Simulation of temperature-dependent quantum gates in silicon quantum dots with frequency shifts

To achieve quantum computing using semiconductor spin qubits, the spin qubits must be precisely controlled. However, unexpected noise limits this precision and prevents the implementation of error correction codes. Specifically, frequency shifts have been found to suppress one-qubit gate fidelity. Although the exact source of the frequency shifts remains unclear, several experiments have indicated a relationship between the frequency shift and heating from the control signal. Based on these results, we modeled the heating effect using the low-temperature dependence of specific heat from the Debye model to simulate qubit control with frequency shifts. This model quantitatively reproduces some of the experimental results and makes it possible to simulate qubit gates with temperature-dependent frequency shifts. The simulated control fidelity of the proposed model was consistent with the experimental results, demonstrating that a gate fidelity above $99.9$% can be achieved in a hot environment. Additionally, our comparison of the two temperature-dependent frequency shift models reveals the condition for a microscopic frequency shift model in which the variance of the frequency shift is limited to a specific range. Furthermore, we investigated gate fidelity using the DRAG method and demonstrated the utility of temperature-dependent simulations.