论文标题
Pauli旋转矩阵对不均匀介质中Maxwell方程的量子晶格算法的影响
The Effect of the Pauli Spin Matrices on the Quantum Lattice Algorithm for Maxwell Equations in Inhomogeneous Media
论文作者
论文摘要
使用Riemann-Silberstein表示，开发了用于标量介质介质中的麦克斯韦方程的量子晶格算法（QLA）。对于X依赖性和Y依赖性的不均匀性，相应的QLA重新QURIES 8 QUBITS/空间晶格位点。这是因为相应的Pauli旋转矩阵具有偏对分量，允许两个量子位的碰撞纠缠。但是，由于Pauli旋转矩阵$σ_z$是对角线，因此Z依赖性的不均匀性需要一个具有16个Qubits/晶格位点的QLA。在最初的电磁脉冲的时间演化中，进行了QLA模拟，该脉冲正常传播到边界层区域，并连接两个具有不同折射率的介质。所有三个表示之间都有良好的一致性，并且与几乎所有标准平面波边界条件的结果都具有很好的一致性，以反射和传输介电不连续性。在QLA模拟中，没有在连续但急剧增加的边界层处施加边界条件。
A quantum lattice algorithm (QLA) is developed for the solution of Maxwell equations in scalar dielectric media using the Riemann-Silberstein representation. For x-dependent and y-dependent inhomogeneities, the corresponding QLA requries 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the collisional entanglement of two qubits. However, z-dependent inhomogeneities require a QLA with 16 qubits/lattice site since the Pauli spin matrix $σ_z$ is diagonal. QLA simulations are performed for the time evolution of an initial electromagnetic pulse propagating normally to a boundary layer region joining two media of different refractive index. There is excellent agreement between all three representations, as well as very good agreement with nearly all the standard plane wave boundary condition results for reflection and transmission off a dielectric discontinuity. In the QLA simulation, no boundary conditions are imposed at the continuous, but sharply increasing, boundary layer.
