Utilizing the similarity between the spinor representation of the Dirac and the Maxwell equations that has been recognized since the early days of relativistic quantum mechanics, a quantum lattice algorithm (QLA) representation of unitary collision-stream operators of Maxwell's equations is derived for both homogeneous and inhomogeneous media. A second-order accurate 4-spinor scheme is developed and tested successfully for two-dimensional (2-D) propagation of a Gaussian pulse in a uniform medium whereas for normal (1-D) incidence of an electromagnetic Gaussian wave packet onto a dielectric interface requires 8-component spinors because of the coupling between the two electromagnetic polarizations. In particular, the well-known phase change, field amplitudes and profile widths are recovered by the QLA asymptotic profiles without the imposition of electromagnetic boundary conditions at the interface. The QLA simulations yield the time-dependent electromagnetic fields as the wave packet enters and straddles the dielectric boundary. QLA involves unitary interleaved non-commuting collision and streaming operators that can be coded onto a quantum computer: the non-commutation being the very reason why one perturbatively recovers the Maxwell equations.

中文翻译：

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真空和介电介质中麦克斯韦方程的酉量子晶格模拟

利用狄拉克的旋量表示与麦克斯韦方程组之间的相似性，这一点自相对论量子力学早期就已被认识到，麦克斯韦方程组的酉碰撞流算子的量子晶格算法 (QLA) 表示被推导出用于齐次和不均匀的介质。针对高斯脉冲在均匀介质中的二维 (2-D) 传播以及电磁高斯波包在电介质上的法向 (1-D) 入射，开发并成功测试了二阶精确 4 旋量方案由于两个电磁极化之间的耦合，接口需要 8 个分量的旋量。特别是众所周知的相变，场振幅和剖面宽度由 QLA 渐近剖面恢复，而无需在界面处施加电磁边界条件。当波包进入并跨越电介质边界时，QLA 模拟产生与时间相关的电磁场。QLA 涉及可以编码到量子计算机上的酉交错非对易碰撞和流式算子：非对易正是人们以微扰方式恢复麦克斯韦方程的原因。