arxiv: 2605.07876 · v1 · submitted 2026-05-08 · 💻 cs.ET

Recognition: no theorem link

Per-Phase Fidelity Attribution for Quantum Compilers using HBR Decomposition

Chandrachud Pati , Yogesh Simmhan

Authors on Pith no claims yet

Pith reviewed 2026-05-11 02:30 UTC · model grok-4.3

classification 💻 cs.ET

keywords quantum compilersfidelity attributionHBR decompositionquantum SDK benchmarkingrouting overheadcircuit synthesisquantum circuit optimization

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The pith

HBR decomposition attributes fidelity loss to high-level, basis, and routing phases in quantum compilation, showing losses vary by circuit class and optimization level.

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

The paper introduces HBR decomposition to break down where fidelity is lost inside the quantum compilation pipeline rather than reporting only overall post-transpilation numbers. It splits the process into High-level structural decomposition, Basis translation, and Routing, then measures relative fidelity impact at each step across three production SDKs and eight circuits. The results show that the dominant loss source is circuit-class dependent, with routing responsible for up to 60 percent of loss in search circuits while synthesis leads in Hamiltonian simulation workloads. SDK performance orderings at diagnostic settings reverse at production optimization levels for deep circuits, and the HBR predictions match both noisy simulations and real IBM hardware runs.

Core claim

HBR decomposition quantifies relative fidelity loss across the H, B, and R stages of compilation. Applied to eight algorithms on IBM Heron and IonQ Forte backends with Qiskit, PennyLane, and TKET, it shows routing accounts for up to 60 percent of relative fidelity loss in search-class circuits while synthesis dominates Hamiltonian simulation, early synthesis choices amplify or reduce later routing overhead, and SDK rankings at opt=0 reverse at opt=2 for deep circuits. The decomposition correctly predicts SDK orderings on both simulation and real hardware.

What carries the argument

HBR decomposition, a per-phase fidelity attribution model that isolates relative loss contributions from High-level structural decomposition (H), Basis translation (B), and Routing (R) stages.

If this is right

For search-class circuits, routing optimizations can recover up to 60 percent of lost fidelity.
Early synthesis decisions in one stage change the routing burden in later stages depending on final connectivity.
SDK rankings observed at diagnostic optimization levels do not predict rankings at production levels for deep circuits.
Aggregate compiler benchmarks miss stage-specific bottlenecks that HBR makes visible.

Where Pith is reading between the lines

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

Compilers could adaptively choose synthesis and routing strategies according to detected circuit class before full compilation.
The same decomposition could be applied to additional hardware topologies to test whether the circuit-class dependence generalizes.
Stage-wise diagnostics might be integrated into real-time compilation loops to adjust parameters mid-process.

Load-bearing premise

Relative fidelity losses can be cleanly separated and added across the three phases without large interaction effects or measurement artifacts invalidating the decomposition.

What would settle it

Execute the same circuits with each phase isolated on hardware, sum the measured fidelity losses, and compare to the full-pipeline loss; systematic mismatch would show the additive attribution does not hold.

Figures

Figures reproduced from arXiv: 2605.07876 by Chandrachud Pati, Yogesh Simmhan.

**Figure 1.** Figure 1: HBR compilation pipeline. Each stage X ∈ {H, B, R} is metered by changing physical gate counts, which are mapped to ∆ log10(FX). 2.3 Noise models While metrics like Estimated Success Probability (ESP) or Map-Fidelity [28] provide single-value hardware readiness estimates, they lack the stage-wise attribution required for compiler diagnostics. The independent depolarizing channel composition underlying our … view at source ↗

**Figure 2.** Figure 2: HBR compilation pipeline for each SDK. Operations assigned to each con [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: Example of cumulative contributions to log10(F) from H/B/R stages and compiler-agnostic terms (readout and T2 idle decoherence) for QFT at n=10. where X ∈ {H, B, R} denotes a compiler stage, and ∆N (X) 2Q and ∆N (X) 1Q,phy are the gate counts changed at stage X relative to the preceding stage. Eqn. 1 is exact under independent depolarizing noise [31], i.e., each gate contributes a multiplicative factor (1 … view at source ↗

**Figure 4.** Figure 4: Per-phase fidelity attribution for shallow algorithms across three SDKs on [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

**Figure 5.** Figure 5: Per-phase fidelity attribution for significant algorithms. R-stage dominates [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗

**Figure 6.** Figure 6: log10(F) vs qubit count (n=[3,20]). Dashed line marks the −1 threshold. QFT’s inter-SDK gap is due to routing. All three SDKs reach identical H+B gate counts on QFT (n=10, 105 CXeq after basis translation), confirmed on IonQ’s routingfree execution where no inter-SDK gap appears (log10 F: Qiskit −0.424, TKET −0.423, PennyLane −0.439). On IBM Heron the entire gap is routing-driven: TKET’s deterministic Ro… view at source ↗

**Figure 7.** Figure 7: Optimization level winner, comparing Tier 1 (diag) vs Tier 2 (prod). [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗

**Figure 8.** Figure 8: Total 2Q gate counts by SDK for production (Tier 2) compilation [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗

