scholarly journals Neural-network quantum states at finite temperature

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Naoki Irikura ◽  
Hiroki Saito
Keyword(s):  
Neural Network ◽  
Finite Temperature ◽  
Quantum States

scholarly journals Neural network operations and Susuki–Trotter evolution of neural network states

2018 ◽  
Vol 16 (08) ◽  
pp. 1840008 ◽  
Author(s):  
Nahuel Freitas ◽  
Giovanna Morigi ◽  
Vedran Dunjko
Keyword(s):  
Neural Network ◽  
Optimization Techniques ◽  
Quantum States ◽  
Stochastic Methods ◽  
Many Body ◽  
Boltzmann Machines ◽  
Quantum Operations ◽  
Model Complex ◽  
Network States ◽  
Hidden Nodes

It was recently proposed to leverage the representational power of artificial neural networks, in particular Restricted Boltzmann Machines, in order to model complex quantum states of many-body systems [G. Carleo and M. Troyer, Science 355(6325) (2017) 602.]. States represented in this way, called Neural Network States (NNSs), were shown to display interesting properties like the ability to efficiently capture long-range quantum correlations. However, identifying an optimal neural network representation of a given state might be challenging, and so far this problem has been addressed with stöchastic optimization techniques. In this work, we explore a different direction. We study how the action of elementary quantum operations modifies NNSs. We parametrize a family of many body quantum operations that can be directly applied to states represented by Unrestricted Boltzmann Machines, by just adding hidden nodes and updating the network parameters. We show that this parametrization contains a set of universal quantum gates, from which it follows that the state prepared by any quantum circuit can be expressed as a Neural Network State with a number of hidden nodes that grows linearly with the number of elementary operations in the circuit. This is a powerful representation theorem (which was recently obtained with different methods) but that is not directly useful, since there is no general and efficient way to extract information from this unrestricted description of quantum states. To circumvent this problem, we propose a step-wise procedure based on the projection of Unrestricted quantum states to Restricted quantum states. In turn, two approximate methods to perform this projection are discussed. In this way, we show that it is in principle possible to approximately optimize or evolve Neural Network States without relying on stochastic methods such as Variational Monte Carlo, which are computationally expensive.

Quaternion quantum neurocomputing

2020 ◽  
pp. 2040001
Author(s):  
Eduardo Bayro-Corrochano ◽  
Samuel Solis-Gamboa
Keyword(s):  
Neural Network ◽  
Geometric Algebra ◽  
Neuron Model ◽  
Quaternion Algebra ◽  
Quantum States ◽  
Robust Performance ◽  
Quantum Neural Network ◽  
Quantum Operator ◽  
New Type

Since the introduction of quaternion by Hamilton in 1843, quaternions have been used in a lot of applications. One of the most interesting qualities is that we can use quaternions to carry out rotations and operate on other quaternions; this characteristic of the quaternions inspired us to investigate how the quantum states and quantum operator work in the field of quaternions and how we can use it to construct a quantum neural network. This new type of quantum neural network (QNN) is developed in the quaternion algebra framework that is isomorphic to the rotor algebra [Formula: see text] of the geometric algebra and is based on the so-called qubit neuron model. The quaternion quantum neural network (QQNN) is tested and shows robust performance.

scholarly journals Learning a compass spin model with neural network quantum states

2021 ◽  
Author(s):  
Eric Zou ◽  
Erik Long ◽  
Erhai Zhao
Keyword(s):  
Neural Network ◽  
Ground States ◽  
Spin Model ◽  
Quantum Spin ◽  
Quantum States ◽  
Stochastic Gradient Descent ◽  
Tuning Parameter ◽  
Honeycomb Lattice ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines

Abstract Neural network quantum states provide a novel representation of the many-body states of interacting quantum systems and open up a promising route to solve frustrated quantum spin models that evade other numerical approaches. Yet its capacity to describe complex magnetic orders with large unit cells has not been demonstrated, and its performance in a rugged energy landscape has been questioned. Here we apply restricted Boltzmann machines and stochastic gradient descent to seek the ground states of a compass spin model on the honeycomb lattice, which unifies the Kitaev model, Ising model and the quantum 120-degree model with a single tuning parameter. We report calculation results on the variational energy, order parameters and correlation functions. The phase diagram obtained is in good agreement with the predictions of tensor network ansatz, demonstrating the capacity of restricted Boltzmann machines in learning the ground states of frustrated quantum spin Hamiltonians. The limitations of the calculation are discussed. A few strategies are outlined to address some of the challenges in machine learning frustrated quantum magnets.

scholarly journals Approximating Ground States by Neural Network Quantum States

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 82 ◽  
Author(s):  
Ying Yang ◽  
Chengyang Zhang ◽  
Huaixin Cao
Keyword(s):  
Neural Network ◽  
Tensor Product ◽  
Relative Error ◽  
Ground State ◽  
Ground States ◽  
Quantum States ◽  
The Neural Network

Motivated by the Carleo’s work (Science, 2017, 355: 602), we focus on finding the neural network quantum statesapproximation of the unknown ground state of a given Hamiltonian H in terms of the best relative error and explore the influences of sum, tensor product, local unitary of Hamiltonians on the best relative error. Besides, we illustrate our method with some examples.

scholarly journals Entanglement classification via neural network quantum states

2020 ◽  
Vol 22 (4) ◽  
pp. 045001 ◽  
Author(s):  
Cillian Harney ◽  
Stefano Pirandola ◽  
Alessandro Ferraro ◽  
Mauro Paternostro
Keyword(s):  
Neural Network ◽  
Quantum States
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