# Systematic improvement of neural network quantum states using a Lanczos recursion

@inproceedings{Chen2022SystematicIO, title={Systematic improvement of neural network quantum states using a Lanczos recursion}, author={Hongwei Chen and Douglas Hendry and Phillip Weinberg and Adrian E. Feiguin}, year={2022} }

The quantum many-body problem lies at the center of the most important open challenges in condensed matter, quantum chemistry, atomic, nuclear, and high-energy physics. While quantum Monte Carlo, when applicable, remains the most powerful numerical technique capable of treating dozens or hundreds of degrees of freedom with high accuracy, it is restricted to models that are not afﬂicted by the infamous sign problem. A powerful alternative that has emerged in recent years is the use of neural…

## References

SHOWING 1-10 OF 47 REFERENCES

### Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry

- Physics, Computer ScienceJournal of physics. Condensed matter : an Institute of Physics journal
- 2021

This work constructs a variational wave function with one of the simplest neural networks, the restricted Boltzmann machine (RBM), and applies it to a fundamental but unsolved quantum spin Hamiltonian, the two-dimensional J 1–J 2 Heisenberg model on the square lattice.

### Machine learning approach to dynamical properties of quantum many-body systems

- PhysicsPhysical Review B
- 2019

Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight…

### Symmetries and Many-Body Excitations with Neural-Network Quantum States.

- PhysicsPhysical review letters
- 2018

Interestingly, it is found that deep networks typically outperform shallow architectures for high-energy states, and an algorithm to compute low-lying excited states without symmetries is given.

### Solving the quantum many-body problem with artificial neural networks

- Computer Science, PhysicsScience
- 2017

A variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons and a reinforcement-learning scheme that is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems.

### Purifying Deep Boltzmann Machines for Thermal Quantum States.

- Physics, Computer SciencePhysical review letters
- 2021

Two cutting-edge approaches to construct deep neural networks representing the purified finite-temperature states of quantum many-body systems are developed, which strongly assures the remarkable flexibility of the ansatz which can fully exploit the quantum-to-classical mapping.

### Neural network evolution strategy for solving quantum sign structures

- Computer SciencePhysical Review Research
- 2022

This work proposes a specific neural network ansatz suitable for systems with real-valued wave functions to encode the all-important rugged sign structure of a quantum wave function in a convolutional neural network with discrete output.

### Two-dimensional frustrated J1−J2 model studied with neural network quantum states

- Computer Science, PhysicsPhysical Review B
- 2019

This paper uses a fully convolutional neural network model as a variational ansatz to study the frustrated spin-1/2 J1-J2 Heisenberg model on the square lattice and demonstrates that the resulting predictions for both ground-state energies and properties are competitive with, and often improve upon, existing state-of-the-art methods.

### Neural network wave functions and the sign problem

- PhysicsArXiv
- 2020

This work proposes a neural network architecture with a simple, explicit, and interpretable phase ansatz, which can robustly represent low-energy states and achieve state-of-the-art variational energies for both conventional and frustrated antiferromagnets.

### Machine Learning Quantum States — Extensions to Fermion–Boson Coupled Systems and Excited-State Calculations

- Physics, Computer ScienceJournal of the Physical Society of Japan
- 2020

It is shown that the machine-learning solver achieves highly accurate ground-state energy, improving the accuracy substantially compared to that obtained by the variational Monte Carlo method.

### Neural Gutzwiller-projected variational wave functions

- PhysicsPhysical Review B
- 2019

Variational wave functions have enabled exceptional scientific breakthroughs related to the understanding of novel phases of matter. Examples include the Bardeen-Cooper-Schrieffer theory of…