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.
Featured image: The windmill layout for implementing the distance-5 surface code with measurement-based qubits. Black nodes are data qubits; at the center of each X-type or Z-type plaquette, there is a green or yellow ancilla qubit, respectively. The measurement of a plaquette will require two-qubit measurements between the data qubits and the center ancilla (black edges), and between the center ancilla and its neighbor ancilla (blue edge).
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