Year: 2021
Type: article
Abstract: ``Magic'' is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the ${\mathbb{Z}}_{3}$ Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the $q=3$ ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the three-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer and constrain tensor network models of AdS-CFT.
Authors: Christopher David White, ChunJun Cao, Brian Swingle
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
OpenAlex ID: W3039626760