Pauli webs spun by transversal $|Y\rangle$ state initialisation

TL;DR

This paper uses ZX-calculus and Pauli webs to analyze the transversal initialization of $|Y angle$ states in surface codes, providing insights into fault-tolerant quantum computing methods.

Contribution

It introduces a novel application of ZX-calculus and Pauli webs to understand $|Y angle$ state initialization in surface codes, extending previous work on transversal gates.

Findings

Clarifies the structure of $|Y angle$ state initialization

Provides a graphical framework for fault-tolerant state preparation

Enhances understanding of transversal gate implementations

Abstract

Originally motivated by the (fold-)transversal related initialisation of logical surface code $|Y\rangle$ states from [arXiv:1603.02286, arXiv:2302.07395, arXiv:2302.12292], which was then explicitly extended to the fold-transversal $S$ gate implementation in [arXiv:2412.01391] for the rotated surface code, we employ ZX-calculus and Pauli web to understand the $|Y\rangle=S|+\rangle$ state transversal initialisation scheme.