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.

Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape

“…The advent of machine learning (ML) techniques [55][56][57] has brought new hope in addressing challenging many-body problems, with neural networks being used as a generic variational ansatz [58]. In particular, much like the MNIST data set of handwritten digits in the ML community [59], the ground state search of the frustrated J 1 − J 2 model has recently turned into a test bed for ideas attempting to push the boundaries of neural-network-based variational approaches [60][61][62][63][64][65].…”

A NEAT quantum error decoder

“…We implemented this game as a reinforcement learning problem using the OpenAI Gym [26] framework, and made it publicly available as part of SciGym [27]. Using this environment we use the NEAT algorithm to optimize a policy network N (s) → a that takes as input the state s of the game and outputs the probability to take action a (which qubit to act on with which Pauli operator) 2 . The state s of the game is taken to be the current measurements of the stabilizer operators P and S (amounting to 2d 2 values), meaning that the input has no memory of the past.…”

“…Over the recent years, machine learning techniques for quantum physics have become more and more commonplace [1,2]. These techniques provide a rather different paradigm to solving hard problems than traditional algorithms do.…”

Supervised learning of few dirty bosons with variable particle number

“…Supervised machine learning is emerging as a potentially disruptive technique to accurately predict the properties of complex quantum systems. It has already allowed researchers to drastically speedup various important computational tasks in quantum chemistry and in condensedmatter physics [1,2], including: molecular dynamics simulations [3][4][5][6][7], electronic structure calculations [8][9][10][11][12][13], structure-based molecular design [14][15][16], and protein-molecule bindingaffinity predictions [17][18][19]. Deep neural networks represent the most powerful and versatile models.…”