Title of the talk: Quantum walks in ordered and disordered scenarios: applications of permutation matrices

Date & Time: Nov 11,2025 at 12 noon (ONLINE)

Abstract: We focus on the quantum mechanical properties of the ordered and the disordered two-dimensional discrete-time quantum walks (2D-DTQWs) defined on a regular 2D lattice and their connections to permutation matrices. At first, we define the clean or ordered 2D-DTQWs with the coin operators as one-parameter orthogonal matrices called generalized Grover matrices, which can be expressed

as linear combinations of permutation matrices, a combinatorial structure inherited by the Grover matrix. We discuss the group structure of such matrices. We show some applications of generalized Grover matrices in discrete-time quantum walk with special attention to the localization phenomena. Localization makes the propagation dynamics of a walker strikingly different from that of classical random walks. We show that the proposed quantum walks localize at their initial position for canonical initial coin states when the coin is the parametric one containing the Grover matrix. Then, we define disordered 2D-DTQWs by considering glassy disorder in the jump length and discuss the spreading behavior of such walks. In clean 2D-DTQWs, there is a quadratic speedup in the spreading rate over the diffusive classical spreading. We see that the ballistic spreading of the clean walk is inhibited in the presence of disorder, and the walk becomes sub-ballistic but remains super-diffusive. At last, I will discuss shortly the spectral properties of doubly stochastic matrices, which are convex combinations of permutation matrices, for some specially structured matrices, for example, matrices for which rows are permutations of each other and trace-zero matrices.

About the Speaker: Dr. Amrita is working as an Assistant Professor in the Dept. of Mathematics, BIT Mesra since 2024. Her current research focuses on Quantum information and computation, Combinatorial matrix theory. She has completed her Ph.D. from IIT Kharagpur in 2022 and master's from Jadavpur University in 2015.