Some comments on unitary qubit lattice algorithms for classical problems

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.

针对张量电介质中的电磁波传播问题，本文提出了量子比特晶格算法（Qubit Lattice Algorithm, QLA），该算法由一组交错排布的幺正碰撞流算子构成。为处理折射率梯度问题，需引入外势算子，这类算子通常为非幺正且稀疏的。针对科特韦格-德弗里斯方程（Korteweg-de Vries Equation, KdV）的QLA中也存在类似问题：用于建模KdV非线性项的势算子同样为非幺正算子。本文提出了多款通过摄动碰撞算子以规避此类非幺正势算子需求的QLA，此类算法的所有算子均为严格幺正的。