Distributed Quantum-Enhanced Optimization: A Topographical Preconditioning Approach for High-Dimensional Search

TL;DR

This paper introduces D-QEO, a hybrid quantum-classical framework that leverages quantum topographical preconditioning and separable function structure to efficiently solve high-dimensional optimization problems.

Contribution

It proposes a scalable distributed quantum-enhanced optimization method that uses quantum processors as preconditioners for classical solvers, enabling practical high-dimensional searches.

Findings

D-QEO prevents exponential failure in classical algorithms on benchmark functions.

Quantum warm-start reduces classical BFGS iterations for convergence.

Separable function structure allows parallelization with minimal quantum resource overhead.

Abstract

Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex functions. While quantum optimization offers a potential alternative, mapping continuous problems onto near-term quantum hardware introduces severe scaling limits and barren plateaus. To bridge this gap, we propose the Distributed Quantum-Enhanced Optimization (D-QEO) framework. Instead of forcing the quantum processor to find the exact minimum, we use it simply as a topographical preconditioner. The QPU maps the landscape to locate the most promising basin of attraction, generating high-quality seed points for a classical GPU-accelerated solver to refine. To make this approach viable for utility-scale problems, we exploit the mathematical structure of separable functions. This allows us to cut a 50-qubit (i.e., $2^{50}$) global search space into independent and manageable sub-spaces using 5-qubit subcircuits. By executing these fragments concurrently with CUDA-Q, we completely bypass the overhead of cross-register entanglement and classical tensor knitting for separable functions. Benchmarks on the 10-dimensional Rastrigin and Ackley functions show that D-QEO prevents the exponential failure rates observed in purely classical algorithms. Furthermore, this quantum warm-start significantly reduces the number of classical BFGS iterations required to converge, providing a highly practical blueprint for utilizing near-term quantum resources in complex global search.