# Neural-network quantum states at finite temperature

@article{Irikura2020NeuralnetworkQS, title={Neural-network quantum states at finite temperature}, author={Naoki Irikura and Hiroki Saito}, journal={Physical Review Research}, year={2020} }

We propose a method to obtain the thermal-equilibrium density matrix of a many-body quantum system using artificial neural networks. The variational function of the many-body density matrix is represented by a convolutional neural network with two input channels. We first prepare an infinite-temperature state, and the temperature is lowered by imaginary-time evolution. We apply this method to the one-dimensional Bose-Hubbard model and compare the results with those obtained by exact…

## 8 Citations

### 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.

### 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.

### Neural Quantum States of frustrated magnets: generalization and sign structure

- Physics
- 2019

The main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility.

### Generalization properties of neural network approximations to frustrated magnet ground states

- PhysicsNature Communications
- 2020

The authors show that limited generalization capacity of neural network representations of quantum states is responsible for convergence problems for frustrated systems.

### Compact neural-network quantum state representations of Jastrow and stabilizer states

- Physics
- 2021

This work unifies Jastrow and stabilizer states into a new exact NQS representation that requires at most M = N − 1 hidden units, illustrating how highly expressive α ⩽ 1 can be and could pave the way for more families of quantum states to be represented exactly by compact NZS.

### Neural-Network Quantum States for Spin-1 Systems: Spin-Basis and Parameterization Effects on Compactness of Representations

- Computer ScienceEntropy
- 2021

A more direct generalization of RBMs forspin-1 that retains the key properties of the standard spin-1/2 RBM, specifically trivial product states representations, labeling freedom for the visible variables and gauge equivalence to the tensor network formulation is proposed.

### Machine learning for quantum matter

- Physics
- 2020

ABSTRACT Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials…

### Finding efficient observable operators in entanglement detection via convolutional neural network

- Physics
- 2022

In quantum information, it is of high importance to eﬃciently detect entanglement. Generally, it needs quantum tomography to obtain state density matrix. However, it would consumes a lot of…

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