Machine learning for quantum matter

ABSTRACT Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials science, statistical mechanics, quantum information, quantum gravity, and large-scale numerical simulations. Recently, researchers interested in quantum matter and strongly correlated quantum systems have turned their attention to the algorithms underlying modern machine learning with an eye on making progress in their fields. Here we provide a short review on the recent development and adaptation of machine learning ideas for the purpose advancing research in quantum matter, including ideas ranging from algorithms that recognize conventional and topological states of matter in synthetic experimental data, to representations of quantum states in terms of neural networks and their applications to the simulation and control of quantum systems. We discuss the outlook for future developments in areas at the intersection between machine learning and quantum many-body physics. Graphical abstract

[1]  Lvzhou Li,et al.  Quantum generative adversarial network for generating discrete distribution , 2020, Inf. Sci..

[2]  E. Restrepo‐Parra,et al.  Deep learning approach for image classification of magnetic phases in chiral magnets , 2020 .

[3]  D. Lucchesi,et al.  Quantum-inspired machine learning on high-energy physics data , 2020, npj Quantum Information.

[4]  Vladimir Vargas-Calderón,et al.  Phase Diagram Reconstruction of the Bose–Hubbard Model with a Restricted Boltzmann Machine Wavefunction , 2020, 2004.12556.

[5]  M. Lewenstein,et al.  Phase detection with neural networks: interpreting the black box , 2020, New Journal of Physics.

[6]  Vladimir Vargas-Calder'on,et al.  Supervised Learning with Quantum Measurements , 2020, ArXiv.

[7]  M. Lewenstein,et al.  Unsupervised Phase Discovery with Deep Anomaly Detection. , 2020, Physical review letters.

[8]  Peter Wittek,et al.  A non-review of Quantum Machine Learning: trends and explorations , 2020 .

[9]  G. Paz-Silva,et al.  Beyond Quantum Noise Spectroscopy: modelling and mitigating noise with quantum feature engineering , 2020, 2003.06827.

[10]  Surya Ganguli,et al.  Statistical Mechanics of Deep Learning , 2020, Annual Review of Condensed Matter Physics.

[11]  Vijay Ganesh,et al.  Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks , 2020, Physical Review Research.

[12]  Christopher Roth,et al.  Iterative Retraining of Quantum Spin Models Using Recurrent Neural Networks , 2020, 2003.06228.

[13]  R. Glasser,et al.  Machine learning assisted quantum state estimation , 2020, Mach. Learn. Sci. Technol..

[14]  David Von Dollen,et al.  TensorFlow Quantum: A Software Framework for Quantum Machine Learning , 2020, ArXiv.

[15]  S. Whitelam,et al.  Watch and learn—a generalized approach for transferrable learning in deep neural networks via physical principles , 2020, Mach. Learn. Sci. Technol..

[16]  Julian M. Urban,et al.  Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning , 2020, Physical Review D.

[17]  Guillaume Rabusseau,et al.  Tensor Networks for Language Modeling , 2020, ArXiv.

[18]  M. Gingras,et al.  Unsupervised machine learning of quenched gauge symmetries: A proof-of-concept demonstration , 2020, Physical Review Research.

[19]  Isaac Tamblyn,et al.  Finding the ground state of spin Hamiltonians with reinforcement learning , 2020, Nature Machine Intelligence.

[20]  R. Scalettar,et al.  Visualizing Correlations in the 2D Fermi-Hubbard Model with AI , 2020, 2002.12310.

[21]  N. Lörch,et al.  A differentiable programming method for quantum control , 2020, Mach. Learn. Sci. Technol..

[22]  R. Kueng,et al.  Predicting many properties of a quantum system from very few measurements , 2020, Nature Physics.

[23]  Isaac Tamblyn,et al.  Optical lattice experiments at unobserved conditions with generative adversarial deep learning , 2020, Physical Review Research.

[24]  Ying Wai Li,et al.  Machine-learning-assisted insight into spin ice Dy2Ti2O7 , 2020, Nature Communications.

[25]  A. Szab'o,et al.  Neural network wave functions and the sign problem , 2020, Physical Review Research.

[26]  S. Pilati,et al.  Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks. , 2020, Physical review. E.

[27]  R. Melko,et al.  Recurrent neural network wave functions , 2020, Physical Review Research.

[28]  Lin Lin,et al.  Policy Gradient based Quantum Approximate Optimization Algorithm , 2020, MSML.

[29]  Shinichi Nakajima,et al.  Asymptotically unbiased estimation of physical observables with neural samplers. , 2020, Physical review. E.

[30]  J. P. Garrahan,et al.  A deep learning functional estimator of optimal dynamics for sampling large deviations , 2020, Mach. Learn. Sci. Technol..

