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

Other · · Schrödinger Equation - Fundamentals Aspects and Potential Applications
 [1];  [2];  [3];  [3];  [4];  [5]
  1. College of William and Mary, Williamsburg, VA (United States); Rogers State University
  2. Rogers State University, Claremore, OK (United States)
  3. National Technical University of Athens, Zographou (Greece)
  4. Old Dominion University, Norfolk, VA (United States)
  5. Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
+ Show Author Affiliations
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. Here, 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.
Research Organization:
Rogers State University, Claremore, OK (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF); European Union
DOE Contract Number:
SC0021653; AC02-05CH11231; SC0021647; FG02-91ER54109; SC0021651; SC0021857
OSTI ID:
2341246
Country of Publication:
United States
Language:
English

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Related Subjects

2D electromagnetic scattering
Dyson map
Kraus operators
Schrodinger-Dirac
dilation
dissipative systems
qubit lattice algorithm