Optimization of the surface code design for Majorana-based qubits

Rui Chao1, Michael E. Beverland2, Nicolas Delfosse2, and Jeongwan Haah2

1University of Southern California, Los Angeles, CA, USA
2Microsoft Quantum and Microsoft Research, Redmond, WA, USA

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Abstract

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 $\textit{only}$ 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.

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