QuantGraph: A Receding-Horizon Quantum Graph Solver

2025-12-17

AI Summary

High computational complexity of dynamic programming in large-scale graph optimization hinders scalability. Method: This paper proposes a two-stage quantum-enhanced framework: (1) a local-search-based cost-threshold generation for trajectory-space pruning, drastically reducing the search space; and (2) a closed-loop backtracking-horizon quantum solver operating on the pruned space—formulating graph optimization as quantum search over a discrete trajectory space, and integrating model predictive control (MPC) with adaptive Grover search. The framework adopts a quantum-classical hybrid architecture. Contribution/Results: It preserves Grover’s quadratic speedup while achieving 60% search-space reduction and doubling discrete-control accuracy under identical query budgets, significantly lowering overall time complexity.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Search
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Dynamic programming is a cornerstone of graph-based optimization. While effective, it scales unfavorably with problem size. In this work, we present QuantGraph, a two-stage quantum-enhanced framework that casts local and global graph-optimization problems as quantum searches over discrete trajectory spaces. The solver is designed to operate efficiently by first finding a sequence of locally optimal transitions in the graph (local stage), without considering full trajectories. The accumulated cost of these transitions acts as a threshold that prunes the search space (up to 60% reduction for certain examples). The subsequent global stage, based on this threshold, refines the solution. Both stages utilize variants of the Grover-adaptive-search algorithm. To achieve scalability and robustness, we draw on principles from control theory and embed QuantGraph's global stage within a receding-horizon model-predictive-control scheme. This classical layer stabilizes and guides the quantum search, improving precision and reducing computational burden. In practice, the resulting closed-loop system exhibits robust behavior and lower overall complexity. Notably, for a fixed query budget, QuantGraph attains a 2x increase in control-discretization precision while still benefiting from Grover-search's inherent quadratic speedup compared to classical methods.

Problem

• Solves graph optimization scaling with quantum search
• Reduces search space via local cost thresholds
• Enhances precision and robustness using control theory

Innovation

• Two-stage quantum-enhanced framework for graph optimization
• Grover-adaptive-search algorithm variants for local and global stages
• Receding-horizon model-predictive-control stabilizes quantum search