QuantGraph: A Receding-Horizon Quantum Graph Solver

TL;DR

QuantGraph introduces a quantum-enhanced, receding-horizon framework for graph optimization that improves scalability, robustness, and solution precision by combining local and global quantum search stages within a control-inspired scheme.

Contribution

It presents a novel two-stage quantum algorithm for graph optimization that integrates control theory principles to enhance scalability and robustness.

Findings

Achieves up to 60% search space reduction.

Attains 2x higher control-discretization precision.

Demonstrates lower computational complexity with quantum speedup.

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.