# Nonlinear Network Description for Many-Body Quantum Systems in Continuous Space.

@article{Ruggeri2018NonlinearND, title={Nonlinear Network Description for Many-Body Quantum Systems in Continuous Space.}, author={Michele Ruggeri and Saverio Moroni and Markus Holzmann}, journal={Physical review letters}, year={2018}, volume={120 20}, pages={ 205302 } }

We show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units. Using this wave function in variational Monte Carlo simulations of liquid ^{4}He in two and three dimensions, we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its…

## 20 Citations

### Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions.

- PhysicsPhysical review letters
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The NNB is benchmarked on Hubbard models at intermediate doping, finding that it significantly decreases the relative error, restores the symmetry of both observables and single-particle orbitals, and decreases the double-occupancy density.

### Fermionic neural-network states for ab-initio electronic structure

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An extension of neural-network quantum states to model interacting fermionic problems and use neural-networks to perform electronic structure calculations on model diatomic molecules to achieve chemical accuracy.

### Phase diagram reconstruction of the Bose-Hubbard model with a Restricted Boltzmann Machine wavefunction

- Physics
- 2020

Recently, the use of neural quantum states for describing the ground state of many- and few-body problems has been gaining popularity because of their high expressivity and ability to handle…

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- Physics, ChemistryNature Chemistry
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High-accuracy quantum chemistry methods struggle with a combinatorial explosion of Slater determinants in larger molecular systems, but now a method has been developed that learns electronic wavefunctions with deep neural networks and reaches high accuracy with only a few determinants.

### Artificial Neural Networks as Trial Wave Functions for Quantum Monte Carlo

- Computer Science, PhysicsAdvanced Theory and Simulations
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Feed‐forward neural networks are proposed as a general purpose trial wave function for quantum Monte Carlo simulations of continuous many‐body systems and the antisymmetry condition of non‐trivial fermionic systems is incorporated by means of a Slater determinant.

### Simulating disordered quantum Ising chains via dense and sparse restricted Boltzmann machines.

- Computer SciencePhysical review. E
- 2020

Sparse RBMs are implemented, whereby the visible spins are connected only to a subset of local hidden neurons, thus reducing the amount of parameters, and used as guiding functions for PQMC simulations at a reduced computational cost, avoiding possible biases due to finite random-walker populations.

### Ab-initio study of interacting fermions at finite temperature with neural canonical transformation

- PhysicsJournal of Machine Learning
- 2022

The variational density matrix approach to the thermal properties of interacting fermions in the continuum is parametrized by a permutation equivariant many-body unitary transformation together with a discrete probabilistic model and holds the promise to deliver new physical results on strongly correlated fermIONS in the context of ultracold quantum gases, condensed matter, and warm dense matter physics.

### Ab-initio study of interacting fermions at finite temperature with neural canonical transformation

- Physics
- 2021

We present a variational density matrix approach to the thermal properties of interacting fermions in the continuum. The variational density matrix is parametrized by a permutation equivariant…

### Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines.

- PhysicsPhysical review. E
- 2019

The high accuracy of this self-learning PQMC technique is demonstrated for a paradigmatic sign-problem-free model, namely, the ferromagnetic quantum Ising chain, showing very precise agreement with the predictions of the Jordan-Wigner theory and of loop quantum Monte Carlo simulations performed in the low-temperature limit.

### Neural-network quantum states at finite temperature

- PhysicsPhysical Review Research
- 2020

This work proposes a method to obtain the thermal-equilibrium density matrix of a many-body quantum system using artificial neural networks and applies this method to the one-dimensional Bose-Hubbard model and compares the results with those obtained by exact diagonalization.

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