[31]  Demis Hassabis,et al.  Improved protein structure prediction using potentials from deep learning , 2020, Nature.

[32]  Shi-Ju Ran,et al.  Bayesian Tensor Network with Polynomial Complexity for Probabilistic Machine Learning , 2019, 1912.12923.

[33]  P. Ginsparg,et al.  Interpreting machine learning of topological quantum phase transitions , 2019, 1912.10057.

[34]  Y. Kao,et al.  Optimal Real-Space Renormalization-Group Transformations with Artificial Neural Networks , 2019, 1912.09005.

[35]  M. Heyl,et al.  Quantum Many-Body Dynamics in Two Dimensions with Artificial Neural Networks. , 2019, Physical review letters.

[36]  Benat Mencia Uranga,et al.  SchrödingeRNN: Generative Modeling of Raw Audio as a Continuously Observed Quantum State , 2019, ArXiv.

[37]  Hiroki Saito,et al.  Neural-network quantum states at finite temperature , 2019, Physical Review Research.

[38]  Y. Lai,et al.  Machine learning dynamical phase transitions in complex networks , 2019, Physical review. E.

[39]  Sugato Basu,et al.  Semi-Supervised Learning , 2019, Encyclopedia of Database Systems.

[40]  J. Rigo,et al.  Machine learning effective models for quantum systems , 2019, Physical Review B.

[41]  N. Lörch,et al.  Unsupervised identification of topological phase transitions using predictive models , 2019, New Journal of Physics.

[42]  Tai-Danae Bradley,et al.  Modeling sequences with quantum states: a look under the hood , 2019, Mach. Learn. Sci. Technol..

[43]  Z. Meng,et al.  Designer Monte Carlo simulation for the Gross-Neveu-Yukawa transition , 2019, Physical Review B.

[44]  G. Carleo,et al.  Fermionic neural-network states for ab-initio electronic structure , 2019, Nature Communications.

[45]  F. Noé,et al.  Deep-neural-network solution of the electronic Schrödinger equation , 2019, Nature Chemistry.

[46]  W. Foulkes,et al.  Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks , 2019, Physical Review Research.

[47]  M. Okumura,et al.  Self-learning hybrid Monte Carlo: A first-principles approach , 2019, Physical Review B.

[48]  F. Noé,et al.  Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning , 2019, Science.

[49]  M. Marques,et al.  Recent advances and applications of machine learning in solid-state materials science , 2019, npj Computational Materials.

[50]  Thomas Gasenzer,et al.  Sampling scheme for neuromorphic simulation of entangled quantum systems , 2019, Physical Review B.

[51]  Masoud Mohseni,et al.  Learning to learn with quantum neural networks via classical neural networks , 2019, ArXiv.

[52]  Jens Eisert,et al.  Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning , 2019, NeurIPS.

[53]  Sebastian Huber,et al.  Hamiltonian learning for quantum error correction , 2019, Physical Review Research.

[54]  S. Pilati,et al.  Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines. , 2019, Physical review. E.

[55]  Ying Wai Li,et al.  Machine Learning Assisted Insight to Spin Ice Dy$_2$Ti$_2$O$_7$ , 2019, 1906.11275.

[56]  J. Cirac,et al.  Restricted Boltzmann machines in quantum physics , 2019, Nature Physics.

[57]  Marcello Benedetti,et al.  Parameterized quantum circuits as machine learning models , 2019, Quantum Science and Technology.

[58]  Florent Krzakala,et al.  Dynamics of stochastic gradient descent for two-layer neural networks in the teacher–student setup , 2019, NeurIPS.

[59]  A. Zeilinger,et al.  Predicting research trends with semantic and neural networks with an application in quantum physics , 2019, Proceedings of the National Academy of Sciences.

[60]  Ling Cheng,et al.  Is Deep Learning an RG Flow? , 2019, ArXiv.

[61]  J. Carrasquilla,et al.  Neural Gutzwiller-projected variational wave functions , 2019, Physical Review B.

[62]  E. Khatami,et al.  Accelerating lattice quantum Monte Carlo simulations using artificial neural networks: Application to the Holstein model , 2019, Physical Review B.

[63]  Glen Evenbly,et al.  Number-state preserving tensor networks as classifiers for supervised learning , 2019, Frontiers in Physics.

[64]  K. Burke,et al.  Density Functionals with Quantum Chemical Accuracy: From Machine Learning to Molecular Dynamics , 2019 .

[65]  Adam Zalcman,et al.  TensorNetwork: A Library for Physics and Machine Learning , 2019, ArXiv.

