Variational quantum evolution equation solver.

Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through implicit time-stepping of the Laplacian operator. The use of encoded source states informed by preceding solution vectors results in faster convergence compared to random re-initialization. Through statevector simulations of the heat equation, we demonstrate how the time complexity of our algorithm scales with the Ansatz volume for gradient estimation and how the time-to-solution scales with the diffusion parameter. Our proposed algorithm extends economically to higher-order time-stepping schemes, such as the Crank-Nicolson method. We present a semi-implicit scheme for solving systems of evolution equations with non-linear terms, such as the reaction-diffusion and the incompressible Navier-Stokes equations, and demonstrate its validity by proof-of-concept results.

Volume integral equation analysis of surface plasmon resonance of nanoparticles.

The interactions between electromagnetic field and arbitrarily shaped metallic nanoparticles are numerically investigated. The scattering and near field intensity of nanoparticles are characterized by using volume integral equation which is formulated by considering the total electric field, i.e. the sum of incident fields and radiated fields by equivalent electric volume currents, within the scatterers. The resultant volume integral equation is then discretized using divergence-conforming vector basis functions and is subsequently solved numerically. Numerical examples are presented to demonstrate the application of volume integral equation to capture and analyze the surface plasmon resonance of arbitrarily shaped metallic nanoparticles. The effects of illumination angles and background media to the surface plasmon resonance are also investigated. The results show that our proposed method is particularly useful and accurate in characterizing the surface plasmon properties of metallic nanoparticles.

Analysis of sub-wavelength light propagation through long double-chain nanowires with funnel feeding.

The surface integral equation (SIE) method is utilized to characterize plasmonic waveguide made of two parallel chains of silver nanowires with radius of 25nm fed by a V-shaped funnel at a working wavelength of 600nm. The efficiency of energy transport along the waveguide due to surface plasmonic coupling is investigated for different dimensions and shapes. The opening angle of the V-shaped funnel region for optimum light capturing is included in the investigation as well. A long plasmonic double-chain waveguide of length ~3.3mum has been analyzed and optimized.