Variational Quantum-Neural Hybrid Eigensolver

TL;DR

The paper introduces VQNHE, a hybrid quantum-neural approach that enhances VQE for ground-state energy simulations, significantly improving accuracy and scalability in the NISQ era.

Contribution

It presents a novel hybrid quantum-neural eigensolver that outperforms traditional VQE and offers scalable exponential acceleration with polynomial overhead.

Findings

VQNHE outperforms VQE in simulating ground-state energies.

VQNHE achieves significant accuracy improvements with the same quantum resources.

The method is scalable and efficiently implementable in the NISQ era.

Abstract

The variational quantum eigensolver (VQE) is one of the most representative quantum algorithms in the noisy intermediate-size quantum (NISQ) era, and is generally speculated to deliver one of the first quantum advantages for the ground-state simulations of some non-trivial Hamiltonians. However, short quantum coherence time and limited availability of quantum hardware resources in the NISQ hardware strongly restrain the capacity and expressiveness of VQEs. In this Letter, we introduce the variational quantum-neural hybrid eigensolver (VQNHE) in which the shallow-circuit quantum ansatz can be further enhanced by classical post-processing with neural networks. We show that VQNHE consistently and significantly outperforms VQE in simulating ground-state energies of quantum spins and molecules given the same amount of quantum resources. More importantly, we demonstrate that for arbitrary post-processing neural functions, VQNHE only incurs an polynomial overhead of processing time and represents the first scalable method to exponentially accelerate VQE with non-unitary post-processing that can be efficiently implemented in the NISQ era.