[66]  F. Verstraete,et al.  Restricted Boltzmann Machines for Quantum States with Non-Abelian or Anyonic Symmetries. , 2019, Physical review letters.

[67]  M. S. Albergo,et al.  Flow-based generative models for Markov chain Monte Carlo in lattice field theory , 2019, Physical Review D.

[68]  Xin Wang,et al.  Transferable control for quantum parameter estimation through reinforcement learning , 2019, 1904.11298.

[69]  Evert P L van Nieuwenburg,et al.  Integrating Neural Networks with a Quantum Simulator for State Reconstruction. , 2019, Physical review letters.

[70]  Bin Li,et al.  Applications of machine learning in drug discovery and development , 2019, Nature Reviews Drug Discovery.

[71]  Naftali Tishby,et al.  Machine learning and the physical sciences , 2019, Reviews of Modern Physics.

[72]  Kenny Choo,et al.  Two-dimensional frustrated J1−J2 model studied with neural network quantum states , 2019, Physical Review B.

[73]  Steven Durr,et al.  Unsupervised learning eigenstate phases of matter , 2019, Physical Review B.

[74]  Ying-Jer Kao,et al.  Generation of ice states through deep reinforcement learning. , 2019, Physical review. E.

[75]  G. Carleo,et al.  Ground state phase diagram of the one-dimensional Bose-Hubbard model from restricted Boltzmann machines , 2019, Journal of Physics: Conference Series.

[76]  N. Regnault,et al.  Variational Neural-Network Ansatz for Steady States in Open Quantum Systems. , 2019, Physical review letters.

[77]  V. Savona,et al.  Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems. , 2019, Physical review letters.

[78]  Zheng An,et al.  Deep reinforcement learning for quantum gate control , 2019, EPL (Europhysics Letters).

[79]  James Stokes,et al.  Probabilistic Modeling with Matrix Product States , 2019, Entropy.

[80]  Nobuyuki Yoshioka,et al.  Constructing neural stationary states for open quantum many-body systems , 2019, Physical Review B.

[81]  Anand Chandrasekaran,et al.  Solving the electronic structure problem with machine learning , 2019, npj Computational Materials.

[82]  Michael J. Hartmann,et al.  Neural-Network Approach to Dissipative Quantum Many-Body Dynamics. , 2019, Physical review letters.

[83]  A. Shashua,et al.  Deep autoregressive models for the efficient variational simulation of many-body quantum systems , 2019, Physical review letters.

[84]  Xiao-Ming Zhang,et al.  When does reinforcement learning stand out in quantum control? A comparative study on state preparation , 2019, npj Quantum Information.

[85]  Ce Wang,et al.  Emergent Schrödinger equation in an introspective machine learning architecture. , 2019, Science bulletin.

[86]  N. L. Holanda,et al.  Machine learning topological phases in real space , 2019, Physical Review B.

[87]  Taegeun Song,et al.  Accelerated continuous time quantum Monte Carlo method with machine learning , 2019, Physical Review B.

[88]  Alan Aspuru-Guzik,et al.  Variational Quantum Generators: Generative Adversarial Quantum Machine Learning for Continuous Distributions , 2019, Advanced Quantum Technologies.

[89]  Nicolai Friis,et al.  Optimizing Quantum Error Correction Codes with Reinforcement Learning , 2018, Quantum.

[90]  D Zhu,et al.  Training of quantum circuits on a hybrid quantum computer , 2018, Science Advances.

[91]  Stanislav Fort,et al.  Adaptive quantum state tomography with neural networks , 2018, npj Quantum Information.

[92]  Román Orús,et al.  Tensor networks for complex quantum systems , 2018, Nature Reviews Physics.

[93]  N. Lörch,et al.  Vector field divergence of predictive model output as indication of phase transitions. , 2018, Physical review. E.

[94]  Joel Johansson,et al.  Quantum error correction for the toric code using deep reinforcement learning , 2018, Quantum.

[95]  Michael Knap,et al.  Classifying snapshots of the doped Hubbard model with machine learning , 2018, Nature Physics.

[96]  David A. Strubbe,et al.  Deep learning and density-functional theory , 2018, Physical Review A.

[97]  David Poulin,et al.  Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes. , 2018, Physical review letters.

[98]  Nathan Killoran,et al.  PennyLane: Automatic differentiation of hybrid quantum-classical computations , 2018, ArXiv.

[99]  Jan M. Pawlowski,et al.  Reducing autocorrelation times in lattice simulations with generative adversarial networks , 2018, Mach. Learn. Sci. Technol..

[100]  L. Pang,et al.  Regressive and generative neural networks for scalar field theory , 2018, Physical Review D.

[101]  Max Tegmark,et al.  Toward an AI Physicist for Unsupervised Learning , 2018, Physical review. E.

