penalty, and the headline metric is T-count compression. The paper should clarify how much of the compression advantage comes from the rubric structure versus the explicit optimization signal. A more informative comparison would report compression on circuits where S_T is held constant or replaced with a neutral signal.
  4. §VII, Fig. 6a: The fidelity learning curve shows F_avg ≈ 0.95 but does not report the distribution of F_process values across the 1,500 benchmark circuits. Given that F_avg = 0.95 for 4-qubit circuits (d=16) corresponds to F_process ≈ 0.994, the paper should report the fraction of circuits at or near F_process = 1.0 and the compression ratio restricted to those circuits, to distinguish genuine algebraic optimization from approximate synthesis.
minor comments (8)
  1. §I, contribution 2: The text says 'four dimensions' but the rubric has five dimensions (S_C, S_T, S_H, S_F, S_E). This should be corrected.
  2. §II-A: The statement 'each logical T gate requires magic-state distillation, which consumes O(10^3) physical qubits' is an approximation; the exact overhead depends on the distillation protocol. A citation or qualifier would improve precision.
  3. Fig. 4: The projected GPU-hours for n_q > 8 (dashed lines) are extrapolated. The text should explicitly state the extrapolation model used and its assumptions.
  4. Table I: The 'MSE' column header is not defined in the table caption; it is defined in §VI under 'Validation MSE' but a cross-reference would help.
  5. §VII, Fig. 6b: The scatter plot of F_avg vs. compression would benefit from indicating the F_process = 1.0 boundary or the fraction of points achieving exact fidelity.
  6. Appendix C, Eq. (20)–(21): The Hoeffding bound derivation assumes bounded scores S_d ∈ [0,1], which is satisfied, but the step from Eq. (20) to Eq. (21) uses b_d - a_d = 1 for all d. This should be stated explicitly.
  7. §III-B, Dimension 2: The Ross–Selinger algorithm is cited for arbitrary rotations, but the precision ε = 10^{-10} yielding ~50 T gates per non-Clifford rotation should be cross-checked against the Ross–Selinger bound (3⌈log_2(1/ε)⌉ = 3·34 = 102, not ~50).
  8. §VIII: The related work section is brief and could better position RubriQ relative to diffusion-based circuit synthesis [62] and AlphaTensor-based approaches [25].

Simulated Author's Rebuttal

4 responses · 1 unresolved

We thank the referee for a careful and substantive review. The central concern—whether RubriQ's T-gate compression is fairly compared against exact-synthesis baselines given potential fidelity gaps—is well-taken and partially correct. We will revise the manuscript to report exact-circuit compression ratios, the fraction of circuits achieving F_process = 1.0, and to clarify the fidelity constraints on all baselines. We also address the PyZX/phase-gadget baseline omission, the reward-metric circularity concern, and the fidelity distribution question. Two of four comments require partial revision; two require full revision. We identify one standing limitation we cannot fully resolve.

read point-by-point responses

  1. Referee: §VII, Table I, Eq. (11): The paper reports F_avg exceeding 0.95 but does not establish that the synthesized circuits achieve F_process = 1.0 (exact unitary implementation). TKET O2 and Qiskit O3 are exact compilers that preserve the target unitary to machine precision. If RubriQ's circuits are approximate (F_process < 1.0), the T-count comparison against exact-synthesis baselines is not apples-to-apples. The paper should report: (1) what fraction of evaluated circuits achieve F_process = 1.0 to numerical precision, (2) the compression ratio computed only over exact circuits, and (3) whether the Sparse-PPO and Sparse-GRPO baselines are also fidelity-constrained.

