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.

Efficient Optimization of Deep Neural Quantum States Toward Machine Precision

“…While keeping to use SR for high accuracy, large-scale supercomputers are employed to enlarge the allowed number of parameters by a few orders of magnitudes [28,29], thus compensating the training complexity by computing power. Furthermore, a sequential local optimization approach has also been proposed in which SR only optimizes a portion of all parameters to reduce the time cost [30]. In all these studies, however, the O(N 3 p ) complexity or the non-parallelizable iterative solvers of SR still remain to represent the key limitation for further increasing the network sizes.…”

Lee-Yang theory of quantum phase transitions with neural network quantum states

“…Neural network quantum states are a recently developed class of variational states [8] that have shown great potential for parametrizing and finding the ground state of interacting quantum many-body systems [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Neural network quantum states represent the wave function of a quantum many-body system as a neural network.…”

“…Neural network quantum states exploit the fact that neural networks can faithfully represent many complex functions [27], including a variety of quantum many-body wave functions. They have already been applied to find the wave functions of several spin models [9][10][11][12][13][14]28], including the J 1 − J 2 Heisenberg model [15][16][17][18][19][20][21]. Moreover, their use has been extended to fermionic [22,29] and bosonic [30][31][32] systems, as well as to molecules [22,23] and nuclei [24][25][26].…”