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math-ph2024
Two-dimensional quantum central limit theorem by quantum walks
Keisuke Asahara, Daiju Funakawa, Motoki Seki +1
The weak limit theorem (WLT), the quantum analogue of the central limit theorem, is foundational to quantum walk (QW) theory. Unlike the universal Gaussian limit of classical walks…
math-ph2021
The bulk-edge correspondence for the split-step quantum walk on the one-dimensional integer lattice
Yasumichi Matsuzawa, Motoki Seki, Yohei Tanaka
Suzuki's split-step quantum walk on the one-dimensional integer lattice can be naturally viewed as a chirally symmetric quantum walk. Given the unitary time-evolution of such a chi…
math-ph2020
The Witten Index for One-dimensional Non-unitary Quantum Walks with Gapless Time-evolution
Keisuke Asahara, Daiju Funakawa, Motoki Seki +1
Recent developments in the index theory of discrete-time quantum walks allow us to assign a certain well-defined supersymmetric index to a pair of a unitary time-evolution and…