Machine Learning and the Complexity of Quantum Simulation

Computational approaches to condensed matter have long influenced the theoretical development of quantum many-body physics. For example, quantum Monte Carlo (QMC) ties our understanding of the computational efficiency of simulating quantum systems to the sign structure of the Hamiltonian. The Density Matrix Renormalization Group motivated the modern field of Tensor Networks (TNs), which relate computational efficiency to the entanglement entropy of a wavefunction. This trend now continues with the rapidly-developing field of machine learning, which has introduced a host of new strategies and architectures for the simulation and data-driven reconstruction of quantum many-body systems. Over the last three years, progress has been made in framing various machine learning approaches within the context of traditional methods such as QMC or TNs; however, it has also become apparent that some aspects differ substantially. In this talk I will provide an overview of the landscape of machine learning strategies in simulating quantum systems. I will speculate on how our theoretical framework of quantum many-body physics can influence the development of new machine learning strategies, and vice versa.