Quantum simulation of Maxwell's equations via Schr\"odingersation
- URL: http://arxiv.org/abs/2308.08408v1
- Date: Wed, 16 Aug 2023 14:52:35 GMT
- Title: Quantum simulation of Maxwell's equations via Schr\"odingersation
- Authors: Shi Jin and Nana Liu and Chuwen Ma
- Abstract summary: We present quantum algorithms for electromagnetic fields governed by Maxwell's equations.
The algorithms are based on the Schr"odingersation approach.
Instead of qubits, the quantum algorithms can also be formulated in the continuous variable quantum framework.
- Score: 27.193565893837356
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present quantum algorithms for electromagnetic fields governed by
Maxwell's equations. The algorithms are based on the Schr\"odingersation
approach, which transforms any linear PDEs and ODEs with non-unitary dynamics
into a system evolving under unitary dynamics, via a warped phase
transformation that maps the equation into one higher dimension. In this paper,
our quantum algorithms are based on either a direct approximation of Maxwell's
equations combined with Yee's algorithm, or a matrix representation in terms of
Riemann-Silberstein vectors combined with a spectral approach and an upwind
scheme. We implement these algorithms with physical boundary conditions,
including perfect conductor and impedance boundaries. We also solve Maxwell's
equations for a linear inhomogeneous medium, specifically the interface
problem. Several numerical experiments are performed to demonstrate the
validity of this approach. In addition, instead of qubits, the quantum
algorithms can also be formulated in the continuous variable quantum framework,
which allows the quantum simulation of Maxwell's equations in analog quantum
simulation.
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