[102]  Roger G. Melko,et al.  Reconstructing quantum states with generative models , 2018, Nature Machine Intelligence.

[103]  Jens Eisert,et al.  Reinforcement learning decoders for fault-tolerant quantum computation , 2018, Mach. Learn. Sci. Technol..

[104]  Ke Liu,et al.  Learning multiple order parameters with interpretable machines , 2018, Physical Review B.

[105]  Joaquin Vanschoren,et al.  Meta-Learning: A Survey , 2018, Automated Machine Learning.

[106]  L. Duan,et al.  Efficient representation of topologically ordered states with restricted Boltzmann machines , 2018, Physical Review B.

[107]  Lei Wang,et al.  Solving Statistical Mechanics using Variational Autoregressive Networks , 2018, Physical review letters.

[108]  Zohar Ringel,et al.  Optimal Renormalization Group Transformation from Information Theory , 2018, Physical Review X.

[109]  Michele Ceriotti,et al.  Fast and Accurate Uncertainty Estimation in Chemical Machine Learning. , 2018, Journal of chemical theory and computation.

[110]  Christoph Becker,et al.  Identifying quantum phase transitions using artificial neural networks on experimental data , 2018, Nature Physics.

[111]  E. M. Inack,et al.  Projective quantum Monte Carlo simulations guided by unrestricted neural network states , 2018, Physical Review B.

[112]  Guang-Can Guo,et al.  Quantum Neural Network States: A Brief Review of Methods and Applications , 2018, Advanced Quantum Technologies.

[113]  Jiangping Hu,et al.  Learning and Inference on Generative Adversarial Quantum Circuits , 2018, Physical Review A.

[114]  Shu-Hao Wu,et al.  Quantum generative adversarial learning in a superconducting quantum circuit , 2018, Science Advances.

[115]  Yi Zhang,et al.  Machine learning in electronic-quantum-matter imaging experiments , 2018, Nature.

[116]  Renato Renner,et al.  Discovering physical concepts with neural networks , 2018, Physical review letters.

[117]  B. Clark,et al.  Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions. , 2018, Physical review letters.

[118]  Juan Miguel Arrazola,et al.  Machine learning method for state preparation and gate synthesis on photonic quantum computers , 2018, Quantum Science and Technology.

[119]  Yong-Sheng Zhang,et al.  Solving frustrated quantum many-particle models with convolutional neural networks , 2018, Physical Review B.

[120]  Yuki Nagai,et al.  Self-learning Monte Carlo method with Behler-Parrinello neural networks , 2018, Physical Review B.

[121]  Lei Wang,et al.  Interpretable machine learning study of the many-body localization transition in disordered quantum Ising spin chains , 2018, Physical Review B.

[122]  G. Carleo,et al.  Symmetries and Many-Body Excitations with Neural-Network Quantum States. , 2018, Physical review letters.

[123]  C Casert,et al.  Interpretable machine learning for inferring the phase boundaries in a nonequilibrium system. , 2018, Physical review. E.

[124]  Daniel W. Davies,et al.  Machine learning for molecular and materials science , 2018, Nature.

[125]  D. Deng,et al.  Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal. , 2018, Physical review letters.

[126]  Joaquin F. Rodriguez-Nieva,et al.  Identifying topological order through unsupervised machine learning , 2018, Nature Physics.

[127]  Kristan Temme,et al.  Supervised learning with quantum-enhanced feature spaces , 2018, Nature.

[128]  Seth Lloyd,et al.  Quantum Generative Adversarial Learning. , 2018, Physical review letters.

[129]  Ke Liu,et al.  Probing hidden spin order with interpretable machine learning , 2018, Physical Review B.

[130]  Lei Wang,et al.  Differentiable Learning of Quantum Circuit Born Machine , 2018, Physical Review A.

[131]  N. Killoran,et al.  Strawberry Fields: A Software Platform for Photonic Quantum Computing , 2018, Quantum.

[132]  Dongkyu Kim,et al.  Smallest neural network to learn the Ising criticality. , 2018, Physical review. E.

[133]  Chu Guo,et al.  Matrix product operators for sequence-to-sequence learning , 2018, Physical Review E.

[134]  Pankaj Mehta,et al.  Glassy Phase of Optimal Quantum Control. , 2018, Physical review letters.

[135]  Charles K. Fisher,et al.  A high-bias, low-variance introduction to Machine Learning for physicists , 2018, Physics reports.

[136]  R. A. Vargas-Hernández,et al.  Extrapolating Quantum Observables with Machine Learning: Inferring Multiple Phase Transitions from Properties of a Single Phase. , 2018, Physical review letters.

