Optimization of the surface code design for Majorana-based qubits

• URL: http://arxiv.org/abs/2007.00307v2
• Date: Mon, 26 Oct 2020 15:58:51 GMT
• Title: Optimization of the surface code design for Majorana-based qubits
• Authors: Rui Chao, Michael E. Beverland, Nicolas Delfosse, Jeongwan Haah
• Abstract summary: The surface code is a prominent topological error-correcting code exhibiting high fault-tolerance accuracy thresholds. Here, we present error-correction schemes using $textitonly$ Pauli measurements on single qubits and on pairs of nearest-neighbor qubits.
• Score: 2.309914459672557
• License: http://creativecommons.org/licenses/by/4.0/
• 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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