NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems

Vicentini, Filippo; Hofmann, Damian; Szabó, Attila; Wu, Dian; Roth, Christopher G.; Giuliani, Clemens; Pescia, Gabriel; Nys, Jannes; Vargas-Calderón, Vladimir; Astrakhantsev, Nikita; Carleo, Giuseppe

doi:10.21468/scipostphyscodeb.7

Cited by 52 publications

(19 citation statements)

References 87 publications

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“…Appendix A: Details of calculations All of our calculations were implemented in Netket 3.3 [68,75]. In one dimension, we found that a restricted Boltzmann machine works well, while in two dimensions, a group convolutional neural network functions better.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Lee-Yang theory of quantum phase transitions with neural network quantum states

M.¹,

Flindt²,

Lado³

2023

Preprint

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Predicting the phase diagram of interacting quantum many-body systems is a central problem in condensed matter physics and related fields. A variety of quantum many-body systems, ranging from unconventional superconductors to spin liquids, exhibit complex competing phases whose theoretical description has been the focus of intense efforts. Here, we show that neural network quantum states can be combined with a Lee-Yang theory of quantum phase transitions to predict the critical points of strongly-correlated spin lattices. Specifically, we implement our approach for quantum phase transitions in the transverse-field Ising model on different lattice geometries in one, two, and three dimensions. We show that the Lee-Yang theory combined with neural network quantum states yields predictions of the critical field, which are consistent with large-scale quantum many-body methods. As such, our results provide a starting point for determining the phase diagram of more complex quantum many-body systems, including frustrated Heisenberg and Hubbard models.

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Section: Acknowledgmentsmentioning

confidence: 99%

Lee-Yang theory of quantum phase transitions with neural network quantum states

M.¹,

Flindt²,

Lado³

2023

Preprint

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“…However, there still exists scalability issue as the parameter number continues to increase. One solution is to adopt approximate solutions, such as the sparse distributed solver as introduced in NetKet [41] and hybrid low-rank natural gradient method in [42]. Investigating the performance of these highly scalable sparse algorithms is one of our future directions.…”

Section: Distributed Sr Computationmentioning

confidence: 99%

Deep learning representations for quantum many-body systems on heterogeneous hardware

Liang

Li²,

Xiao³

et al. 2023

Mach. Learn.: Sci. Technol.

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The quantum many-body problems are important for condensed matter physics, however solving the problems are challenging because the Hilbert space grows exponentially with the size of the problem. The recently developed deep learning methods provide a promising new route to solve long-standing quantum many-body problems. We report that a deep learning based simulation can achieve solutions with competitive precision for the spin $J1$-$J2$ model and fermionic $t$-$J$ model, on rectangular lattices within periodic boundary conditions. The optimizations of the deep neural networks are performed on the heterogeneous platforms, such as the new generation Sunway supercomputer and the multi graphical-processing-unit clusters. Both high scalability and high performance are achieved within an AI-HPC hybrid framework. The accomplishment of this work opens the door to simulate spin and fermionic lattice models with state-of-the-art lattice size and precision.

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“…Once we have the subset of approximate eigenstates in the form of an RBM, we use Metropolis sampling to estimate the matrix elements given in Equations ( 49) and (50). We used N σ = 5 × 10 6 samples for the estimate, resulting in a relative statistical error <10 −2 for the relevant matrix elements.…”

Section: Perturbation Theorymentioning

confidence: 99%

Finding the Dynamics of an Integrable Quantum Many‐Body System via Machine Learning

Wei,

Orfi,

Fehse

et al. 2023

Advanced Physics Research

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The dynamics of the Gaudin magnet (“central‐spin model”) is studied using machine‐learning methods. This model is of practical importance, for example, for studying non‐Markovian decoherence dynamics of a central spin interacting with a large bath of environmental spins and for studies of nonequilibrium superconductivity. The Gaudin magnet is also integrable, admitting many conserved quantities. Machine‐learning methods may be well suited to exploiting the high degree of symmetry in integrable problems, even when an explicit analytic solution is not obvious. Motivated in part by this intuition, a neural‐network representation (restricted Boltzmann machine) is used for each variational eigenstate of the model Hamiltonian. Accurate representations of the ground state and of the low‐lying excited states of the Gaudin‐magnet Hamiltonian are then obtained through a variational Monte Carlo calculation. From the low‐lying eigenstates, the non‐perturbative dynamic transverse spin susceptibility is found, describing the linear response of a central spin to a time‐varying transverse magnetic field in the presence of a spin bath. Having an efficient description of this susceptibility opens the door to improved characterization and quantum control procedures for qubits interacting with an environment of quantum two‐level systems.

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NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems

Cited by 52 publications

References 87 publications

Lee-Yang theory of quantum phase transitions with neural network quantum states

Lee-Yang theory of quantum phase transitions with neural network quantum states

Deep learning representations for quantum many-body systems on heterogeneous hardware

Finding the Dynamics of an Integrable Quantum Many‐Body System via Machine Learning

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