Requirements for Early Quantum Advantage and Quantum Utility in the Capacitated Vehicle Routing Problem

2025-09-14

AI Summary

This work addresses the Capacitated Vehicle Routing Problem (CVRP) and systematically evaluates the feasibility frontier of early quantum advantage and quantum utility in the Noisy Intermediate-Scale Quantum (NISQ) era. Method: We propose an encoding-agnostic decision framework introducing three unified criteria—quantum feasibility point, quantum-gate feasibility line, and qubit-gate feasibility line—to construct a scalable decision diagram. Our analysis integrates closed-form resource estimation with state-of-the-art hardware benchmarks. Contribution/Results: We quantitatively reveal, for the first time, an order-of-magnitude resource gap between higher-order binary optimization (HOBO) and conventional quadratic unconstrained binary optimization (QUBO) encodings: on the Golden-5 benchmark, HOBO requires only 7,685 logical qubits versus over 200,000 for QUBO. The framework accepts arbitrary encoding strategies and hardware parameters, enabling precise identification of CVRP instances with quantum advantage potential—providing both theoretical criteria and engineering guidance for practical quantum optimization.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

We introduce a transparent, encoding-agnostic framework for determining when the Capacitated Vehicle Routing Problem (CVRP) can achieve early quantum advantage. Our analysis shows this is unlikely on noisy intermediate scale quantum (NISQ) hardware even in best case scenarios that use the most qubit-efficient direct encodings. Closed-form resource counts, combined with recent device benchmarks, yield three decisive go/no-go figures of merit: the quantum feasibility point and the qubit- and gate-feasibility lines, which place any CVRP instance on a single decision diagram. Contrasting a direct QUBO mapping with a space-efficient higher-order (HOBO) encoding reveals a large gap. Applied to early-advantage benchmarks such as Golden-5, our diagram shows that HOBO circuits require only 7,685 qubits, whereas comparable QUBO encodings still exceed 200,000 qubits. In addition to identifying candidate instances for early quantum advantage in CVRP, the framework provides a unifying go/no-go metric that ingests any CVRP encoding together with any hardware profile and highlights when quantum devices could challenge classical heuristics. Quantum advantage in CVRP would likely require innovative problem decomposition techniques.

Problem

• Assessing quantum feasibility for vehicle routing problems
• Comparing qubit requirements across different encoding methods
• Identifying hardware thresholds for quantum advantage over classical

Innovation

• Framework for quantum advantage feasibility
• Higher-order encoding reduces qubit requirements
• Unifying metric for hardware-encoding compatibility