Generative flow-based warm start of the variational quantum eigensolver

• URL: http://arxiv.org/abs/2507.01726v1
• Date: Wed, 02 Jul 2025 14:00:37 GMT
• Title: Generative flow-based warm start of the variational quantum eigensolver
• Authors: Hang Zou, Martin Rahm, Anton Frisk Kockum, Simon Olsson,
• Abstract summary: Flow-VQE is a generative framework leveraging conditional normalizing flows with parameterized quantum circuits.<n>By embedding a generative model into the VQE optimization loop through preference-based training, Flow-VQE enables quantum gradient-free optimization.
• Score: 0.09999629695552192
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hybrid quantum-classical algorithms like the variational quantum eigensolver (VQE) show promise for quantum simulations on near-term quantum devices, but are often limited by complex objective functions and expensive optimization procedures. Here, we propose Flow-VQE, a generative framework leveraging conditional normalizing flows with parameterized quantum circuits to efficiently generate high-quality variational parameters. By embedding a generative model into the VQE optimization loop through preference-based training, Flow-VQE enables quantum gradient-free optimization and offers a systematic approach for parameter transfer, accelerating convergence across related problems through warm-started optimization. We compare Flow-VQE to a number of standard benchmarks through numerical simulations on molecular systems, including hydrogen chains, water, ammonia, and benzene. We find that Flow-VQE outperforms baseline optimization algorithms, achieving computational accuracy with fewer circuit evaluations (improvements range from modest to more than two orders of magnitude) and, when used to warm-start the optimization of new systems, accelerates subsequent fine-tuning by up to 50-fold compared with Hartree--Fock initialization. Therefore, we believe Flow-VQE can become a pragmatic and versatile paradigm for leveraging generative modeling to reduce the costs of variational quantum algorithms.

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