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From Quantum Algorithm Primitives to Design Patterns: A Unified Framework for NISQ and Fault-Tolerant Regimes
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DOI：10.1002/qute.70310.png)
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Abstract
En 中文
Existing surveys of quantum algorithms largely treat noisy intermediate-scale quantum (nisq) heuristics and fault-tolerant (ft) protocols in isolation. This review bridges that divide through a primitives-to-patterns framework, decomposing modern quantum algorithms into seven reusable building blocks, namely block-encodings, quantum signal processing (qsp), quantum singular value transformation (qsvt), amplitude amplification, quantum walks, shadow tomography, and variational ansatz circuits, from which eight recurring design patterns are extracted. The framework supplies: (i) lifecycle mappings from problem formulations through nisq-feasible heuristics to asymptotically optimal ft algorithms, with particular scrutiny of the nascent early fault-tolerant regime; (ii) multi-dimensional algorithm comparisons by T-count, circuit depth, qubit overhead, and classical co-processing cost under explicit error-correction assumptions; (iii) decision guidelines linking problem characteristics to algorithm families alongside regime-dependent caveats; (iv) a consolidated treatment of trainability barriers, classical simulability bounds, shadow-based certification, and error-mitigation strategies; and (v) an evidence-grounded appraisal of recent “Willow era” benchmarks redefining verifiable quantum utility. Validation against end-to-end resource estimates for quantum chemistry, combinatorial optimization, machine learning, and differential-equation solvers exposes boundary cases and failure modes. A research roadmap highlights under-explored primitive, problem, and hardware combinations alongside open questions that remain beyond the framework's current reach.
Keywords:
block-encoding
design patterns
fault-tolerant quantum computing
NISQ
quantum error correction
quantum machine learning
quantum singular value transformation
variational quantum algorithms
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