MESSAGE
| DATE | 2017-02-11 |
| FROM | Ruben Safir
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| SUBJECT | Subject: [Hangout-NYLXS] Researchers use artificial neural network to
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(Phys.org)—A pair of physicists with ETH Zurich has developed a way to
use an artificial neural network to characterize the wave function of a
quantum many-body system. In their paper published in the journal
Science, Giuseppe Carleo and Matthias Troyer describe how they coaxed a
neural network to simulate some aspects of a quantum many-body system.
Michael Hush with the University of New South Wales offers a
Perspectives piece on the work done by the pair in the same journal
issue and also outlines the problems other researchers have faced when
attempting to solve the same problem.
One of the difficult challenges facing physicists today is coming up
with a way to simulate quantum many-body systems, i.e., showing all the
states that exist in a given system, such as a chunk of matter. Such
systems grow complicated quickly—a group of just 100 quantum particles,
for example, could have as many as 1035 spin states. Even the most
powerful modern computers very quickly become overwhelmed trying to
depict such systems. In this new effort, the researchers took a
different approach—instead of attempting to calculate every possible
state, they used a neural network to generalize the entire system.
The pair began by noting that the system used to defeat a Go world
champion last year might be modified in a way that could simulate a
many-body system. They created a simplified version of the same type of
neural network and programed it to simulate the wave function of a
multi-body system (by using a set of weights and just one layer of
hidden biases). They then followed up by getting the neural network to
figure out the ground state of a system. To see how well their system
worked, they ran comparisons with problems that have already been solved
and report that their system was better than those that rely on a
brute-force approach.
Taming complexity
The neural network detects specific patterns in the quantum system. In
this case, the network correctly recognises that atoms with an opposite
spin tend to pair up. Credit: ETH Zurich / G. Carleo
The system was a proof-of-concept rather than an actual tool for use by
physicists, but it demonstrates what is possible—large efforts, as Hush
notes, that involve more hidden biases and weights could result in a
tool with groundbreaking applications.
Explore further: Convolutional neural network able to identify rare eye
disorder
More information: Solving the quantum many-body problem with artificial
neural networks, Science 10 Feb 2017: vol. 355, Issue 6325, pp. 602-606
science.sciencemag.org/cgi/doi/10.1126/science.aag2302
Abstract
The challenge posed by the many-body problem in quantum physics
originates from the difficulty of describing the nontrivial correlations
encoded in the exponential complexity of the many-body wave function.
Here we demonstrate that systematic machine learning of the wave
function can reduce this complexity to a tractable computational form
for some notable cases of physical interest. We introduce a variational
representation of quantum states based on artificial neural networks
with a variable number of hidden neurons. A reinforcement-learning
scheme we demonstrate is capable of both finding the ground state and
describing the unitary time evolution of complex interacting quantum
systems. Our approach achieves high accuracy in describing prototypical
interacting spins models in one and two dimensions.
Press release
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