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Convergence theorems on multi-dimensional homogeneous quantum walks.
- Source :
- Quantum Information Processing; Mar2021, Vol. 20 Issue 3, p1-24, 24p
- Publication Year :
- 2021
-
Abstract
- We propose a general framework for quantum walks on d-dimensional spaces. We investigate asymptotic behavior of these walks. We prove that every homogeneous walks with finite degree of freedom have limit distribution. This theorem can also be applied to every crystal lattice. In this theorem, it is not necessary to assume that the support of the initial unit vector is finite. We also pay attention on 1-cocycles, which is related to Heisenberg representation of time evolution of observables. For homogeneous walks with finite degree of freedom, convergence of averages of 1-cocycles associated with the position observable is also proved. [ABSTRACT FROM AUTHOR]
- Subjects :
- COCYCLES
DEGREES of freedom
CRYSTAL lattices
FINITE, The
Subjects
Details
- Language :
- English
- ISSN :
- 15700755
- Volume :
- 20
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Quantum Information Processing
- Publication Type :
- Academic Journal
- Accession number :
- 149847734
- Full Text :
- https://doi.org/10.1007/s11128-021-03002-6