A Neural-Guided Variational Quantum Algorithm for Efficient Sign Structure Learning in Hybrid Architectures

TL;DR

This paper introduces sVQNHE, a hybrid quantum-classical algorithm that efficiently learns sign structures in quantum states, significantly reducing measurement costs and improving convergence for complex problems.

Contribution

The paper presents a neural-guided variational quantum algorithm that decouples amplitude and sign learning, enhancing efficiency and scalability in hybrid quantum-classical architectures.

Findings

Reduces error by 98.9% on 6-qubit J1-J2 model

Improves MaxCut solution quality by 19% on 45-vertex graphs

Requires nearly 19x fewer optimization steps than standard VQE

Abstract

Variational quantum algorithms hold great promise for unlocking the power of near-term quantum processors, yet high measurement costs, barren plateaus, and challenging optimization landscapes frequently hinder them. Here, we introduce sVQNHE, a neural-guided variational quantum algorithm that decouples amplitude and sign learning across classical and quantum modules, respectively. Our approach employs shallow quantum circuits composed of commuting diagonal gates to efficiently model quantum phase information, while a classical neural network learns the amplitude distribution and guides circuit optimization in a bidirectional feedback loop. This hybrid quantum-classical synergy not only reduces measurement costs but also achieves high expressivity with limited quantum resources and improves the convergence rate of the variational optimization. We demonstrate the advancements brought by sVQNHE through extensive numerical experiments. For the 6-qubit J1-J2 model, a prototypical system with a severe sign problem for Monte Carlo-based methods, it reduces the mean absolute error by 98.9% and suppresses variance by 99.6% relative to a baseline neural network, while requiring nearly 19x fewer optimization steps than a standard hardware-efficient VQE. Furthermore, for MaxCut problems on 45-vertex Erdos-Renyi graphs, sVQNHE improves solution quality by 19% and quantum resource efficiency by 85%. Importantly, this framework is designed to be scalable and robust against hardware noise and finite-sampling uncertainty, making it well-suited for both current NISQ processors and future high-quality quantum computers. Our results highlight a promising path forward for efficiently tackling complex many-body and combinatorial optimization problems by fully exploiting the synergy between classical and quantum resources in the NISQ era and beyond.