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One and Two Dimensional Quantum Lattice Algorithms for Maxwell Equations in Inhomogeneous Scalar Dielectric Media I: Theory

Author(s)
Vahala, George; Valhala, Linda; Soe, Min; Ram, Abhay K.
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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
Date issued
2020-12
URI
https://hdl.handle.net/1721.1/158685
Department
Massachusetts Institute of Technology. Plasma Science and Fusion Center
Journal
Radiation Effects and Defects in Solids
Publisher
Taylor & Francis
Other identifiers
20ja104

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