**Figure 9.** Figure 9: Tier 2 compile time (ms) by SDK (ε = 0.01 predicted; 2σ measured). 5.4.1 IBM FakeFez Noisy Simulator All 8 benchmark circuits are executed across all SDK/tier variants on AerSimulator with the FakeFez noise snapshot, which reproduces per-edge CZ, per-qubit SX, readout, T1, and T2 calibration data for ibm_fez (Heron r2, 156 qubits, heavy-hex). Each variant is compiled to the native {CZ, SX, X, RZ} basis and… view at source ↗

read the original abstract

Quantum compilers sit between an algorithm's theoretical promise and what executes on physical hardware. Existing benchmarks report aggregate post-transpilation metrics but cannot attribute where fidelity is lost within the compilation pipeline. We present HBR decomposition, a per-phase fidelity attribution model that quantifies relative fidelity loss across High-level structural decomposition (H), Basis translation (B), and Routing (R). We evaluate three production SDKs (Qiskit, PennyLane, TKET) across eight algorithms on two backend topologies: IBM Heron (heavy-hex) and IonQ Forte (all-to-all). The dominant compiler bottleneck is strongly circuit-class dependent: Routing accounts for up to 60% of relative fidelity loss in search-class circuits, while synthesis dominates Hamiltonian simulation workloads. Early synthesis choices amplify or compress downstream routing overhead depending on circuit connectivity. SDK rankings at diagnostic optimization level (opt=0) reverse at production levels (opt=2) for deep circuits, showing that stagewise diagnostics and production results answer different questions. HBR correctly predicts SDK rank ordering across noisy simulations (8 circuits x 3 SDKs x 2 tiers) and real IBM Fez hardware executions, revealing stage-specific bottlenecks that are not observable through aggregate compiler benchmarks.

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

HBR gives a workable way to split fidelity loss by compiler stage and it tracks real hardware rankings on the tested circuits, but the additive split needs direct checks for cross-phase effects.

read the letter

The paper introduces HBR decomposition to measure how much fidelity drops in the high-level structural phase, the basis translation phase, and the routing phase separately. It runs this on Qiskit, PennyLane, and TKET for eight circuits across heavy-hex and all-to-all topologies, then checks the numbers against noisy simulation and actual IBM Fez executions. The results show routing can eat up to 60 percent of the loss on search circuits while synthesis dominates Hamiltonian simulation, and that SDK orderings flip when you move from no optimization to production levels. That is the concrete new piece: stage-wise numbers that aggregate benchmarks do not give you, plus evidence that the split predicts end-to-end rank order on the small test set. The work is useful because it turns a black-box compiler run into something you can point at when tuning or co-designing for NISQ hardware. The numbers line up with hardware, which is better than pure simulation claims. The soft spot is the assumption that the three phases add up cleanly. Early high-level choices change circuit depth and connectivity, which then changes how expensive routing and basis work become later. If those interactions are material, the reported percentages do not isolate true bottlenecks even when the composite scores still match final fidelity. The abstract states empirical matches but does not spell out the exact isolation procedure or controls for measurement artifacts, so the claim that HBR reveals invisible stage-specific problems rests on that untested additivity. This paper is for people building or evaluating quantum compiler stacks who already run the three SDKs and want diagnostics beyond total fidelity. A reader focused on practical NISQ tool chains would find the circuit-class dependence and the ranking predictions directly usable. It deserves a serious referee because the empirical coverage on production tools and real hardware gives it enough weight to review, even if the decomposition needs tighter validation on interactions.

Referee Report

2 major / 2 minor

Summary. The paper introduces HBR decomposition, a model that attributes relative fidelity loss in quantum compilers to three sequential phases: High-level structural decomposition (H), Basis translation (B), and Routing (R). It evaluates Qiskit, PennyLane, and TKET across eight algorithms on IBM Heron (heavy-hex) and IonQ Forte (all-to-all) backends, reporting that routing dominates fidelity loss (up to 60%) in search circuits while synthesis dominates Hamiltonian simulation workloads. Early H choices are shown to modulate downstream R overhead, SDK rankings reverse between diagnostic (opt=0) and production (opt=2) levels for deep circuits, and HBR is claimed to correctly predict end-to-end SDK rank orderings in noisy simulations and real IBM Fez hardware runs, exposing stage-specific bottlenecks invisible to aggregate benchmarks.

