Conformal field theories are magical

TL;DR

This paper explores the concept of 'mana' as a measure of quantum magic in the ground state of the $ ext{Z}_3$ Potts model, revealing its critical role in conformal field theories and implications for quantum computing and tensor networks.

Contribution

It introduces mana as a diagnostic for many-body physics, demonstrating its presence at critical points and linking it to conformal field theories in the $ ext{Z}_3$ Potts model.

Findings

Mana peaks at the critical point of the model.

Mana resides in the system's correlations across scales.

Conformal field theory at the critical point is 'magical' due to mana presence.

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 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.