What question did this study set out to answer?

Evaluate competition of variational circuit families against QAOA+ for CL-QUBO fault tree analysis.

March 22, 2026Open Access

Constraint-Aware Variational Alternatives to QAOA for CL-QUBO Fault Tree Optimization: A Sensitivity Study Under Noiseless Statevector Screening

Key Points

Evaluate competition of variational circuit families against QAOA+ for CL-QUBO fault tree analysis.
Tested six variational circuit constructions against QAOA+ baseline on fault tree subtrees.
Used noiseless statevector simulation with deterministic multi-restart optimization.
Conducted feasible-subspace audits on family constructions.
All alternative families concentrated probability on a single non-minimal cut set state.
QAOA+ effectively distributed probability across feasible subspace leading to successful MCS identification.
No alternative construction provided sufficient evidence for hardware execution.

Abstract

This paper evaluates whether feasible-subspace-preserving variational circuit families can compete with the frozen QAOA+ baseline from Peters (2026) for Constraint-Level QUBO (CL-QUBO) fault tree minimal cut set identification. Six alternative constructions—an independently parameterized XX+YY generator family, a cost-phase-augmented variant, a transpiled-matched variant, a structure-ordered variant, an n = 6 restricted screen, and a warm-start variant—were tested against the QAOA+ comparator on a frozen pilot cohort of 14 reactor-scale fault tree subtrees (10 n = 6, 4 n = 8a instances) under noiseless statevector simulation with deterministic multi-restart optimization. The directly materialized family constructions passed feasible-subspace closure audits, and the screen-only variants inherited closure-qualified source families. These audits confirmed that the excitation-number-conserving XX+YY construction remained inside the intended fixed-Hamming-weight sector for the tested CL-QUBO instances. The failure mechanism is identified through per-instance analysis: the alternative families concentrate essentially all statevector probability (≈99.99%) on a single computational basis state that does not correspond to a minimal cut set, while QAOA+ distributes probability across the feasible subspace with sufficient structure to place MCS among the highest-ranked outcomes. The independently parameterized generator family lacks the problem-specific cost–mixer alternation that gives QAOA+ its concentration advantage, and adding a single cost phase layer does not rescue this deficit. The result is a disciplined negative finding: within the tested family definitions and frozen screening protocol, no approved alternative produced evidence strong enough to justify hardware execution. The contribution is a careful narrowing of the viable variational design space for CL-QUBO fault tree optimization, establishing that feasible-subspace preservation alone is insufficient for competitive MCS enrichment. Complete experimental artifacts with SHA-256 verification are provided.

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