Polynomially efficient quantum enabled variational Monte Carlo for training neural-network quantum states for physico-chemical applications

TL;DR

This paper introduces a polynomially efficient quantum-assisted variational Monte Carlo method for training neural-network quantum states, enabling accurate simulation of complex physical systems with near-term quantum devices.

Contribution

It presents a scalable, quantum-enhanced Monte Carlo algorithm that improves training efficiency and expands the trial space for neural-network quantum states in physics applications.

Findings

Successfully learned ground states of spin models and electronic Hamiltonians

Achieved robust agreement with traditional methods in benchmarks

Enhanced sampling speed and fidelity with quantum devices

Abstract

Neural-network quantum states (NQS) offer a versatile and expressive alternative to traditional variational ans\"atze for simulating physical systems. Energy-based frameworks, like Hopfield networks and Restricted Boltzmann Machines, leverage statistical physics to map quantum states onto an energy landscape, functioning as memory descriptors. Here, we show that such models can be efficiently trained using Monte Carlo techniques enhanced by quantum devices. Our algorithm scales linearly with circuit width and depth, requires constant measurements, avoids mid-circuit measurements, and is polynomial in storage, ensuring optimal efficiency. It applies to both phase and amplitude fields, significantly expanding the trial space compared to prior methods. Quantum-assisted sampling accelerates Markov Chain convergence and improves sample fidelity, offering advantages over classical approaches. We validate our method by accurately learning ground states of local spin models and non-local electronic structure Hamiltonians, even in distorted molecular geometries with strong multi-reference correlations. Benchmark comparisons show robust agreement with traditional methods. This work highlights the potential of combining machine learning protocols with near-term quantum devices for quantum state learning, with promising applications in theoretical chemistry and condensed matter physics.