A note on Ito's formula for discrete-time quantum walk
Norio Konno
TL;DR
This paper introduces an Ito's formula for one-dimensional discrete-time quantum walks, providing new mathematical tools and examples, including a quantum version of Tanaka's formula, and discusses related integrals.
Contribution
It presents the first Ito's formula for discrete-time quantum walks and explores associated integrals, extending classical stochastic calculus to quantum walk models.
Findings
Derived an Ito's formula for quantum walks
Provided examples including quantum Tanaka's formula
Discussed integrals related to quantum walks
Abstract
We present an Ito's formula for the one-dimensional discrete-time quantum walk and give some examples including a Tanaka's formula by using the formula. Moreover we discuss integrals for the quantum walk.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum-Dot Cellular Automata