Year: 2022
Type: preprint
Abstract: We prove a nontrivial circuit-depth lower bound for preparing a low-energy state of a locally interacting quantum many-body system in two dimensions, assuming the circuit is geometrically local. For preparing any state which has an energy density of at most $ε$ with respect to Kitaev's toric code Hamiltonian on a two dimensional lattice $Λ$, we prove a lower bound of $Ω\left(\min\left(1/ε^{\frac{1-α}{2}}, \sqrt{|Λ|}\right)\right)$ for any $α>0$. We discuss two implications. First, our bound implies that the lowest energy density obtainable from a large class of existing variational circuits (e.g., Hamiltonian variational ansatz) cannot, in general, decay exponentially with the circuit depth. Second, if long-range entanglement is present in the ground state, this can lead to a nontrivial circuit-depth lower bound even at nonzero energy density. Unlike previous approaches to prove circuit-depth lower bounds for preparing low energy states, our proof technique does not rely on the ground state to be degenerate.
Source: arXiv (Cornell University)
Authors: Tikku, Arkin, Kim, Isaac H.
Institution: University of California, Davis
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4306309306