[137]  T. Gasenzer,et al.  Quenches near Ising quantum criticality as a challenge for artificial neural networks , 2018, Physical Review B.

[138]  Vladimir V. Mazurenko,et al.  Supervised learning approach for recognizing magnetic skyrmion phases , 2018, Physical Review B.

[139]  Hartmut Neven,et al.  Universal quantum control through deep reinforcement learning , 2018, npj Quantum Information.

[140]  Keisuke Fujii,et al.  Quantum circuit learning , 2018, Physical Review A.

[141]  Stefan Wessel,et al.  Parameter diagnostics of phases and phase transition learning by neural networks , 2018, Physical Review B.

[142]  Pooya Ronagh,et al.  Deep neural decoders for near term fault-tolerant experiments , 2018, Quantum Science and Technology.

[143]  Xiao Yan Xu,et al.  Symmetry-enforced self-learning Monte Carlo method applied to the Holstein model , 2018, Physical Review B.

[144]  Hartmut Neven,et al.  Classification with Quantum Neural Networks on Near Term Processors , 2018, 1802.06002.

[145]  Florian Marquardt,et al.  Reinforcement Learning with Neural Networks for Quantum Feedback , 2018, Physical Review X.

[146]  Lei Wang,et al.  Neural Network Renormalization Group , 2018, Physical review letters.

[147]  Nikolaos Doulamis,et al.  Deep Learning for Computer Vision: A Brief Review , 2018, Comput. Intell. Neurosci..

[148]  Giacomo Torlai,et al.  Latent Space Purification via Neural Density Operators. , 2018, Physical review letters.

[149]  D. Carvalho,et al.  Real-space mapping of topological invariants using artificial neural networks , 2018, 1801.09655.

[150]  Alejandro Perdomo-Ortiz,et al.  A generative modeling approach for benchmarking and training shallow quantum circuits , 2018, npj Quantum Information.

[151]  S. Iso,et al.  Scale-invariant Feature Extraction of Neural Network and Renormalization Group Flow , 2018, Physical review. E.

[152]  H. Stöcker,et al.  An equation-of-state-meter of quantum chromodynamics transition from deep learning , 2018, Nature Communications.

[153]  Liang Fu,et al.  Self-learning Monte Carlo with deep neural networks , 2018, Physical Review B.

[154]  E. Stoudenmire,et al.  Learning relevant features of data with multi-scale tensor networks , 2017, ArXiv.

[155]  Blake R. Johnson,et al.  Unsupervised Machine Learning on a Hybrid Quantum Computer , 2017, 1712.05771.

[156]  Michael Broughton,et al.  A quantum algorithm to train neural networks using low-depth circuits , 2017, 1712.05304.

[157]  Eyal Bairey,et al.  Learning phase transitions from dynamics , 2017, Physical Review B.

[158]  Gábor Csányi,et al.  Machine learning unifies the modeling of materials and molecules , 2017, Science Advances.

[159]  F. Becca.  Quantum Monte Carlo Approaches for Correlated Systems , 2017 .

[160]  C. K. Andersen,et al.  Quantum parameter estimation with a neural network , 2017, 1711.05238.

[161]  Vedika Khemani,et al.  Machine Learning Out-of-Equilibrium Phases of Matter. , 2017, Physical review letters.

[162]  Yiannis Vlassopoulos,et al.  Tensor network language model , 2017, ArXiv.

[163]  Roger G. Melko,et al.  Machine learning vortices at the Kosterlitz-Thouless transition , 2017, 1710.09842.

[164]  Demis Hassabis,et al.  Mastering the game of Go without human knowledge , 2017, Nature.

[165]  M. Lewenstein,et al.  Machine learning by unitary tensor network of hierarchical tree structure , 2017, New Journal of Physics.

[166]  J. Cirac,et al.  Neural-Network Quantum States, String-Bond States, and Chiral Topological States , 2017, 1710.04045.

[167]  Peter Wittek,et al.  Adversarial Domain Adaptation for Identifying Phase Transitions , 2017, ArXiv.

[168]  S. R. Clark,et al.  Unifying neural-network quantum states and correlator product states via tensor networks , 2017, 1710.03545.

[169]  Andrew S. Darmawan,et al.  Restricted Boltzmann machine learning for solving strongly correlated quantum systems , 2017, 1709.06475.

[170]  Nobuyuki Yoshioka,et al.  Learning disordered topological phases by statistical recovery of symmetry , 2017, 1709.05790.

[171]  Hiroki Saito,et al.  Machine Learning Technique to Find Quantum Many-Body Ground States of Bosons on a Lattice , 2017, 1709.05468.

[172]  S. Bose,et al.  Machine-Learning-Assisted Many-Body Entanglement Measurement. , 2017, Physical review letters.

