Classification of measurement-based quantum wire in stabilizer PEPS

TL;DR

This paper classifies the transmission capabilities of a specific class of 2D tensor network states with stabilizer symmetry, revealing 13 distinct behavior classes including Clifford automata.

Contribution

It provides a complete classification of measurement-based quantum wire behaviors in stabilizer PEPS, identifying 13 distinct transmission classes.

Findings

13 classes of transmission behaviors identified

Clifford quantum cellular automata included in classification

Complete categorization of stabilizer PEPS transmission capabilities

Abstract

We consider a class of translation-invariant 2D tensor network states with a stabilizer symmetry, which we call stabilizer PEPS. The cluster state, GHZ state, and states in the toric code belong to this class. We investigate the transmission capacity of stabilizer PEPS for measurement-based quantum wire, and arrive at a complete classification of transmission behaviors. The transmission behaviors fall into 13 classes, one of which corresponds to Clifford quantum cellular automata. In addition, we identify 12 other classes.