One- and two-dimensional quantum lattice algorithms for Maxwell equations in inhomogeneous scalar dielectric media I: theory. Issue 1 (1st February 2021) - Vahala, George; Vahala, Linda; Soe, Min; Ram, Abhay K.
ABSTRACT: A quantum lattice algorithm (QLA) is developed for Maxwell equations in scalar dielectric media using the Riemann–Silberstein representation on a Cartesian grid. For x -dependent and y -dependent dielectric inhomogeneities, the corresponding QLA requires a minimum of 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the local collisional entanglement of these qubits. However, z -dependent inhomogeneities require a QLA with a minimum of 16 qubits/lattice site since the Pauli spin matrix σ z is diagonal. For two-dimensional inhomogeneities, one can readily couple the 8–8 qubit schemes for x − y variations. z − x and y − z variations can be treated by either a 16–8 qubit scheme or a 16–16 qubit representation.