Some Comments on Unitary Qubit Lattice Algorithms for Classical Problems

TL;DR

This paper develops fully unitary qubit lattice algorithms for electromagnetic wave propagation and Korteweg-de Vries equations, avoiding non-unitary potential operators by perturbing collision operators, thus enhancing the applicability of quantum lattice algorithms.

Contribution

It introduces new fully unitary qubit lattice algorithms that eliminate the need for non-unitary potential operators in modeling wave equations.

Findings

Successfully developed fully unitary QLAs for electromagnetic waves.

Demonstrated avoidance of non-unitary operators through perturbation methods.

Enhanced the theoretical framework for quantum lattice algorithms.

Abstract

$\bf{Abstract}$: 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. 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.