Ito's formula for the discrete-time quantum walk in two dimensions
Clement Ampadu
TL;DR
This paper extends Ito's formula to the two-dimensional discrete-time quantum walk on the square lattice, providing a mathematical framework analogous to the continuous case.
Contribution
It derives the Ito's formula specifically for the discrete-time quantum walk on Z^2, expanding the theoretical understanding of quantum walks on higher-dimensional graphs.
Findings
Derived Ito's formula for 2D quantum walk
Established mathematical framework for quantum walks on Z^2
Extended previous 1D results to 2D case
Abstract
Following [Konno, arXiv:1112.4335], it is natural to ask: What is the Ito's formula for the discrete time quantum walk on a graph different than Z, the set of integers? In this paper we answer the question for the discrete time quantum walk on Z^2, the square lattice.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum and electron transport phenomena