Tailoring quantum error correction to spin qubits

Abstract

Spin qubits in semiconductor structures bring the promise of large-scale two-dimensional integration, with the possibility to incorporate the control electronics on the same chip. In order to perform error correction on this platform, the characteristic features of spin qubits need to be accounted for. For example, qubit readout involves an additional qubit which necessitates careful reconsideration of the qubit layout. The noise affecting spin qubits has further peculiarities such as the strong bias towards dephasing. In this work we consider state-of-the-art error correction codes that require only nearest-neighbor connectivity and are amenable to fast decoding via minimum-weight perfect matching. Compared to the surface code, the XZZX code, the reduced-connectivity surface code, the ${\text{XYZ}}^{2}$ matching code, and the Floquet code all bring different advantages in terms of error threshold, connectivity, or logical qubit encoding. We present the spin-qubit layout required for each of these error correction codes, accounting for reference qubits required for spin readout. The performance of these codes is studied under circuit-level noise accounting for distinct error rates for gates, readout, and qubit decoherence during idling stages.