Significance. If the additive decomposition is robust, the work provides a useful diagnostic lens for compiler developers by isolating phase contributions rather than relying on post-transpilation aggregates. The empirical scope—multiple SDKs, circuit classes, topologies, and both simulation/hardware validation—is a clear strength, as is the reproducible rank-order prediction across 8 circuits × 3 SDKs × 2 tiers. The observation that optimization level and circuit connectivity alter which stage is the bottleneck has practical implications for targeted improvements in quantum software stacks.

major comments (2)

[Abstract and HBR decomposition description] Abstract and HBR decomposition description: the central claim that relative fidelity loss decomposes additively into H, B, and R contributions (with routing up to 60% for search circuits) rests on the untested assumption that cross-phase interactions are negligible. Compilation is sequential; H-phase structural choices alter depth and connectivity, which nonlinearly affect R-phase overhead. The manuscript provides no ablation study, sensitivity analysis, or error bounds demonstrating that the attributed percentages remain stable when early-stage decisions are controlled, undermining the assertion that HBR isolates true stage-specific bottlenecks.
[Experimental methodology and results sections] Experimental methodology and results sections: insufficient detail is given on how per-phase fidelity is isolated and measured. The text reports empirical matches on simulation and hardware but omits the concrete procedure for per-phase attribution, error propagation through the pipeline, controls for measurement artifacts, or how interaction effects between stages are mitigated or quantified. This gap is load-bearing because the rank-order predictions and bottleneck claims cannot be independently verified without these specifics.

minor comments (2)

[Abstract] The abstract states that HBR 'correctly predicts SDK rank ordering' but does not specify the quantitative success metric (e.g., rank correlation coefficient or top-1 accuracy) or the exact held-out protocol used to establish this prediction.
[Notation for 'relative fidelity loss'] Notation for 'relative fidelity loss' should be formalized with an explicit equation early in the manuscript to remove ambiguity in how the percentages are normalized across phases.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation of HBR decomposition. We address each major comment below and will revise the manuscript accordingly to improve rigor and reproducibility.

read point-by-point responses

Referee: [Abstract and HBR decomposition description] Abstract and HBR decomposition description: the central claim that relative fidelity loss decomposes additively into H, B, and R contributions (with routing up to 60% for search circuits) rests on the untested assumption that cross-phase interactions are negligible. Compilation is sequential; H-phase structural choices alter depth and connectivity, which nonlinearly affect R-phase overhead. The manuscript provides no ablation study, sensitivity analysis, or error bounds demonstrating that the attributed percentages remain stable when early-stage decisions are controlled, undermining the assertion that HBR isolates true stage-specific bottlenecks.

Authors: We agree that phases are sequential and that H-phase choices can nonlinearly influence R-phase overhead, as already noted in the manuscript when discussing how early synthesis modulates downstream routing. The HBR attribution is computed via incremental fidelity measurements after each phase, and its practical utility is evidenced by the model's ability to correctly predict end-to-end SDK rank orderings on both noisy simulation and real IBM Fez hardware across all 8 circuits, 3 SDKs, and 2 optimization tiers. This match provides empirical support that the additive decomposition captures dominant contributions for bottleneck identification, even if interactions exist. Nevertheless, we acknowledge that an explicit ablation study would strengthen the claims. In the revision we will add a dedicated subsection performing sensitivity analysis: we will fix or vary H-phase decompositions while holding later stages constant, quantify stability of the attributed R percentages, and include basic error bounds derived from repeated runs. revision: yes
Referee: [Experimental methodology and results sections] Experimental methodology and results sections: insufficient detail is given on how per-phase fidelity is isolated and measured. The text reports empirical matches on simulation and hardware but omits the concrete procedure for per-phase attribution, error propagation through the pipeline, controls for measurement artifacts, or how interaction effects between stages are mitigated or quantified. This gap is load-bearing because the rank-order predictions and bottleneck claims cannot be independently verified without these specifics.

Authors: We agree that the current description of the attribution procedure is insufficient for full reproducibility. In the revised manuscript we will substantially expand the Experimental Methodology section with a step-by-step account of per-phase fidelity isolation. This will include: the precise formulas for computing relative fidelity loss at each stage (H, B, R), the method for propagating measurement uncertainties, controls for shot noise and backend calibration artifacts, and how we bound or quantify cross-stage interactions (via the ablation study noted above). We will also add a workflow diagram and pseudocode to make the pipeline transparent and verifiable. revision: yes

Circularity Check

0 steps flagged

No significant circularity: HBR attribution uses direct per-phase measurements on held-out executions

full rationale

The paper defines HBR phases (High-level structural decomposition, Basis translation, Routing) and reports relative fidelity loss percentages and SDK rank orderings from explicit executions of 8 circuits across 3 SDKs, 2 optimization tiers, noisy simulations, and real IBM hardware. These are presented as empirical observations rather than outputs of a fitted model whose parameters are defined in terms of the same target data. No equations reduce the per-phase attributions or rank predictions to self-referential inputs, no self-citations bear the central claim, and no ansatz or uniqueness theorem is invoked to force the decomposition. The additive model is an explicit modeling choice whose validity is tested externally via correlation with end-to-end results; this does not constitute circularity under the enumerated patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated beyond the HBR phases themselves, which function as an analysis framework rather than new physical postulates.

invented entities (1)

HBR decomposition no independent evidence
purpose: Per-phase fidelity attribution model splitting compilation into High-level structural decomposition (H), Basis translation (B), and Routing (R)
Introduced as the core analysis tool; no independent evidence provided in abstract

pith-pipeline@v0.9.0 · 5514 in / 1193 out tokens · 33891 ms · 2026-05-11T02:30:31.486937+00:00 · methodology

discussion (0)

Reference graph

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