Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute.

The ability to prepare a physical system in a desired quantum state is central to many areas of physics such as nuclear magnetic resonance, cold atoms, and quantum computing. Yet, preparing states quickly and with high fidelity remains a formidable challenge. In this work we implement cutting-edge Reinforcement Learning (RL) techniques and show that their performance is comparable to optimal control methods in the task of finding short, high-fidelity driving protocol from an initial to a target state in non-integrable many-body quantum systems of interacting qubits. RL methods learn about the underlying physical system solely through a single scalar reward (the fidelity of the resulting state) calculated from numerical simulations of the physical system. We further show that quantum state manipulation, viewed as an optimization problem, exhibits a spinglass-like phase transition in the space of protocols as a function of the protocol duration. Our RL-aided approach helps identify variational protocols with nearly optimal fidelity, even in the glassy phase, where optimal state manipulation is exponentially hard. This study highlights the potential usefulness of RL for applications in out-of-equilibrium quantum physics. S = {s = (t, h x (t))}, A = {a = δh x }, R = {r ∈ [0, 1]}.

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We use numerical linked cluster (NLC) expansions to compute the specific heat, C(T ), and entropy, S(T ), of a quantum spin ice model of Yb2Ti2O7 using anisotropic exchange interactions recently determined from inelastic neutron scattering measurements and find good agreement with experimental calorimetric data. In the perturbative weak quantum regime, this model has a ferrimagnetic ordered ground state, with two peaks in C(T ): a Schottky anomaly signalling the paramagnetic to spin ice crossover followed at lower temperature by a sharp peak accompanying a first order phase transition to the ferrimagnetic state. We suggest that the two C(T ) features observed in Yb2Ti2O7 are associated with the same physics. Spin excitations in this regime consist of weakly confined spinon-antispinon pairs. We suggest that conventional ground state with exotic quantum dynamics will prove a prevalent characteristic of many real quantum spin ice materials.PACS numbers: 75.10.Jm,75.40.Gb,75.30.Ds The experimental search for quantum spin liquids (QSLs), magnetic systems disordered by large quantum fluctuations, has remained unabated for over twenty years [1]. One direction that is rapidly gathering momentum is the search for QSLs among materials that are close relatives to spin ice systems [2], but with additional quantum fluctuations, or quantum spin ice [3,4].Spin ices are found among insulating pyrochlore oxides, such as R 2 M 2 O 7 (R=Ho, Dy; M=Ti, Sn) [5]. In these compounds, the magnetic R rare earth ions sit on a lattice of corner-sharing tetrahedra, experiencing a large singleion anisotropy forcing the magnetic moment to point strictly "in" or "out" of the two tetrahedra it joins (see. Fig. 1a). Consequently, the direction of a moment can be described by a classical Ising spin [2]. In these materials, the combination of nearest-neighbor exchange and longrange magnetostatic dipolar interactions lead to an exponentially large number of low-energy states characterized by two spins pointing in and two spins pointing out on each tetrahedron (see Fig. 1a). This energetic constraint is equivalent to the Bernal-Fowler ice rule which gives water ice a residual entropy S P ∼ k B ( 1 2 ) ln(3/2) per proton, estimated by Pauling [6] and in good agreement with experiments on water ice [7]. Since they share the same "ice-rule", the (Ho,Dy) 2 (Ti,Sn) 2 O 7 pyrochlores also possess a residual low-temperature Pauling entropy S P [8], hence the name spin ice. The spin ice state is not thermodynamically distinct from the paramagnetic phase. Yet, because of the ice-rules, it is a strongly correlated state of matter -a classical spin liquid of sorts [1,2].For infinite Ising anisotropy, quantum effects are absent [2]. However, these can be restored when considering the realistic situation of finite anisotropy. In two closely related papers, Hermele et al. [9] and Castro-Neto et al. [10] considered effective spins one-half on a py- rochlore lattice where the highly degenerate classical spin ice state is promoted via quantum fluctuations to a QS...