Learning State Preparation Circuits for Quantum Phases of Matter

Understand

Many-body ground state preparation is an important subroutine used in the simulation of physical systems.

• In this paper, we introduce a flexible and efficient framework for obtaining a state preparation circuit for a large class of many-body ground states.
• We introduce polynomial-time classical algorithms that take reduced density matrices over $\mathcal{O}(1)$-sized balls as inputs, and output a circuit that prepares the global state.
• We introduce algorithms applicable to (i) short-range entangled states (e.g., states prepared by shallow quantum circuits in any number of dimensions, and more generally, invertible states) and (ii) long-range entangled ground states (e.g., the toric code on a disk).