Abstract: 

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 algorithms that take reduced density matrices over bounded balls as inputs, and output a circuit that prepares the global state. We introduce algorithms applicable to (i) long-range entangled states (e.g., toric code on a sphere) and (ii) short-range entangled states (e.g., states prepared by shallow quantum circuits in any dimension, and more generally, invertible states). Both algorithms provably find a circuit whose depth is asymptotically optimal. While the inputs to our algorithm can be obtained from experiments using methods such as classical shadows, they can be also obtained from exact diagonalization of the parent Hamiltonian on local regions, provided that the Hamiltonian is weakly perturbed from some solvable fixed-point Hamiltonian.

Based on an ongoing work with Hyun-Soo Kim (UC Davis) and Daniel Ranard (Caltech)

Contact: Eun Gook Moon(egmoon@kaist.ac.kr)