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 Z3 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&⋕39;s critical point, and that this mana resides in the system&⋕39;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 3-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.

Publication Details
Publication Type
Journal Article
Year of Publication
2021
Volume
103
Number of Pages
075145
DOI
10.1103/PhysRevB.103.075145
URL
https://arxiv.org/abs/2007.01303
Journal
Physical Review B
Contributors
Groups
Date Published
02/2021