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Qubit Lattice Algorithms Based on the Schrodinger-Dirac Representation of Maxwell Equations and Their Extensions

Author(s)
Vahala, George; Soe, Min; Kououtsis, Efstratios; Hizanidis, Kyriakos; Vahala, Linda; Ram, Abhay K.; ... Show more Show less
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Abstract
It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomogeneous media. A Dyson map points to a unitary field qubit basis, but the standard qubit lattice algorithm of interleaved unitary collision-stream operators must be augmented by some sparse non-unitary potential operators that recover the derivatives on the refractive indices. The effect of the steepness of these derivatives on two-dimensional scattering is examined with simulations showing quite complex wavefronts emitted due to transmissions/reflections within the dielectric objects. Maxwell equations are extended to handle dissipation using Kraus operators. Then, our theoretical algorithms are extended to these open quantum systems. A quantum circuit diagram is presented as well as estimates on the required number of quantum gates for implementation on a quantum computer.
Description
Submitted for publication in IntechOpen
Date issued
2023-07
URI
https://hdl.handle.net/1721.1/158723
Department
Massachusetts Institute of Technology. Plasma Science and Fusion Center
Journal
IntechOpen
Publisher
IntechOpen
Other identifiers
23ja024

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