[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Machine learning (ML) encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. This article reviews in a selective way the recent research on the interface between machine learning and the physical sciences. This includes conceptual developments in ML motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross fertilization between the two fields. After giving a basic notion of machine learning methods and principles, examples are described of how statistical physics is used to understand methods in ML. This review then describes applications of ML methods in particle physics and cosmology, quantum many-body physics, quantum computing, and chemical and material physics. Research and development into novel computing architectures aimed at accelerating ML are also highlighted. Each of the sections describe recent successes as well as domain-specific methodology and challenges.

Machine learning and the physical sciences

A neural-network technique can exploit the power of machine learning to mine the exponentially large data sets characterizing the state space of condensed-matter systems. Topological transitions and many-body localization are first on the list. Classifying phases of matter is key to our understanding of many problems in physics. For quantum-mechanical systems in particular, the task can be daunting due to the exponentially large Hilbert space. With modern computing power and access to ever-larger data sets, classification problems are now routinely solved using machine-learning techniques1. Here, we propose a neural-network approach to finding phase transitions, based on the performance of a neural network after it is trained with data that are deliberately labelled incorrectly. We demonstrate the success of this method on the topological phase transition in the Kitaev chain2, the thermal phase transition in the classical Ising model3, and the many-body-localization transition in a disordered quantum spin chain4. Our method does not depend on order parameters, knowledge of the topological content of the phases, or any other specifics of the transition at hand. It therefore paves the way to the development of a generic tool for identifying unexplored phase transitions.

/pdf/learning-phase-transitions-by-confusion-3tgj8gh1jx.pdf

Learning phase transitions by confusion

Fermionic Quantum Magnetism Optical lattices loaded with cold atoms have been used successfully as quantum simulators of condensed matter systems; however, in the case of fermionic quantum magnetism, achieving low enough temperatures has been a major obstacle. Greif et al. (p. 1307, published online 23 May; see the Perspective by Porto) selectively tuned the exchange interactions in an optical lattice of fermions, forcing a redistribution of entropy such that in the low-entropy subsystem the effective temperature was sufficiently low enough to lead to magnetic correlations. A redistribution of entropy in an optical lattice loaded with atoms leads to magnetic correlations. [Also see Perspective by Porto] Quantum magnetism originates from the exchange coupling between quantum mechanical spins. Here, we report on the observation of nearest-neighbor magnetic correlations emerging in the many-body state of a thermalized Fermi gas in an optical lattice. The key to obtaining short-range magnetic order is a local redistribution of entropy, which allows temperatures below the exchange energy for a subset of lattice bonds. When loading a repulsively interacting gas into either dimerized or anisotropic simple cubic configurations of a tunable-geometry lattice, we observe an excess of singlets as compared with triplets consisting of two opposite spins. For the anisotropic lattice, the transverse spin correlator reveals antiferromagnetic correlations along one spatial axis. Our work facilitates addressing open problems in quantum magnetism through the use of quantum simulation.

http://absimage.aps.org/image/MAR14/MWS_MAR14-2013-005819.pdf

Short-range Quantum Magnetism of Ultracold Fermions in an Optical Lattice

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases. 

/pdf/provably-efficient-machine-learning-for-quantum-many-body-1gxa5z2e.pdf

Provably efficient machine learning for quantum many-body problems

Quantum gas microscopes for ultracold atoms can provide high-resolution real-space snapshots of complex many-body systems. We implement machine learning to analyse and classify such snapshots of ultracold atoms. Specifically, we compare the data from an experimental realization of the two-dimensional Fermi–Hubbard model to two theoretical approaches: a doped quantum spin liquid state of resonating valence bond type1,2, and the geometric string theory3,4, describing a state with hidden spin order. This technique considers all available information without a potential bias towards one particular theory by the choice of an observable and can therefore select the theory that is more predictive in general. Up to intermediate doping values, our algorithm tends to classify experimental snapshots as geometric-string-like, as compared to the doped spin liquid. Our results demonstrate the potential for machine learning in processing the wealth of data obtained through quantum gas microscopy for new physical insights. Quantum gas microscopes provide high-resolution real-space snapshots of quantum many-body systems. Now machine-learning techniques are used in choosing theoretical descriptions according to the consistency of their predictions with these snapshots.

/pdf/classifying-snapshots-of-the-doped-hubbard-model-with-57ajlvnoqq.pdf

Classifying snapshots of the doped Hubbard model with machine learning

Quantum gas microscopes for ultracold atoms can provide high-resolution real-space snapshots of complex many-body systems. We implement machine learning to analyze and classify such snapshots of ultracold atoms. Specifically, we compare the data from an experimental realization of the two-dimensional Fermi-Hubbard model to two theoretical approaches: a doped quantum spin liquid state of resonating valence bond type, and the geometric string theory, describing a state with hidden spin order. This approach considers all available information without a potential bias towards one particular theory by the choice of an observable and can therefore select the theory which is more predictive in general. Up to intermediate doping values, our algorithm tends to classify experimental snapshots as geometric-string-like, as compared to the doped spin liquid. Our results demonstrate the potential for machine learning in processing the wealth of data obtained through quantum gas microscopy for new physical insights.

Classifying Snapshots of the Doped Hubbard Model with Machine Learning

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Classifying snapshots of the doped Hubbard model with machine learning

Classifying Snapshots of the Doped Hubbard Model with Machine Learning

Classifying Snapshots of the Doped Hubbard Model with Machine Learning