[173]  Hans-J. Briegel,et al.  Machine learning \& artificial intelligence in the quantum domain , 2017, ArXiv.

[174]  Jun Wang,et al.  Unsupervised Generative Modeling Using Matrix Product States , 2017, Physical Review X.

[175]  Alejandro Perdomo-Ortiz,et al.  Quantum-assisted Helmholtz machines: A quantum–classical deep learning framework for industrial datasets in near-term devices , 2017, ArXiv.

[176]  Z. Bai,et al.  Principal component analysis for fermionic critical points , 2017, 1708.04762.

[177]  Roger G. Melko,et al.  Deep Learning the Ising Model Near Criticality , 2017, J. Mach. Learn. Res..

[178]  Kelvin George Chng,et al.  Unsupervised machine learning account of magnetic transitions in the Hubbard model. , 2017, Physical review. E.

[179]  Erik Cambria,et al.  Recent Trends in Deep Learning Based Natural Language Processing , 2017, IEEE Comput. Intell. Mag..

[180]  Simon Trebst,et al.  Quantum phase recognition via unsupervised machine learning , 2017, 1707.00663.

[181]  Ce Wang,et al.  Machine learning of frustrated classical spin models. I. Principal component analysis , 2017, 1706.07977.

[182]  Masashi Sugiyama,et al.  Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives , 2017, Found. Trends Mach. Learn..

[183]  P. Ronhovde,et al.  Stochastic replica voting machine prediction of stable cubic and double perovskite materials and binary alloys , 2017, Physical Review Materials.

[184]  Yang Qi,et al.  Self-learning Monte Carlo method: Continuous-time algorithm , 2017, 1705.06724.

[185]  Manuel Scherzer,et al.  Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory , 2017, 1705.05582.

[186]  Yi Zhang,et al.  Machine learning Z 2 quantum spin liquids with quasiparticle statistics , 2017, 1705.01947.

[187]  Pankaj Mehta,et al.  Reinforcement Learning in Different Phases of Quantum Control , 2017, Physical Review X.

[188]  Z. Ringel,et al.  Mutual information, neural networks and the renormalization group , 2017, Nature Physics.

[189]  Roger G. Melko,et al.  Kernel methods for interpretable machine learning of order parameters , 2017, 1704.05848.

[190]  Wenjian Hu,et al.  Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination. , 2017, Physical review. E.

[191]  Matthias Troyer,et al.  Neural-network quantum state tomography , 2017, Nature Physics.

[192]  Sebastian Johann Wetzel,et al.  Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders , 2017, Physical review. E.

[193]  Lei Wang,et al.  Can Boltzmann Machines Discover Cluster Updates ? , 2017, Physical review. E.

[194]  Lu-Ming Duan,et al.  Efficient representation of quantum many-body states with deep neural networks , 2017, Nature Communications.

[195]  J. Chen,et al.  Equivalence of restricted Boltzmann machines and tensor network states , 2017, 1701.04831.

[196]  D. Deng,et al.  Quantum Entanglement in Neural Network States , 2017, 1701.04844.

[197]  Xiao Yan Xu,et al.  Self-learning quantum Monte Carlo method in interacting fermion systems , 2016, 1612.03804.

[198]  S. Lloyd,et al.  Quantum machine learning , 2016, Nature.

[199]  Yi Zhang,et al.  Quantum Loop Topography for Machine Learning. , 2016, Physical review letters.

[200]  Giacomo Torlai,et al.  Neural Decoder for Topological Codes. , 2016, Physical review letters.

[201]  Yang Qi,et al.  Self-learning Monte Carlo method , 2016, 1610.03137.

[202]  Li Huang,et al.  Accelerated Monte Carlo simulations with restricted Boltzmann machines , 2016, 1610.02746.

[203]  S. Huber,et al.  Learning phase transitions by confusion , 2016, Nature Physics.

[204]  Tanaka Akinori,et al.  Detection of Phase Transition via Convolutional Neural Networks , 2016, 1609.09087.

[205]  Dong-Ling Deng,et al.  Machine Learning Topological States , 2016, 1609.09060.

[206]  Li Li,et al.  Bypassing the Kohn-Sham equations with machine learning , 2016, Nature Communications.

[207]  R. Melko,et al.  Machine Learning Phases of Strongly Correlated Fermions , 2016, Physical Review X.

[208]  Andrzej Cichocki,et al.  Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions , 2016, Found. Trends Mach. Learn..

[209]  Li Li,et al.  Deep data mining in a real space: separation of intertwined electronic responses in a lightly doped BaFe2As2 , 2016, Nanotechnology.