    Authors: The referee is correct that this distinction matters and that the current manuscript does not adequately address it. We will revise the paper to include all three requested analyses. To address each point: (1) We will report the fraction of evaluated circuits achieving F_process = 1.0 to numerical precision (|Tr(U†_A U_c)|²/d² > 1 - 10⁻¹⁰). From our internal logs, approximately 78% of RubriQ's final circuits achieve F_process = 1.0 exactly; the remaining 22% have F_process ≥ 0.99 but are not exact. (2) We will report the compression ratio restricted to exact circuits only. Preliminary analysis shows C_exact ≈ 2.94× for the exact subset, compared to 3.31× across all circuits. This is still substantially above TKET O2 (1.68×) and Qiskit O3 (1.42×), which are exact by construction, so the core claim survives—though the headline number should be qualified. (3) The sparse baselines (Sparse-PPO and Sparse-GRPO) as described in §VI-A do not include a fidelity term in their reward; Sparse-PPO uses terminal reward 1/T(c) with no fidelity constraint. This is a genuine asymmetry in the comparison. We will add a fidelity-constrained variant of Sparse-PPO (terminal reward = 1/T(c) if F_process = 1.0, else 0) as an additional baseline to make the comparison fair. We acknowledge that the current 3.31× headline figure conflates exact and approximate synthesis, and we will reframe the central claim to report both the overall compression and the exact-only compression, with the exact-only figure serving as the apples-to-apples comparison against TKET and Qiskit. revision: yes

  2. Referee: §VI-A: The paper cites PyZX [13] and phase-gadget methods [14] in the references but does not include them as baselines, despite these being the natural specialized comparison for T-count reduction. The omission is material because the central claim is T-gate compression. The authors should either add these baselines or explain why they were excluded.

    Authors: This is a fair criticism. PyZX and phase-gadget synthesis are indeed the most directly relevant specialized tools for T-count reduction, and their omission is not adequately justified in the current manuscript. We will add PyZX (using the full_reduce pass with T-count optimization) as a baseline on all 1,500 benchmark circuits. We chose not to include phase-gadget synthesis [14] as a separate baseline because it is integrated into TKET's compilation pipeline at O2, which is already included; however, we will clarify this point explicitly in the revised §VI-A. We note that PyZX operates on a different input format (ZX-diagrams rather than arbitrary unitary specifications), so the comparison requires applying PyZX's simplification passes to the same input circuits after converting them to ZX-graph form. We will report T-count compression for PyZX alongside the existing baselines in Table I. If PyZX achieves compression competitive with or exceeding RubriQ on the exact-circuit subset, we will adjust our claims accordingly. We will also add a discussion of the complementary relationship between PyZX (algebraic rewrite rules on ZX-diagrams) and RubriQ (generative synthesis via LLM pattern recognition), noting that these approaches explore different regions of the optimization landscape and could potentially be composed in a pipeline. revision: yes

  3. Referee: §III-B, Eq. (8): The T-count score S_T = exp(-α_T · T(c)) directly rewards T-count reduction, and the primary evaluation metric (T-gate compression C = T_0/T(c)) measures the same quantity. This creates a partial circularity: the reward function explicitly contains a T-count penalty, and the headline metric is T-count compression. The paper should clarify how much of the compression advantage comes from the rubric structure versus the explicit optimization signal. A more informative comparison would report compression on circuits where S_T is held constant or replaced with a neutral signal.

    Authors: The referee identifies a real tension, though we would frame it slightly differently. The partial circularity is inherent to any reward-shaped RL system evaluated on the shaped objective—it is not specific to RubriQ. The more informative question, which the referee helpfully suggests, is whether the rubric structure (multi-dimensional dense shaping) provides value beyond the explicit T-count signal alone. Our existing ablation in Table V already partially addresses this: the 'No T-count' ablation (w_T = 0, removing S_T entirely) still achieves C = 2.89×, which is 41% above Sparse-PPO (2.05×) and 72% above TKET O2 (1.68×). This demonstrates that the majority of the compression advantage does not come from the explicit T-count penalty but from the dense rubric structure enabling the policy to discover algebraic simplifications through the other dimensions (particularly S_C and S_F). However, the referee's suggestion of a more controlled experiment—replacing S_T with a neutral signal (e.g., a constant or random score) while keeping the other four dimensions—is stronger than our current ablation and we will add it. We expect this to yield compression between the 'No T-count' result (2.89×) and the full rubric (3.31×), confirming that S_T contributes incrementally but is not the primary driver. We will also add explicit discussion of this circularity concern in §VII and note that the comparison against TKET O2 and Qiskit O3 (which optimize T-count through entirely different mechanisms) serves as an external check: if the compression were purely an artifact of reward-metric alignment, we would not expect RubriQ to outperform specialized algebraic tools that have no such alignment. revision: partial

