An improved eigensolver for quantum-dot cellular automata simulations

The work in this paper describes the applicati on of an optimized eigensolver algorithm to produce the kernel calculations for simulating quantum-dot cellular automata (QCA) circuits, an emerging implementation of quantum computing The application of the locally optimal block preconditioned conjugate gradient (LOBPCG) method to calculate the eigenvalues and eigenvectors for this simulation was shown to exhibit a 15.6 speedup over the commonly used QR-method for a representative simulation and has specific advantages for the Hermitian, positive-definite, sparse matrices commonly encountered in simulating the Time-Independent Schrödinger equation. We present the computational savings for a simulation analyzing the effect of stray charges near a four-cell line of QCA cells with a single driver cell, and we discuss implications for wider application. We further discuss issues of problem preconditioning which are specific to QCA simulation when utilizing the LOBPCG method.