Simulated non-Markovian Noise Resilience of Silicon-Based Spin Qubits with Surface Code Error Correction

We investigate the resilience of silicon-based spin qubits against non-Markovian noise within the framework of quantum error correction. We consider a realistic non-Markovian noise model that affects both the Larmor frequency and exchange energy of qubits, allowing accurate simulations of noisy quantum circuits. We employ numerical emulation to assess the performance of the distance-3 rotated surface code and its XZZX variant, using a logical qubit coherence time metric based on Ramsey-like experiments. Our numerical results suggest that quantum error correction converts non-Markovian physical noise into Markovian logical noise, resulting in a quartic dependence of coherence time between physical and logical qubits. Additionally, we analyze the effects of spatial noise correlations and sparse architectures, substantiating the robustness of quantum error correction in silicon-based spin qubit systems.