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arXiv:2501.16986

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

Shunya Minami, Kouhei Nakaji, Yohichi Suzuki, Alán Aspuru‐Guzik, Tadashi Kadowaki

Published Jan 28, 2025• 1 citation
arXivHTMLPDF

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.

DOI
10.48550/arxiv.2501.16986

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The ground state search problem is central to quantum computing, with applications spanning quantum chemistry, condensed matter physics, and optimization. The Variational Quantum Eigensolver (VQE) has shown promise for small systems but faces significant limitations. These include barren plateaus, restricted ansatz expressivity, and reliance on domain-specific structure. We present SpinGQE, an extension of the Generative Quantum Eigensolver (GQE) framework to spin Hamiltonians. Our approach reframes circuit design as a generative modeling task. We employ a transformer-based decoder to learn distributions over quantum circuits that produce low-energy states. Training is guided by a weighted mean-squared error loss between model logits and circuit energies evaluated at each gate subsequence. We validate our method on the four-qubit Heisenberg model, demonstrating successfulconvergencetonear-groundstates. Throughsystematichyperparameterexploration, we identify optimal configurations: smaller model architectures (12 layers, 8 attention heads), longer sequence lengths (12 gates), and carefully chosen operator pools yield the most reliable convergence. Our results show that generative approaches can effectively navigate complex energy landscapes without relying on problem-specific symmetries or structure. This provides a scalable alternative to traditional variational methods for general quantum systems. An open-source implementation is available at https://github.com/Mindbeam-AI/SpinGQE.
We introduce the generative quantum eigensolver (GQE), a new quantum computational framework that operates outside the variational quantum algorithm paradigm by applying classical generative models to quantum simulation. The GQE algorithm optimizes a classical generative model to produce quantum circuits with desired properties. Here, we develop a transformer-based implementation, which we name the generative pre-trained transformer-based (GPT) quantum eigensolver (GPT-QE). We show a proof-of-concept of training and pretraining of GPT-QE applied to electronic structure Hamiltonians, and demonstrate its ability illustrated by surpassing coupled cluster singles and doubles (CCSD) for the strong bond dissociation of the nitrogen molecule and approaching chemical accuracy. We also demonstrate the method on real quantum hardware.
Quantum computing and artificial intelligence (AI) are positioned as groundbreaking tools capable of tackling complexities inherent to modern computation posed by high-dimensional optimization problems.This research presents a quantum-enhanced optimization framework that leverages the QAOA (Quantum Approximate Optimization Algorithm) and VQE (Variational Quantum Eigen solver) within a hybrid quantum-classical paradigm.Machine learning models, including reinforcement learning and NN (neural networks), are integrated to optimize the quantum circuit parameters, enhance convergence, and improve scalability for complex problem spaces.Experimental evaluations demonstrate that this approach outperforms traditional optimization techniques in terms of efficiency and solution accuracy, particularly for large-scale multi-objective tasks.The framework is applied to key domains such as smart energy systems, logistics, and scientific modeling, illustrating its versatility and alignment with sustainable development goals.This study also explores the limitations of current quantum hardware and discusses future pathways for advancing hybrid quantum AI systems, offering significant contributions to next generation computational methodologies and intelligent problem solving.
This paper investigates the potential of quantum computing to accelerate combinatorial optimization algorithms. Traditional combinatorial optimization problems, such as the Traveling Salesperson Problem (TSP) and the Integer Linear Programming (ILP), often require exponential time to solve with classical algorithms. We propose a framework leveraging quantum algorithms, specifically the Variational Quantum Eigensolver (VQE), to tackle these problems. The core idea involves mapping the optimization problem into a quantum circuit, where the VQE algorithm iteratively refines a quantum state to find the optimal solution. We explore the theoretical underpinnings of this approach, focusing on the challenges and opportunities associated with quantum state preparation, measurement, and error mitigation. The paper provides a conceptual outline of the methodology and discusses potential improvements and future research directions. We demonstrate the feasibility of applying quantum computing to combinatorial optimization and highlight the potential for significant speedups compared to classical methods, especially as quantum hardware matures.