Xiaoyang He

Qitong Hu, Xiaoyang He, Shi Jin et al.

In this paper, we present a quantum implicit-explicit (IMEX) scheme for multiscale ordinary and partial differential equations whose discretization parameters are independent of the scaling parameter $\varepsilon$. A key ingredient of our approach is a continuous-time formulation of classical IMEX schemes, which decouples the evolution time of the quantum algorithm from the physical time of the differential equation and is therefore particularly useful in multiscale settings. Building on this idea, we employ the Schrödingerization framework [Phys. Rev. Lett. 133 (2024), 230602] to implement IMEX schemes on quantum computers. Compared to previous HHL type quantum AP scheme [J. Comput. Phys. 471 (2022), 111641], this new method requires narrower -- an extra logarithmic factor -- auxiliary register numerical examples on linear heat and multiscale telegraph equations demonstrate the independence in $\varepsilon$ of the method.

Xiaoyang He, Manabu Tsukada

Timely channel information is necessary for vehicles to determine both the serving base station (BS) and the beamforming vector, but frequent estimation of fast-fading mmWave channels incurs significant overhead. To address this challenge, we propose a Beam-aware Kernelized Contextual Upper Confidence Bound (BKC-UCB) algorithm that estimates instantaneous transmission rates without additional channel measurements by exploiting historical contexts such as vehicle location and velocity, together with past observed transmission rates. Specifically, BKC-UCB leverages kernel methods to capture the nonlinear relationship between context and transmission rate by mapping contexts into a reproducing kernel Hilbert space (RKHS), where linear learning becomes feasible. Rather than treating each beam as an independent arm, the beam index is embedded into the context, enabling BKC-UCB to exploit correlations among beams to accelerate convergence. Furthermore, an event-triggered information sharing mechanism is incorporated into BKC-UCB, enabling information exchange only when significant explorations are conducted to improve learning efficiency with limited communication overhead.

Xiaoyang He, Xiaoxia Huang

Vehicles require timely channel conditions to determine the base station (BS) to communicate with, but it is costly to estimate the fast-fading mmWave channels frequently. Without additional channel estimations, the proposed Distributed Kernelized Upper Confidence Bound (DK-UCB) algorithm estimates the current instantaneous transmission rates utilizing past contexts, such as the vehicle's location and velocity, along with past instantaneous transmission rates. To capture the nonlinear mapping from a context to the instantaneous transmission rate, DK-UCB maps a context into the reproducing kernel Hilbert space (RKHS) where a linear mapping becomes observable. To improve estimation accuracy, we propose a novel kernel function in RKHS which incorporates the propagation characteristics of the mmWave signals. Moreover, DK-UCB encourages a vehicle to share necessary information when it has conducted significant explorations, which speeds up the learning process while maintaining affordable communication costs.