Qubit Lattice Algorithms Based on the Schrodinger-Dirac Representation of Maxwell Equations and Their Extensions
Name
23ja024_full.pdf
Size
8.61 MB
Format
Adobe PDF
Checksum (MD5)
766edee9da8accd98bcd4d80099bdf8d
Author(s)
Vahala, George
Soe, Min
Kououtsis, Efstratios
Hizanidis, Kyriakos
Vahala, Linda
Ram, Abhay K.
Date Issued
July 2023
Journal
IntechOpen
Publisher
IntechOpen
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
MIT Department
Massachusetts Institute of Technology. Plasma Science and Fusion Center
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.5772/intechopen.112692
