Generative quantum combinatorial optimization by means of a novel conditional generative quantum eigensolver

2025-01-28

AI Summary

To address the limited flexibility, training difficulty, and poor generalization of hybrid quantum-classical approaches in quantum combinatorial optimization, this paper proposes the Conditional Generative Quantum Eigensolver (conditional-GQE). Built upon an encoder-decoder Transformer architecture, conditional-GQE is the first framework to introduce conditional generative modeling into quantum circuit design, enabling a context-aware, preference-driven, end-to-end trainable pipeline that dynamically synthesizes problem-structure-adapted parameterized quantum circuits. By integrating hybrid quantum-classical training, preference learning, and variational quantum eigensolving, the model achieves near 100% accuracy on combinatorial optimization tasks with up to 10 qubits. It significantly improves cross-problem transferability and scalability, establishing a novel paradigm for practical quantum optimization.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Quantum computing is entering a transformative phase with the emergence of logical quantum processors, which hold the potential to tackle complex problems beyond classical capabilities. While significant progress has been made, applying quantum algorithms to real-world problems remains challenging. Hybrid quantum-classical techniques have been explored to bridge this gap, but they often face limitations in expressiveness, trainability, or scalability. In this work, we introduce conditional Generative Quantum Eigensolver (conditional-GQE), a context-aware quantum circuit generator powered by an encoder-decoder Transformer. Focusing on combinatorial optimization, we train our generator for solving problems with up to 10 qubits, exhibiting nearly perfect performance on new problems. By leveraging the high expressiveness and flexibility of classical generative models, along with an efficient preference-based training scheme, conditional-GQE provides a generalizable and scalable framework for quantum circuit generation. Our approach advances hybrid quantum-classical computing and contributes to accelerate the transition toward fault-tolerant quantum computing.

Problem

• Quantum Combinatorial Optimization
• Hybrid Quantum-Classical Techniques
• Scalability Limitations

Innovation

• conditional-GQE
• quantum circuit generation
• quantum-combinatorial optimization