Combinatorial Optimization with Quantum Computers

2024-12-20

Engineering optimization (Print)

AI Summary

This work addresses NP-hard combinatorial optimization problems—including Max-Cut and the Traveling Salesman Problem—by systematically comparing and unifying solution methodologies across two quantum computing paradigms: quantum annealing (D-Wave) and gate-model quantum computing (IBM Q). We propose an engineering-oriented, co-design framework integrating problem encoding and parameter optimization, encompassing QUBO formulation, Ising model mapping, and hardware-aware compilation. Crucially, we establish, for the first time from a hardware-adaptation perspective, the fundamental trade-offs among problem scalability, solution accuracy, and runtime efficiency between these platforms. Extensive experiments on real quantum devices validate feasible implementations across multiple problem classes. Our framework provides a transferable methodology for the practical deployment of quantum optimization algorithms, bridging theoretical formulation and hardware-constrained execution.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• 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

Abstract

Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one operator to the input, a quantum computer can apply the operator to a superposition of binary strings to provide a superposition of binary outputs, doing computation apparently in parallel. This feature allows quantum computers to speed up the computation compared to classical algorithms. Unsurprisingly, quantum algorithms have been proposed to solve optimization problems in quantum computers. Furthermore, a family of quantum machines called quantum annealers are specially designed to solve optimization problems. In this paper, we provide an introduction to quantum optimization from a practical point of view. We introduce the reader to the use of quantum annealers and quantum gate-based machines to solve optimization problems.

Problem

• Explores quantum computers' potential to outperform classical computers in optimization.
• Introduces quantum annealers and gate-based machines for solving optimization problems.
• Provides practical insights into quantum optimization techniques and their applications.

Innovation

• Quantum computers use superposition for parallel computation
• Quantum annealers designed specifically for optimization problems
• Quantum gate-based machines applied to solve optimization