Pauli web of the $|Y⟩$ state surface code injection

Abstract

We employ ZX-calculus and Pauli web to understand the $|Y⟩$ state injection on the rotated surface code. Under circuit-level noise, we devise an optimised schedule that improves the logical error rate, for which we provide closed forms using parameterised ZX-diagrams.

arXiv commentv5 - major revision on circuit-level noise + parametric ZX-diagrams + T state injection