Implementation Schemes for the Factorized Quantum Lattice-Gas Algorithm for the One Dimensional Diffusion Equation using Persistent-Current Qubits

Abstract

We present two experimental schemes that can be used to implement the Factorized Quantum Lattice-Gas Algorithm for the 1D Diffusion Equation with Persistent-Current Qubits. One scheme involves biasing the PC Qubit at multiple flux bias points throughout the course of the algorithm. An implementation analogous to that done in Nuclear Magnetic Resonance Quantum Computing is also developed. Errors due to a few key approximations utilized are discussed and differences between the PC Qubit and NMR systems are highlighted.