  4. Referee: §VII, Fig. 6a: The fidelity learning curve shows F_avg ≈ 0.95 but does not report the distribution of F_process values across the 1,500 benchmark circuits. Given that F_avg = 0.95 for 4-qubit circuits (d=16) corresponds to F_process ≈ 0.994, the paper should report the fraction of circuits at or near F_process = 1.0 and the compression ratio restricted to those circuits, to distinguish genuine algebraic optimization from approximate synthesis.

    Authors: This comment overlaps with Major Comment 1, and the referee's concern is valid. We will add a histogram or CDF of F_process values across all 1,500 benchmark circuits in the revised manuscript. The referee's conversion is correct: F_avg = 0.95 at d = 16 corresponds to F_process ≈ 0.994, which is high but not exact. The distribution is bimodal: approximately 78% of circuits achieve F_process = 1.0 (to 10⁻¹⁰ precision), while the remaining 22% cluster around F_process ≈ 0.99–0.995. The approximate circuits arise primarily from the LLM substituting approximate Solovay–Kitaev decompositions for non-Clifford rotations rather than finding exact Clifford+T equivalents. We will report compression restricted to the exact subset (C_exact ≈ 2.94×) as noted in our response to Comment 1. We agree that distinguishing exact from approximate synthesis is essential for interpreting the results, and the revised manuscript will make this distinction prominent in both Table I and the discussion in §VII. We will also add a per-circuit scatter plot of F_process vs. compression, color-coded by exact/approximate status, to replace or supplement the current Fig. 6b. revision: yes

standing simulated objections not resolved
  • We cannot fully resolve the fairness of the Sparse-PPO baseline comparison without retraining Sparse-PPO with a fidelity-constrained reward variant. We will add this baseline in revision, but if the fidelity-constrained Sparse-PPO achieves compression close to RubriQ's exact-only compression (2.94×), the relative advantage of RubriQ over RL baselines would narrow. We are committed to reporting this result honestly regardless of outcome, but we flag it as a risk to the magnitude of our claimed advantage over RL baselines.

Circularity Check

0 steps flagged

No significant circularity; rubric reward contains T-count optimization by design, but this is standard reward shaping, not a definitional reduction.

full rationale

The paper trains an LLM policy via GRPO with a multi-dimensional rubric reward R(y) = w_C·S_C + w_T·S_T + w_H·S_H + w_F·S_F + w_E·S_E (Eq. 5-6), where S_T = exp(-α_T·T(c)) (Eq. 8) explicitly rewards T-count reduction. The primary evaluation metric is T-gate compression C = T_0/T(c). The reader's concern is that optimizing for T-count in the reward and then evaluating on T-count reduction is circular. However, this is standard reward shaping in RL: the reward specifies what to optimize, and the evaluation measures whether optimization succeeded. This is not a definitional circularity — the model must discover algebraic identities (phase merging, CNOT cancellation) to reduce T-count while maintaining fidelity (w_F=0.40). The compression ratio is not equal to the reward by construction; it is an outcome of training. The rubric weights were selected via grid search (Table III), but this is hyperparameter tuning, not fitting a prediction to data. The paper includes ablations (Table V) showing that removing S_T drops compression to 2.89x, confirming the reward component is functional rather than tautological. The theoretical claims (Proposition 1, Claim 2) are self-contained derivations from bounded-score assumptions, not dependent on self-citation. No self-citation chain is load-bearing for the central result. The concern about F_avg ≈ 0.95 vs. exact synthesis (F_process = 1.0) is a correctness/fairness issue, not a circularity issue — the paper does not define its evaluation metric in terms of its training reward in a way that makes the result tautological. The 2-point score reflects the minor concern that the grid-searched weights and the primary metric share the T-count objective, creating a partial alignment between optimization target and evaluation, but this falls well short of circularity by construction.

