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March 28, 2026Open Access

Quantum PRA Feasibility Roadmap: Topology-Aware Threshold Behavior, Scaling Requirements, and Public Hardware Compatibility Screening for CL-QUBO Fault Tree Optimization

Key Points

This paper aims to develop a topology-aware feasibility roadmap for quantum probabilistic risk assessment focusing on quantum optimization techniques.
Establishment of fidelity threshold behavior using QAOA+ across four topology classes.
Scaled circuit depth measurement across target sizes from 5 to 20 basic events.
Creation of a requirements matrix integrating measured and projected rows for different topology classes.
Classes A and C exhibit favorable threshold behavior, while Classes B and D show unfavorable behaviors under tested conditions.
Mapped qubit counts indicate all hardware platforms exceed the required counts for encoded instances.
Identified topology class as the main factor affecting threshold and scaling behavior.

Abstract

This paper presents a topology-aware feasibility roadmap for quantum probabilistic risk assessment (PRA) under bounded study conditions. The roadmap synthesizes three experimental phases applied to constraint-level quadratic unconstrained binary optimization (CL-QUBO) encodings of nuclear fault tree structures. Phase A establishes fidelity threshold behavior for the quantum approximate optimization algorithm with feasibility-preserving mixer (QAOA+) across four topology classes—Class A (anchored at n = 5), Class B (n = 6), Class C (n = 8, variant a), and Class D (n = 8, variant b)—derived from prior structural classification work. Phase B provides measured circuit-depth scaling evidence across target sizes from 5 to 20 basic events, including a deterministic constructor amendment that closes a previously missing Class B measured family. Phase C synthesizes measured and projected requirement rows into a 28-row requirements matrix spanning four topology classes and seven target sizes, with explicit evidence-tier marking distinguishing 19 measured rows from 9 projected rows. A public hardware capability screen maps the roadmap’s required-qubit count (equal to the number of basic events n in each encoded instance) against publicly reported qubit counts for Google Willow (105 qubits) 31, IBM Heron r2 (156 qubits) 32, IonQ Forte Enterprise (36 qubits) 33, and Quantinuum H2 (56 qubits) 34; the required-qubit count does not exceed the published qubit counts for any mapped platform. A bounded C3 utility bridge links the roadmap outputs to local PRA importance-measure behavior across Fussell–Vesely, Risk Achievement Worth, and Birnbaum importance families, with interpretation restricted to the studied setting. The roadmap identifies topology class as the dominant differentiator of threshold and scaling behavior: Classes A and C are threshold-favorable under the tested conditions, while Classes B and D are threshold-unfavorable. Pooled treatment across topology classes would mask these real structural differences. This paper does not claim quantum advantage, does not include live IBM hardware execution, and does not make deployment readiness or commercialization forecasts.

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