Evaluating Surface code for Silicon-based Spin Qubits

The last few years have seen significant progress in silicon-based quantum technology, with increasing controllability and fidelity of single- and two-qubit gates. A key component for realizing a large-scale fault-tolerant quantum computer is quantum error correction, offering exponentially scalable resilience to noise. We report the logical qubit performance of the 17-qubit rotated surface code, based on the emulation of syndrome circuits with Si-qubit native gates and realistic noise models on the Qaptiva quantum emulator. We rely on physical-level simulations to derive noise models for single- and two-qubit gates, considering noise affecting the Larmor frequency and the exchange energy. Furthermore, we define the logical qubit coherence time, obtained through a Ramsey-like experiment on the logical qubit, serving as a performance metric directly comparable to the coherence time of the physical qubit. Our numerical results reveal a substantial improvement in the logical qubit coherence time compared to the physical qubit, exhibiting a quartic dependency as a result of the 1/f noise characteristic of spin qubits. This work paves the way for exploring different architectures integrating shuttling and readout qubits, while also providing a means to evaluate the resources required for large-scale QEC codes necessary to achieve fault-tolerant quantum computing with spin qubits.