Triangle Quantum Computing Seminar Series: Feynman Formula for Discrete-time Quantum Walks

ABSTRACT: We explicitly connect discrete-time quantum walks on Z with a four-state Markov additive process via a Feynman-type formula. This representation yields a relation between the spectral decomposition of the Markov process and the limiting density of the homogeneous quantum walk. By rescaling quantum walks in space and time, we obtain systems of quantum transport PDEs with phase interaction terms. Our probabilistic approach-using both the Poisson and telegraph processes-provides an efficient Monte Carlo method for these PDEs. This talk is based on recent joint work with Jean-Pierre Fouque and Tomoyuki Ichiba: https://arxiv.org/abs/2510.12038. BIO: Ka Lok Lam is a 4th-year Ph.D. candidate in Statistics and Applied Probability at UC Santa Barbara (UCSB), co-supervised by Prof. Jean-Pierre Fouque and Prof. Tomoyuki Ichiba. His research focuses on quantum and stochastic dynamics and their applications in finance. In October 2025, he presented at the 3rd Workshop on Quantum Algorithms/Formalisms in Finance (Fields Institute) and the 9th Eastern Conference on Mathematical Finance. Previously, he earned his BSc and MPhil in Mathematics at the Chinese University of Hong Kong (CUHK) under Prof. Chi Wai Leung, focusing on functional analysis and Banach space theory. The Duke Quantum Center, the IBM Quantum Innovation Center at NC State, and the UNC Kenan-Flagler's Rethinc. Labs are pleased to present the Fall 2025 Semester Triangle Quantum Computing Seminar series.