QC-PHAST Search: Classical--Quantum Query Benchmarks for Finite-Pool Rare-Regime Discovery

2026-07-24

AI Summary

This work addresses the challenge of efficiently discovering rare states—parameter configurations satisfying specific scientific thresholds—in parametric dynamical systems, particularly when feasible solutions are sparse, non-convex, or fragmented. The authors propose the QC-PHAST protocol, which integrates scientific metadata and pilot evidence into an auditable decision framework that dynamically selects the optimal search strategy among equation-aware, scalar-scoring active search, predicate-only search, or model comparison. For the first time, scientific validation predicates, dynamic object generation, and quantum Grover/BBHT query oracles are unified within an evidence-gated workflow. Through region mapping and boundary analysis, the method explicitly characterizes when classical structural or resource overheads outweigh quantum advantages, thereby providing an auditable basis for choosing between classical or resource-aware search paradigms.

Abstract

Rare-regime discovery in parameterized dynamical systems is an active-search problem: find one verified parameter at which a scientifically defined qualitative threshold is crossed, even when acceptable candidates are rare, nonconvex, or fragmented. We introduce Quantum-Classical Phase-space and Stability-Threshold Search (QC-PHAST), an evidence-gated decision protocol and query-accounting framework for finite candidate libraries. A candidate induces a dynamical object, simulator-derived criticality score, and verified first-hit predicate. Scientific metadata and charged pilot evidence are used to assess whether equation-aware search, scalar-score active search, predicate-only search, or only a query-model comparison is admissible. The quantum row is the inherited Grover/Boyer--Brassard--Hoyer--Tapp (BBHT) unknown-$M$ marked-set query reference; it is not a new quantum-search theorem, materialized circuit, or hardware-speedup claim. The result is a regime map. Direct boundary constructions, geometry controls, online simulator loops, and learned-label accounting further identify when classical structure, false positives, calibration cost, or state preparation erases the query-model margin. QC-PHAST is therefore an auditable protocol for deciding when a finite-pool marked-set reference is informative and when classical or resource-aware search should dominate.

Problem

• rare-regime discovery
• parameterized dynamical systems
• active search
• finite-pool search
• marked-set query

Innovation

• quantum-classical hybrid search
• rare-regime discovery
• evidence-gated protocol
• query-accounting framework
• finite-pool marked-set search