Some comments on unitary qubit lattice algorithms for classical problems
P. B. Anderson, Lillian Finegold-Sachs, George Vahala, Linda L. Vahala, Abhay K. Ram, Min Soe, Efstratios Koukoutsis, Kyriakos Hizandis · Radiation effects and defects in solids · 2023
A qubit lattice algorithm (QLA), which consists of a set of interleaved unitary collision-streaming operators, is developed for electromagnetic wave propagation in tensor dielectric media. External potential operators are required to handle gradients in the refractive indices, and these operators are typically non-unitary but sparse. A similar problem arises in the QLA for the Korteweg–de Vries equation, as the potential operator that models the KdV nonlinear term is also non-unitary. Several QLAs are presented here that avoid the need of this non-unitary potential operator by perturbing the collision operator. These QLAs are fully unitary.