A rigorous hybridization of variational quantum eigensolver with classical neural network

Abstract:Combining variational quantum process with classical neural learning offers a flexible route to improve ground-state estimation. We establish an integrated framework that connects neural transformations, measurement statistics, and guarantees physical stability through three requirements: self-contained training, polynomial resource scaling, and variational consistency. Its constructive realization, termed \emph{unitary variational quantum-neural hybrid eigensolver}~(U-VQNHE), couples a variational quantum circuit to a neural phase function through norm-preserving post-processing. The learned transformation is evaluated from measurement records, preserves the exact variational bound, and admits range-independent concentration guarantees for independent finite-shot evaluations. Complementing this construction, we characterize the statistical and representational constraints of amplitude reweighting: sampled-support mismatch can destabilize empirical normalization, while exact distribution matching can require exponentially large dynamic range for Haar-random targets and structured ansatz--target pairs under specified near-tensorizability and mismatch conditions. Finite-shot simulations on Ising and disordered XYZ spin models demonstrate improved energy accuracy over the underlying variational quantum eigensolver and greater robustness than the amplitude-reweighting baselines. Together, these results provide a principled foundation for quantum--neural eigensolvers in which physical consistency, expressive capacity, and measurement cost are treated as a single design problem.

arXiv:2602.17295 [quant-ph]

(or arXiv:2602.17295v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2602.17295 Focus to learn more arXiv-issued DOI via DataCite

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