Ground state search by local and sequential updates of neural network quantum states

Abstract

Neural network quantum states are a promising tool to analyze complex quantum systems given their representative power. It can however be difficult to optimize efficiently and effectively the parameters of this type of ansatz. Here we propose a local optimization procedure which, when integrated with stochastic reconfiguration, outperforms previously used global optimization approaches. Specifically, we analyze both the ground state energy and the correlations for the non-integrable tilted Ising model with restricted Boltzmann machines. We find that sequential local updates can lead to faster convergence to states which have energy and correlations closer to those of the ground state, depending on the size of the portion of the neural network which is locally updated. To show the generality of the approach we apply it to both 1D and 2D non-integrable spin systems.

6 pages, 4 figures

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• Empowering deep neural quantum states through efficient optimization
• Improved Optimization for the Neural-network Quantum States and Tests on the Chromium Dimer
• Variational optimization of the amplitude of neural-network quantum many-body ground states
• Scalable Imaginary Time Evolution with Neural Network Quantum States
• Lee-Yang theory of quantum phase transitions with neural network quantum states
• Supervised Training of Neural-Network Quantum States for the Next Nearest Neighbor Ising model
• Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states