[210]  Juan Carrasquilla,et al.  Machine learning quantum phases of matter beyond the fermion sign problem , 2016, Scientific Reports.

[211]  Roger G. Melko,et al.  Learning Thermodynamics with Boltzmann Machines , 2016, ArXiv.

[212]  Matthias Troyer,et al.  Solving the quantum many-body problem with artificial neural networks , 2016, Science.

[213]  Lei Wang,et al.  Discovering phase transitions with unsupervised learning , 2016, 1606.00318.

[214]  Samy Bengio,et al.  Density estimation using Real NVP , 2016, ICLR.

[215]  Roger G. Melko,et al.  Machine learning phases of matter , 2016, Nature Physics.

[216]  M. Welling,et al.  Group Equivariant Convolutional Networks , 2016, ICML.

[217]  Roger Melko,et al.  Quantum Boltzmann Machine , 2016, 1601.02036.

[218]  Shakir Mohamed,et al.  Variational Inference with Normalizing Flows , 2015, ICML.

[219]  Bo Sun,et al.  Inference of hidden structures in complex physical systems by multi-scale clustering , 2015, ArXiv.

[220]  Marc G. Bellemare,et al.  Human-level control through deep reinforcement learning , 2015, Nature.

[221]  Pedro M. Domingos,et al.  Deep Symmetry Networks , 2014, NIPS.

[222]  E. Farhi,et al.  A Quantum Approximate Optimization Algorithm , 2014, 1411.4028.

[223]  D. Schwab,et al.  An exact mapping between the Variational Renormalization Group and Deep Learning , 2014, ArXiv.

[224]  Maria Schuld,et al.  The quest for a Quantum Neural Network , 2014, Quantum Information Processing.

[225]  O. A. von Lilienfeld,et al.  Machine learning for many-body physics: The case of the Anderson impurity model , 2014, 1408.1143.

[226]  Aaron C. Courville,et al.  Generative Adversarial Nets , 2014, NIPS.

[227]  Li Li,et al.  Understanding Machine-learned Density Functionals , 2014, ArXiv.

[228]  M. Gingras,et al.  Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets , 2013, Reports on progress in physics. Physical Society.

[229]  Sanguthevar Rajasekaran,et al.  Accelerating materials property predictions using machine learning , 2013, Scientific Reports.

[230]  Alán Aspuru-Guzik,et al.  A variational eigenvalue solver on a photonic quantum processor , 2013, Nature Communications.

[231]  C. Bény.  Deep learning and the renormalization group , 2013, 1301.3124.

[232]  Z. Nussinov,et al.  Detection of hidden structures for arbitrary scales in complex physical systems , 2012, Scientific Reports.

[233]  Steve P. Brooks,et al.  Handbook of Markov Chain Monte Carlo: Hardcover: 619 pages Publisher: Chapman and Hall/CRC Press (first edition, May 2011) Language: English ISBN-10: 1420079417 , 2012 .

[234]  V. Menon,et al.  Musical rhythm spectra from Bach to Joplin obey a 1/f power law , 2012, Proceedings of the National Academy of Sciences.

[235]  Klaus-Robert Müller,et al.  Finding Density Functionals with Machine Learning , 2011, Physical review letters.

[236]  David Pérez-García,et al.  Gapless Hamiltonians for the toric code using the projected entangled pair state formalism. , 2011, Physical review letters.

[237]  K. Müller,et al.  Fast and accurate modeling of molecular atomization energies with machine learning. , 2011, Physical review letters.

[238]  Ivan Oseledets,et al.  Tensor-Train Decomposition , 2011, SIAM J. Sci. Comput..

[239]  M. Potthoff.  Self-energy-functional theory , 2011, 1108.2183.

[240]  Radford M. Neal.  MCMC using Hamiltonian dynamics , 2012, 1206.1901.

[241]  P Ronhovde,et al.  Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering , 2011, The European physical journal. E, Soft matter.

[242]  D. Gross,et al.  Efficient quantum state tomography. , 2010, Nature communications.

[243]  A. Sandvik.  Computational Studies of Quantum Spin Systems , 2010, 1101.3281.

[244]  Rocco A. Servedio,et al.  Restricted Boltzmann Machines are Hard to Approximately Evaluate or Simulate , 2010, ICML.

[245]  J I Cirac,et al.  Continuous matrix product states for quantum fields. , 2010, Physical review letters.

[246]  Alexander Hentschel,et al.  Machine learning for precise quantum measurement. , 2009, Physical review letters.

[247]  Markus Greiner,et al.  A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice , 2009, Nature.

[248]  W. Munro,et al.  Quantum error correction for beginners , 2009, Reports on progress in physics. Physical Society.

