Mathematical Sciences Dept. QIT Thinking Seminar - Takuya Machida, Nihon University (Stratton 301)

DEPARTMENT OF MATHEMATICAL SCIENCES

QIT Thinking Seminar

Speaker: Takuya Machida, 
Nihon University

Friday, August 14, 2026, 10:00 AM – 11:00 AM 
Stratton Hall 301

Title: Long-time limiting theorems for some quantum walks

Abstract: Quantum walks are quantum analogs of random walks in mathematics. While random walks converge in normal
distributions, quantum walks converge in probability distributions different from normal distributions. The speaker has
been working on limiting theorems for quantum walks since 2004.
Picking some of his papers [1-6], he will shortly talk about the limiting theorems for one dimensional quantum walks. The
theorems primarily focus on long-time limiting distributions, from which we will see interesting behavior of quantum
walks (e.g. localization, gap, phase transition).
[1] Takuya Machida, Norio Konno : Limit theorem for a time-dependent coined quantum walk on the line, F. Peper et al.
(Eds.): IWNC 2009, Proceedings in Information and Communications Technology, Vol.2, pp.226-235 (2010).
[2] F. Alberto Grunbaum, Takuya Machida : A limit theorem for a 3-period time-dependent quantum walk, Quantum
Information and Computation, Vol.15 No.1&2, pp.50-60 (2015).
[3] Takuya Machida : A limit theorem for a splitting distribution of a quantum walk, International Journal of Quantum
Information, Vol.16, No.3, 1850023 (2018).
[4] Takuya Machida : Limit theorems of a 3-state quantum walk and its application for discrete uniform measures,
Quantum Information and Computation, Vol.15 No.5&6, pp.406-418 (2015).
[5] Takuya Machida : Limit distribution of a continuous-time quantum walk with a spatially 2-periodic Hamiltonian,
Quantum Information Processing, Vol.22, 332 (2023).
[6] Takuya Machida : Phase transition of a continuous-time quantum walk on the half line, Quantum Information 
Processing, Vol.23, 243 (2024).