One and Two Dimensional Quantum Lattice Algorithms for Maxwell Equations in Inhomogeneous Scalar Dielectric Media I: Theory
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Author(s)
Vahala, George
Valhala, Linda
Soe, Min
Ram, Abhay K.
Date Issued
December 2020
Journal
Radiation Effects and Defects in Solids
Publisher
Taylor & Francis
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 σz is diagonal. For 2 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.
Description
Submitted for publication in Radiation Effects and Defects in Solids
MIT Department
Massachusetts Institute of Technology. Plasma Science and Fusion Center
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1080/10420150.2021.1891058
