Fast Well-Conditioned Volume Integral Equation Solver for Analyzing Nonlocal Optical Responses in Quantum Nanostructures

Solid-state spin qubits are one of the candidate platforms for future quantum computers due to their long coherence time and good controllability. However, qubits are susceptible to noise generated from external magnetic fields. In this paper, we present a fast and accurate volume integral equation solver for analyzing local/nonlocal optical responses in quantum nano-electromagnetic gate circuitry. Due to small electric sizes of quantum circuitry, conventional volume integral equation (VIE) solvers suffer from both numerical difficulties and deteriorated accuracy since the underlying numerical system is highly ill-conditioned. To overcome this problem, we introduce a well-conditioned VIE formulation. We further accelerate the VIE solution by transforming the six-dimensional integral arising from the nonlocal constitutive relation to the spectral domain using fast Fourier transform (FFT). The same FFT is also applied to efficiently compute the convolution of Green's function with equivalent volumetric currents. The resultant fast and robust VIE solver has been applied to analyze large-scale 3-D quantum gate devices. Both local and nonlocal optical responses of the devices are captured accurately and efficiently. This work offers a fast and accurate approach to guide the noise control of high-fidelity quantum gate circuitry design.