Introduction

One of the key components of machine-learning simulations for quantum many-body systems are certainly the machines. In NetKet, artificial neural networks are used to parametrize the many-body wave-function, as introduced in Reference (1).

Generally speaking, a machine is a high-dimensional (typically non-linear) function

of the quantum numbers that define the many-body quantum system, and depending on a set of parameters .

NetKet ships with several state-of-the-art implementations of Restricted Boltzmann Machines, Feedforward Neural Networks, Jastrow factors, and more. Custom machines can be also provided by the user, following the steps described here. Future versions of NetKet will provide an even larger choice of built-in machines. See also our Challenges, if you would like to contribute to the developments in these directions.

Compact parametrizations of the wave-function in terms of artificial neural networks can be used to find the ground-state of a many-body Hamiltonian (see also Ref. (2) for additional details). The algorithms to perform this learning task, as implemented in NetKet, are described in the Learning the Ground State section.

In addition to finding the ground-state of a given Hamiltonian, there are other learning tasks that can be performed using the machines implemented in NetKet. For example, supervised learning with Born machines (3,4), or unsupervised learning to perform state-reconstruction (5).

The corresponding learning algorithms will be implemented in future versions of NetKet. See also our Challenges, if you would like to contribute to the developments in these directions.

References


  1. Carleo, G., & Troyer, M. (2017). Solving the quantum many-body problem with artificial neural networks. Science, 355 602
  2. Carleo, G. (2017). Lecture notes for the Advanced School on Quantum Science and Quantum technology.
  3. Stoudenmire, M., & Schwab, D. (2016). Supervised Learning with Quantum-Inspired Tensor Networks. Advances in Neural Information Processing Systems 29, 4799
  4. Cheng, S., Chen J., & Wang L. (2017). Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines.
  5. Torlai, G. et al. (2018). Neural-network quantum state tomography. Nature Physics doi:10.1038/s41567-018-0048-5