Generative flow-based warm start of the variational quantum eigensolver

TL;DR

Flow-VQE introduces a generative framework using conditional normalizing flows with quantum circuits to efficiently generate variational parameters, significantly reducing optimization costs and enabling effective warm-starts for related quantum problems.

Contribution

This work presents Flow-VQE, a novel generative approach integrating normalizing flows with quantum circuits for improved variational quantum eigensolver optimization.

Findings

Flow-VQE outperforms standard algorithms in accuracy and efficiency.

Achieves up to 100x reduction in circuit evaluations.

Accelerates warm-start optimization by up to 50-fold.

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.