Per-Phase Fidelity Attribution for Quantum Compilers using HBR Decomposition

TL;DR

This paper introduces HBR decomposition, a model for attributing fidelity loss at each compilation stage in quantum compilers, enabling detailed analysis of bottlenecks on different hardware backends.

Contribution

It presents a novel per-phase fidelity attribution method that reveals stage-specific bottlenecks and predicts SDK performance across simulations and real hardware.

Findings

Routing causes up to 60% fidelity loss in certain circuits.

Synthesis dominates fidelity loss in Hamiltonian simulation workloads.

Stagewise diagnostics differ from aggregate benchmarks in revealing bottlenecks.

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.