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 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.
Highlights
Fault tolerance is widely believed to be necessary to run viable applications on a quantum computer
Two crucial properties make the surface code very attractive for a first generation of fault-tolerant quantum computers: (i) Error correction with the surface code can be implemented on a planar grid of qubits using only single-qubit operations and nearest-neighbor gates, (ii) The surface code tolerates qubits and elementary operations affected by relatively high error rates [4, 5]
These properties have been established for qubits equipped with CNOT gates, e.g., superconducting qubits; it is unclear whether similar results hold with other types of qubits
Summary
Fault tolerance is widely believed to be necessary to run viable applications on a quantum computer. Two crucial properties make the surface code very attractive for a first generation of fault-tolerant quantum computers: (i) Error correction with the surface code can be implemented on a planar grid of qubits using only single-qubit operations and nearest-neighbor gates, (ii) The surface code tolerates qubits and elementary operations affected by relatively high error rates [4, 5]. These properties have been established for qubits equipped with CNOT gates, e.g., superconducting qubits; it is unclear whether similar results hold with other types of qubits. The resulting error distribution, called the inclusive error model as explained in Appendix E, is equivalent to the conventional error model (e.g., the depolarizing noise or the bit flip noise) in all important regimes and may be of independent interest
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