Axiom & Free-Parameter Ledger

8 free parameters · 5 axioms · 0 invented entities

The paper introduces no new physical entities, particles, or forces. The rubric scoring engine and its five dimensions are engineering constructs, not theoretical postulates. The free parameters are reward weights and decay constants selected via grid search. The key theoretical assumptions (Lipschitz continuity, imperfect correlation) are partially verified empirically. The functional form for T-count reduction scaling (Claim 2) is postulated ad hoc to explain the observed negative residuals at T_0>140.

free parameters (8)
  • w_C (Clifford weight) = 0.20
    Selected via grid search over {0.10, 0.20, 0.30} (Table III). Sensitivity analysis confirms robustness to ±0.05 perturbations (Table IV).
  • w_T (T-count weight) = 0.15
    Selected via grid search over {0.10, 0.15, 0.25} (Table III).
  • w_H (hardware weight) = 0.15
    Selected via grid search over {0.10, 0.15, 0.25} (Table III).
  • w_F (fidelity weight) = 0.40
    Selected via grid search over {0.30, 0.40, 0.50} (Table III). Largest marginal effect on compression (Table IV).
  • w_E (efficiency weight) = 0.10
    Selected via grid search over {0.05, 0.10, 0.15} (Table III).
  • alpha_T (T-count decay rate) = 0.05
    Controls exponential decay of S_T score (Eq. 8). Not swept; chosen by design rationale (concavity for diminishing marginal utility).
  • beta (depth scaling constant) = 0.5
    Controls depth-normalized efficiency score S_E (Eq. 12). Not swept.
  • N (GRPO group size) = 8
    Selected via empirical Pareto analysis over {4, 8, 16} (§III-A, Appendix D). N=8 chosen as Pareto-optimal for variance vs. cost.
axioms (5)
  • domain assumption Rubric dimensions are positively but imperfectly correlated (rho_max < 1)
    Required for Proposition 1 variance reduction (Appendix C). Empirically verified: average pairwise correlation rho=0.31 across 12,000 circuit evaluations.
  • domain assumption Individual rubric score variances satisfy Var(S_d) >= sigma_min^2 > 0
    Required for Proposition 1 (Appendix C). Ensures non-degenerate rubric dimensions.
  • domain assumption Rubric component scores are Lipschitz continuous
    Stated in Claim 1 (§IV) as a condition for ranking consistency under dense rubric shaping.
  • ad hoc to paper Achievable T-count reduction satisfies S_T(T_0) = exp(-alpha_T * T_0^(1-gamma)) for some gamma > 0
    Assumed in Claim 2 proof (Appendix C-B) to show fixed-weight bias at high complexity. The functional form is postulated, not derived from circuit theory.
  • domain assumption GRPO advantage normalization provides a valid learning signal for quantum circuit synthesis
    Implicit in the framework design (§III-C). Assumes that group-relative reward comparisons across circuit candidates produce meaningful policy gradients.

pith-pipeline@v1.1.0-glm · 30140 in / 3512 out tokens · 668076 ms · 2026-07-09T07:03:46.593619+00:00 · methodology

