The surface code is a prominent topological error-correcting code exhibiting high fault-tolerance accuracy thresholds. Conventional schemes for error correction with the surface code place qubits on a planar grid and assume native CNOT gates between the data qubits with nearest-neighbor ancilla qubits. Here, we present surface code error-correction schemes using only Pauli measurements on single qubits and on pairs of nearest-neighbor qubits. In particular, we provide several qubit layouts that offer favorable trade-offs between qubit overhead, circuit depth and connectivity degree. We also develop minimized measurement sequences for syndrome extraction, enabling reduced logical error rates and improved fault-tolerance thresholds. Our work applies to topologically protected qubits realized with Majorana zero modes and to similar systems in which multi-qubit Pauli measurements rather than CNOT gates are the native operations.
@article{arxiv.2007.00307,
title = {Optimization of the surface code design for Majorana-based qubits},
author = {Rui Chao and Michael E. Beverland and Nicolas Delfosse and Jeongwan Haah},
journal= {arXiv preprint arXiv:2007.00307},
year = {2020}
}