Learning Neural Network Quantum States with the Linear Method

TL;DR

This paper introduces a linear method for optimizing complex neural network quantum states, demonstrating it converges faster than stochastic reconfiguration but with higher variance, especially beneficial when sampling costs are high.

Contribution

The paper formulates the linear method for complex-valued neural network quantum states and shows its advantages over stochastic reconfiguration in convergence speed.

Findings

Linear method converges faster than stochastic reconfiguration.

Linear method is more efficient when sampling costs are high.

Linear method has higher variance compared to SR.

Abstract

Due to the strong correlations present in quantum systems, classical machine learning algorithms like stochastic gradient descent are often insufficient for the training of neural network quantum states (NQSs). These difficulties can be overcome by using physically inspired learning algorithm, the most prominent of which is the stochastic reconfiguration (SR) which mimics imaginary time evolution. Here we explore an alternative algorithms for the optimization of complex valued NQSs based on the linear method (LM), and present the explicit formulation in terms of complex valued parameters. Beyond the theoretical formulation, we present numerical evidence that the LM can be used successfully for the optimization of complex valued NQSs, to our knowledge for the first time. We compare the LM to the state-of-the-art SR algorithm and find that the LM requires up to an order of magnitude fewer iterations for convergence, albeit at a higher cost per epoch. We further demonstrate that the LM becomes the more efficient training algorithm whenever the cost of sampling is high. This advantage, however, comes at the price of a larger variance.