Preparing the XY surface code with high threshold under biased noise

Tailoring quantum surface codes by local Clifford deformation can increase their thresholds under biased noise. A specific example is the XY-surface code, which reduces to a repetition code under pure dephasing noise and achieves code capacity threshold of 50%. However, it is crucial to analyze the performance of the code during logical operations such as state preparation. In the standard approach, a logical X (or Y) state is prepared by initializing each physical qubit in the |+> (or |+i>) state, followed by measuring all stabilizers. However, this technique breaks the underlying symmetry of the XY code under pure dephasing noise, which limits the logical state preparation threshold. In this work, we propose a new logical initialization protocol which maintains the effectiveness of the XY code against dephasing noise. In this protocol, physical qubits are first locally entangled into two- or four-body Bell states, following which all the stabilizers are measured. We prove that in this procedure dephasing errors can be decoded as a repetition code, which guarantees a 50% state preparation threshold. Our analysis is supported by numerical simulations, which also show an overall improvement in threshold when dephasing errors is accompanied by small amount of bit-flip noise.