Machine learning phases of matter
TLDR
It is shown that modern machine learning architectures, such as fully connected and convolutional neural networks, can identify phases and phase transitions in a variety of condensed-matter Hamiltonians.Abstract:
The success of machine learning techniques in handling big data sets proves ideal for classifying condensed-matter phases and phase transitions. The technique is even amenable to detecting non-trivial states lacking in conventional order. Condensed-matter physics is the study of the collective behaviour of infinitely complex assemblies of electrons, nuclei, magnetic moments, atoms or qubits1. This complexity is reflected in the size of the state space, which grows exponentially with the number of particles, reminiscent of the ‘curse of dimensionality’ commonly encountered in machine learning2. Despite this curse, the machine learning community has developed techniques with remarkable abilities to recognize, classify, and characterize complex sets of data. Here, we show that modern machine learning architectures, such as fully connected and convolutional neural networks3, can identify phases and phase transitions in a variety of condensed-matter Hamiltonians. Readily programmable through modern software libraries4,5, neural networks can be trained to detect multiple types of order parameter, as well as highly non-trivial states with no conventional order, directly from raw state configurations sampled with Monte Carlo6,7.read more
Citations
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References
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Gradient-based learning applied to document recognition
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TL;DR: In this article, a graph transformer network (GTN) is proposed for handwritten character recognition, which can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters.
Book
Deep Learning
TL;DR: Deep learning as mentioned in this paper is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts, and it is used in many applications such as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames.
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Dynamic Programming
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
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Crystal statistics. I. A two-dimensional model with an order-disorder transition
TL;DR: In this article, the eigenwert problem involved in the corresponding computation for a long strip crystal of finite width, joined straight to itself around a cylinder, is solved by direct product decomposition; in the special case $n=\ensuremath{\infty}$ an integral replaces a sum.
Journal ArticleDOI
Fault tolerant quantum computation by anyons
TL;DR: A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer Unitary transformations can be performed by moving the excitations around each other Unitary transformation can be done by joining excitations in pairs and observing the result of fusion.