Quenches near Ising quantum criticality as a challenge for artificial neural networks

Czischek, Stefanie; Gärttner, Martin; Gasenzer, Thomas

doi:10.1103/physrevb.98.024311

Cited by 76 publications

(73 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Neural network approaches have already been succesffuly applied to a wide number (see e.g. [27][28][29][30][31]) of close Hamiltonian systems. However, they have not yet been generalized to the important quantum manybody problem of open systems.In this Letter, we present a theoretical approach based on a variational neural network ansatz in order to determine the steady state of the master equation of open quantum lattice systems.…”

mentioning

confidence: 99%

Variational Neural-Network Ansatz for Steady States in Open Quantum Systems

et al. 2019

View full text Add to dashboard Cite

We present a general variational approach to determine the steady state of open quantum lattice systems via a neural network approach. The steady-state density matrix of the lattice system is constructed via a purified neural network ansatz in an extended Hilbert space with ancillary degrees of freedom. The variational minimization of cost functions associated to the master equation can be performed using a Markov chain Monte Carlo sampling. As a first application and proof-of-principle, we apply the method to the dissipative quantum transverse Ising model.In spite of the tremendous experimental progress in the isolation of quantum systems, a finite coupling to the environment [1] is unavoidable and certainly plays a crucial role in the practical implementation of quantum information and quantum simulation protocols [2]. Moreover, through an active control of the environment via the so-called reservoir engineering, an open quantum manybody system can be prepared in non-trivial phases [3][4][5] with also possible quantum applications [6, 7]. The theoretical description of open quantum manybody systems is in general out-of-the equilibrium and much less developed than for equilibrium systems. A mixed state with a finite entropy can be described by a density matrix, whose evolution is described by a master equation. Recently, a few theoretical methods have been developed to solve the master equation of open quantum manybody systems, including analytical approaches based on the Keldysh formalism [8,9], numerical algorithms based on matrix product operator and tensor-network techniques [10][11][12][13][14], cluster mean-field methods [15,16], corner-space renormalization [17][18][19], Gutzwiller mean-field [20], full configuration-interaction Monte Carlo [21], permutationinvariant solvers [22] or efficient stochastic unravelings for disordered systems [23]. The research in the field is very active, since the different methods are optimal for different specific regimes. For example, the corner-space renormalization method is best suited for systems with moderate entropy, while matrix product operator techniques to systems with short-range quantum correlations.In the last decade, the field of artificial neural networks has enjoyed a dramatic expansion and success thanks to remarkable applications in the recognition of complex patterns such as visual images or human speech (for a recent review see, e.g., [24]). The optimization (supervised learning) of the network is obtained by tuning the weights quantifying the connections between neural units via a variational minimization of a properly defined cost function. The wavefunction of a manybody system is in general a complex quantity, which is hard to be recognized. Recent works have proposed to exploit arti-ficial neural networks to construct trial wavefunctions, where the connection weights in the network play the role of variational parameters [25,26]. Neural network approaches have already been succesffuly applied to a wide number (see e.g. [27][28][29][30][31]) of clos...

show abstract

mentioning

confidence: 99%

Variational Neural-Network Ansatz for Steady States in Open Quantum Systems

et al. 2019

View full text Add to dashboard Cite

show abstract

“…The mean-squared error δρ monotonically increases for Eq. (14). This is because the operator e −∆βĤ in the asymmetric form in Eq.…”

Section: Resultsmentioning

confidence: 99%

“…This is because the operator e −∆βĤ in the asymmetric form in Eq. (14) only eliminates excited states in the ket vectors in the density operator, and therefore, once errors arise in the bra vectors during the imaginary-time evolution, the errors remain for β → ∞.…”

Section: Resultsmentioning

confidence: 99%

“…Using artificial neural networks as variational functions, therefore, we expect that quantum many-body wave functions can be approximated efficiently, in which the essential features of quantum many-body states are automatically captured as variational network parameters are optimized. This method has been applied to a variety of quantum many-body problems, and various properties of quantum many-body states represented by neural networks have been investigated [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Neural-network quantum states at finite temperature

Irikura

Saito

2020

Phys. Rev. Research

View full text Add to dashboard Cite

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 infinitetemperature 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 diagonalization.

show abstract

“…Originally invented by Paul Smolensky [125] and popularized by Geoffrey Hinton [126], this architecture has been recently repurposed as a representation of quantum states [116,123]. In this context, the RBM has been used to approximate the ground state of prototypical systems in condensed matter physics such as the transverse field Ising and Heisenberg models in one and two dimensions [123,127,128], the Hubbard model [128], models of frustrated magnetism [127], the Bose-Hubbard model [129,130], ground states of molecules [131], to model spectral properties of many-body systems [132], as well as to study nonequilibrium properties of quantum systems [123,133]. While the simulation of real-time dynamics remains a challenge, Ref.…”

Section: Hidden Layermentioning

confidence: 99%

Machine learning for quantum matter

Carrasquilla

2020

Advances in Physics: X

180

111

View full text Add to dashboard Cite

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 science, statistical mechanics, quantum information, quantum gravity, and large-scale numerical simulations. Recently, researchers interested in quantum matter and strongly correlated quantum systems have turned their attention to the algorithms underlying modern machine learning with an eye on making progress in their fields. Here we provide a short review on the recent development and adaptation of machine learning ideas for the purpose advancing research in quantum matter, including ideas ranging from algorithms that recognize conventional and topological states of matter in synthetic experimental data, to representations of quantum states in terms of neural networks and their applications to the simulation and control of quantum systems. We discuss the outlook for future developments in areas at the intersection between machine learning and quantum many-body physics.

show abstract

Quenches near Ising quantum criticality as a challenge for artificial neural networks

Cited by 76 publications

References 57 publications

Variational Neural-Network Ansatz for Steady States in Open Quantum Systems

Variational Neural-Network Ansatz for Steady States in Open Quantum Systems

Neural-network quantum states at finite temperature

Machine learning for quantum matter

Contact Info

Product

Resources

About