Variational Quantum-Based Simulation of Waveguide Modes

Abstract

Variational quantum algorithms are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a variational quantum algorithm in conjunction with the finite difference method for the calculation of propagation modes of an electromagnetic wave in a hollow metallic waveguide. The two-dimensional (2D) waveguide problem, described by the Helmholtz equation, is approximated by a system of linear equations, whose solutions are expressed in terms of simple quantum expectation values that can be evaluated efficiently on quantum hardware. Numerical examples are presented to validate the proposed method for solving 2D waveguide problems.

9 pages, 7 figures

References in corpus (15)

• Quantum algorithm for solving linear systems of equations
• Variational Quantum Algorithms
• A Quantum Approximate Optimization Algorithm
• Noisy intermediate-scale quantum (NISQ) algorithms
• Hybrid quantum-classical algorithms and quantum error mitigation
• Efficient quantum algorithm for dissipative nonlinear differential equations
• Fundamental limits of quantum error mitigation
• Variational Quantum algorithm for Poisson equation
• Extending quantum probabilistic error cancellation by noise scaling
• Variational quantum algorithm based on the minimum potential energy for solving the Poisson equation
• Quantum algorithm for nonlinear differential equations
• Quantum Fourier analysis for multivariate functions and applications to a class of Schrödinger-type partial differential equations
• Lectures on Theory of Microwave and Optical Waveguides
• Quantum variational PDE solver with machine learning
• Study of using Quantum Computer to Solve Poisson Equation in Gate Insulators

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