Simple and Fast Silicon-Based Quantum Dot/Bit Simulation Method for Large-Scale Quantum Computing

We have developed a simple and fast simulation method that enables the calculation and visualiziation of electrostatic potential in silicon-based quantum bit computers. To achieve high-fidelity operation method, it is essential to develop more convenient and effective simulators based deeply on understanding the quantum effects arising from the behavior of potentials induced by control signals. We propose a method for calculating quantum dot potentials. This involves setting virtual point charges at the plunger gate and barrier gate, then summing the total potential generated by these point charges (calculated as a double-layer potential when required by boundary conditions). By appropriately setting the generation interval of the point charges based on the distance from the point charges to the potential formation surface of the two-dimensional electron gas (2DEG), it is possible to reduce charge quantization errors. Analytical solutions for uniform surface charges are known [1], and our method confirms that its shape matches this analytical solution. Furthermore, our method can be integrated with existing LSI design tools with minimal steps, enabling efficient collaboration with the development of control techniques based on a deep understanding of qubit operation.

[1] John H. Davies; Ivan A. Larkin; E. V. Sukhorukov. “Modeling the patterned two‐dimensional electron gas: Electrostatics,” J. Appl. Phys. 77, 4504–4512 (1995)