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

2026-04-22

AI Summary

This work addresses the challenges of high-dimensional non-convex optimization, which suffers from severe local optima and the curse of dimensionality, while current quantum hardware is limited by scale and barren plateaus. The authors propose a Distributed Quantum-Enhanced Optimization (D-QEO) framework that innovatively employs quantum processors as landscape preconditioners to identify high-quality basins of attraction, thereby providing classical optimizers with superior initial points. For separable functions, the high-dimensional problem is decomposed into parallel small-scale quantum subcircuits—e.g., a 50-dimensional problem requires only five qubits—avoiding costly cross-register entanglement and tensor concatenation. Implemented via CUDA-Q for concurrent quantum subcircuit execution and combined with GPU-accelerated BFGS refinement, D-QEO significantly outperforms purely classical methods on 10-dimensional Rastrigin and Ackley functions, markedly reducing failure rates and iteration counts, thus demonstrating the practical potential of near-term quantum resources in global optimization.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• high-dimensional optimization
• non-convex functions
• barren plateaus
• quantum hardware limitations
• global search

Innovation

• Distributed Quantum Optimization
• Topographical Preconditioning
• Separable Functions
• Quantum Warm-Start
• CUDA-Q