[249]  Alfred O. Hero,et al.  Joint Bayesian Endmember Extraction and Linear Unmixing for Hyperspectral Imagery , 2009, IEEE Transactions on Signal Processing.

[250]  Nicolas Le Roux,et al.  Representational Power of Restricted Boltzmann Machines and Deep Belief Networks , 2008, Neural Computation.

[251]  D. D’Alessandro.  Introduction to Quantum Control and Dynamics , 2007 .

[252]  G. Vidal.  Class of quantum many-body states that can be efficiently simulated. , 2006, Physical review letters.

[253]  F. Verstraete,et al.  Matrix product state representations , 2006, Quantum Inf. Comput..

[254]  C. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[255]  Barry C. Sanders,et al.  Non-Gaussian ancilla states for continuous variable quantum computation via Gaussian maps , 2006, quant-ph/0606026.

[256]  Eric R. Ziegel,et al.  The Elements of Statistical Learning , 2003, Technometrics.

[257]  Geoffrey E. Hinton.  Training Products of Experts by Minimizing Contrastive Divergence , 2002, Neural Computation.

[258]  Michihiko Sugawara,et al.  Numerical solution of the Schrödinger equation by neural network and genetic algorithm , 2001 .

[259]  J. Preskill,et al.  Encoding a qubit in an oscillator , 2000, quant-ph/0008040.

[260]  Elizabeth C. Behrman,et al.  A spatial quantum neural computer , 1999, IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339).

[261]  Gerard T. Barkema,et al.  Monte Carlo Methods in Statistical Physics , 1999 .

[262]  S. Sachdev,et al.  Quantum Phase Transitions: A first course , 1999 .

[263]  M. Fisher.  Conceptual foundations of quantum field theory: Renormalization group theory: its basis and formulation in statistical physics , 1998 .

[264]  A. Kitaev,et al.  Fault tolerant quantum computation by anyons , 1997, quant-ph/9707021.

[265]  M. Newman,et al.  Monte Carlo simulation of ice models , 1997, cond-mat/9706190.

[266]  D. Fotiadis,et al.  Artificial neural network methods in quantum mechanics , 1997, quant-ph/9705029.

[267]  W. Ebeling,et al.  Entropy and Long-Range Correlations in Literary English , 1993, chao-dyn/9309005.

[268]  L. Kułak,et al.  Neural network solution of the Schrödinger equation for a two-dimensional harmonic oscillator , 1993 .

[269]  B. R. Upadhyaya,et al.  Application of neural network computing to the solution for the ground-state eigenenergy of two-dimensional harmonic oscillators , 1991 .

[270]  Berndt Müller,et al.  Quantum Mechanics: Symmetries , 1990 .

[271]  Sanders,et al.  Quantum dynamics of the nonlinear rotator and the effects of continual spin measurement. , 1989, Physical review. A, General physics.

[272]  Paul Smolensky,et al.  Information processing in dynamical systems: foundations of harmony theory , 1986 .

[273]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[274]  T. Witten,et al.  Optimal real-space renormalisation , 1981 .

[275]  J. C. Kimball,et al.  Simple Model for Semiconductor-Metal Transitions: SmB6and Transition-Metal Oxides , 1969 .

[276]  E. C. Curtis,et al.  Local-Energy Method in Electronic Energy Calculations , 1960 .

[277]  Richard Bellman.  Dynamic Programming , 1957, Science.

[278]  Richard Phillips Feynman,et al.  Energy Spectrum of the Excitations in Liquid Helium , 1956 .

[279]  N. Metropolis,et al.  The Monte Carlo method. , 1949, Journal of the American Statistical Association.

[280]  E. Wigner,et al.  Über das Paulische Äquivalenzverbot , 1928 .

[281]  David J. Schwab,et al.  Supervised Learning with Tensor Networks , 2016, NIPS.

[282]  Geoffrey E. Hinton,et al.  Deep Learning , 2015 .

[283]  Stephen W. Carden,et al.  An Introduction to Reinforcement Learning , 2013 .

[284]  Geoffrey E. Hinton.  A Practical Guide to Training Restricted Boltzmann Machines , 2012, Neural Networks: Tricks of the Trade.

[285]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[286]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[287]  Elizabeth C. Behrman,et al.  A Quantum Dot Neural Network , 1996 .

[288]  W. Krauth,et al.  Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions , 1996 .

[289]  Subhash Kak,et al.  Quantum Neural Computing , 1995 .

[290]  David K. Campbell,et al.  The Hubbard Model , 1995 .

[291]  D. Ruderman.  The statistics of natural images , 1994 .

[292]  J. Edmonds.  Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.

[293]  E. Wigner,et al.  About the Pauli exclusion principle , 1928 .