Preparation of Quantum Critical States with Machine Learning

Preparation of entangled many-body states is one of the most important steps in quantum simulation, and yet its difficulty and complexity are significantly increasing with amounts of entanglement of a target many-body state. To overcome the difficulty and complexity, we propose a strategy to prepare entangled many-body states with machine learning with scaling relations and apply it to several quantum critical states. For example, in the transverse-field Ising model with 40 qubits, our construction gives a state close to the exact state, manifested by the central charge of 0.497. We also discuss how our strategy can be implemented in quantum simulations with trapped ions and Rydberg atoms.