Artificial intelligence meets the quantum world


Computational physics lecturer Giuseppe Carleo introduces articial intelligence techniques into the realm of many-body quantum systems.

The quantum many-body problem arguably represents one of the greatest long-standing challenges in physics. Up until today, a century after the development of quantum theory, numerous approaches have been devised in order to tackle the exponentially increasing complexity intrinsic to the simulation of quantum many-body systems, yet the room for progress has once again proven to be significant.

In the recent Science publication [1], Carleo introduces an innovative idea into the realm of condensed matter physics. By making the seemingly simple, yet crucial, observation that a quantum state may be regarded as a kind of computational "black box", mapping configurations of a system's degrees of freedom to complex numbers, he proposes to obtain an approximate representation of quantum states by making use of techniques developed in the artifical intelligence community.

More specifically, Carleo has shown how it is possible to take the notion of a Restricted Boltzmann Machine (RBM), a type of neural network commonly used to learn probability distributions, and couple it together with traditional techniques from quantum Monte Carlo methods to assemble what he has dubbed a Neural Network Quantum State (NQS). The class of NQS embodies a type of computational machine designed to employ a custom form of reinforcement learning, specifically tuned to enable the machine to learn the complex features present in strongly-correlated quantum states.

By employing NQS to simulate standard benchmark problems, Carleo has managed to provide compelling evidence that this approach can achieve higher accuracies than algorithms based on Tensor Network States (TNS), currently considered to be among the state-of-the-art methods in the simulation of strongly-correlated systems, which make use of subtle observations regarding the entanglement properties of typical ground states of local hamiltonians.

Remarkably, the work has spurred a chain of efforts, both in obtaining explicit connections between TNS and NQS [2], as well as in the study of the entanglement properties of NQS [3], paving the way to a novel path towards the understanding of the processes involved in machine learning, using inputs from recent developments in quantum information theory.

For further reading see:

[1] Solving the quantum many-body problem with artificial neural networks - Science 355 (6325), 602-606.

[2] On the Equivalence of Restricted Boltzmann Machines and Tensor Network States - arXiv:1701.04831v1.

[3] Quantum Entanglement in Neural Network States - arXiv:1701.04844v1.

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