The paper "Solving the Quantum Many-Body Problem with Artificial Neural Networks" by Giuseppe Carlo and Matthias Troyer introduces a novel approach to solving the quantum many-body problem using artificial neural networks (ANNs). The authors propose a variational representation of quantum states based on ANNs with a variable number of hidden neurons. They demonstrate a reinforcement-learning scheme that can find the ground state or describe the unitary time evolution of complex interacting quantum systems. The approach achieves high accuracy in describing equilibrium and dynamical properties of prototypical interacting spin models in one and two dimensions, offering a powerful tool to solve the quantum many-body problem. The wave function, a fundamental object in quantum physics, is challenging to describe due to its exponential complexity. The authors introduce a neural network-based representation of the wave function, which can be optimized using variational Monte Carlo (VMC) methods. They validate the approach by studying the Ising and Heisenberg models, showing that the neural-network quantum states (NQS) achieve state-of-the-art accuracy in both ground-state and out-of-equilibrium dynamics. The NQS representation is flexible and can be formulated in a symmetry-conserving manner, reducing the number of variational parameters. The authors also discuss the application of NQS to time-dependent problems, such as quantum quenches, and show that it can accurately describe the evolution induced by complex sets of excited quantum states. The paper highlights the potential of NQS to solve the quantum many-body problem, particularly in regimes where existing methods are limited. The approach offers a new perspective on solving the quantum many-body problem and opens up avenues for further research, including the application to more complex systems and the exploration of non-local correlations.The paper "Solving the Quantum Many-Body Problem with Artificial Neural Networks" by Giuseppe Carlo and Matthias Troyer introduces a novel approach to solving the quantum many-body problem using artificial neural networks (ANNs). The authors propose a variational representation of quantum states based on ANNs with a variable number of hidden neurons. They demonstrate a reinforcement-learning scheme that can find the ground state or describe the unitary time evolution of complex interacting quantum systems. The approach achieves high accuracy in describing equilibrium and dynamical properties of prototypical interacting spin models in one and two dimensions, offering a powerful tool to solve the quantum many-body problem. The wave function, a fundamental object in quantum physics, is challenging to describe due to its exponential complexity. The authors introduce a neural network-based representation of the wave function, which can be optimized using variational Monte Carlo (VMC) methods. They validate the approach by studying the Ising and Heisenberg models, showing that the neural-network quantum states (NQS) achieve state-of-the-art accuracy in both ground-state and out-of-equilibrium dynamics. The NQS representation is flexible and can be formulated in a symmetry-conserving manner, reducing the number of variational parameters. The authors also discuss the application of NQS to time-dependent problems, such as quantum quenches, and show that it can accurately describe the evolution induced by complex sets of excited quantum states. The paper highlights the potential of NQS to solve the quantum many-body problem, particularly in regimes where existing methods are limited. The approach offers a new perspective on solving the quantum many-body problem and opens up avenues for further research, including the application to more complex systems and the exploration of non-local correlations.