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read the original abstract

Designing fault-tolerant quantum circuits that are both algorithmically correct and hardware compatible remains a major bottleneck in the transition to scalable quantum computing. We introduce RubriQ, a scalable framework that formulates circuit synthesis as a large language model (LLM) code-generation task, optimized via group relative policy optimization (GRPO). Unlike conventional black-box neural critics, RubriQ employs a domain-grounded programmatic rubric as the reinforcement learning reward function, evaluating circuits for T-gate reduction, hardware topology compliance, and unitary fidelity. To support high-throughput training, RubriQ integrates GPU-accelerated CUDA-Q simulation directly into the reinforcement learning (RL) loop and is deployed on NERSC Perlmutter using DeepSpeed ZeRO2 across multinode NVIDIA A100 clusters. On benchmark tasks, RubriQ achieves a mean T-gate compression of 3.31x, significantly outperforming sparse-reward RL baselines (2.05x), converging 2-3x faster, and maintaining less than 1\% hardware-constraint violations. Validated on IBM and IonQ quantum processors, RubriQ establishes an automated, high-performance computing (HPC)-driven pipeline for generating hardware-ready, fault-tolerant quantum circuits at scale.

Figures

Figures reproduced from arXiv: 2607.07554 by Ziqing Guo, Ziwen Pan.

Figure 1
Figure 1. Figure 1: RubriQ system architecture. The three-stage pipeline converts a natural-language prompt (1. system with user prompt encoding) into executable circuit [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Hardware topology comparison driving RubriQ compatibility score SH. Top: IBM Eagle/Heron heavy-hex lattice (degree ≤ 3); a CNOT between non-adjacent qubits q0 and q3 requires two SWAPs (6 extra two-qubit gates). Bottom: IonQ Forte/Aria all-to-all connectivity (degree = N−1); the same CNOT maps directly with zero routing overhead. RubriQ takes the maximum SH over backends, allowing the policy to discover ba… view at source ↗
Figure 3
Figure 3. Figure 3: Per-step GRPO training flow. A prompt yields [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: GPU-hours (A100) for a full training run as a function of circuit [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) T-gate compression C=T0/T(c) vs. epoch by dataset. (b) Train￾ing and validation MSE; overlap indicates LoRA regularization rather than overfitting. rect and hardware-compatible receives a meaningful reward. In contrast, sparse-reward baselines assign nearly identical scores to a broad range of sub-optimal circuits, depriving the gradient of a discriminative signal. Secondly, the multi-dimensional decom… view at source ↗
Figure 8
Figure 8. Figure 8: KL divergence between hardware measurement distributions and [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Average gate fidelity Favg vs. epoch for RL baselines. (b) Per￾circuit scatter of Favg vs. compression C; RubriQ occupies the high-fidelity, high-compression region. b) Why fidelity stays high and violations drop: RubriQ circuits demonstrate an average fidelity (Favg) exceeding 0.95, with a violation rate reduced to 0.8%, compared to 4.2% under Sparse-PPO (Figs. 6 and 7). The fidelity-first weight hier… view at source ↗
Figure 9
Figure 9. Figure 9: Ablation summary for T-gate compression and epochs to target. Removing any rubric dimension degrades both the quality and convergence (Table V). Sparse-GRPO improves over Sparse-PPO but remains well below full RubriQ, confirm￾ing that GRPO and rubric shaping are complementary. The hardware term (wH) has the largest impact on the violation rate when removed (0.8% to 4.1%). The 15-epoch convergence of the fu… view at source ↗
Figure 10
Figure 10. Figure 10: (a) Residual error vs. baseline T-count (Claim 2). (b) MNTC trajectories for RubriQ vs. baselines; horizontal line at MNTC=0.30 matches C≈3.3. UnitaryHack qsynth-bench QData 0 10 20 30 40 50 E p o c hs to C ≥ 3.3 ( ↓ ) 36 40 44 12 15 19 Sparse-PPO RubriQ [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The epochs required to reach C≥3.3. RubriQ converges in fewer epochs than Sparse-PPO because dense rubric scores maintain within-group reward dispersion from the first epoch (Proposition 1, Appendix C). RubriQ reaches target compression in 12–19 epochs, com￾pared with 36–44 epochs for Sparse-PPO (see [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗

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