A proposal of quantum computing algorithm to solve Poisson equation for nanoscale devices under Neumann boundary condition. (February 2023) - Matsuo, Shingo; Souma, Satofumi
Abstract: We present an implementation study of gate-type quantum computing algorithms for the purpose of semiconductor device simulations. As one of the representative quantum algorithms we consider the use of HHL (Harrow–Hassidim–Lloyd) algorithm to solve the Poisson equation in semiconductor nanowire p–n junction under the Neumann boundary condition that the electric field is zero at the electrode boundaries. Our proposed model of the quantum gate to implement the Neumann boundary condition along with the appropriately designed non-uniform mesh grid has been found to successfully reproduce the solution obtained by conventional method. Highlights: An efficient quantum computing model to solve Poisson equation under Neumann boundary condition is proposed. Non-uniform discretization are introduced so that adjacent eigenvalues of the capacitance matrix are separated as equally as possible. Proposed scheme is found to reproduce accurate solution by a fewer resister qubits unless the charge profile is highly localized.