Analysis of quantum walks with time-varying coin on d-dimensional lattices
- Dipartmento di Matematica Pura e Applicata, Universita di Padova, Via Trieste 63, 35121 Paodva (Italy)
- Department of Mathematics, Iowa State University, 440 Carver Hall, Ames, Iowa 5001 (United States)
In this paper, we present a study of discrete time quantum walks whose underlying graph is a d-dimensional lattice. The dynamical behavior of these systems is of current interest because of their applications in quantum information theory as tools to design quantum algorithms. We assume that, at each step of the walk evolution, the coin transformation is allowed to change so that we can use it as a control variable to drive the evolution in a desired manner. We give an exact description of the possible evolutions and of the set of possible states that can be achieved with such a system. In particular, we show that it is possible to go from a state where there is probability 1 for the walker to be found in a vertex to a state where all the vertices have equal probability. We also prove a number of properties of the set of admissible states in terms of the number of steps needed to obtain them. We provide explicit algorithms for state transfer in low dimensional cases as well as results that allow to reduce algorithms on two-dimensional lattices to algorithms on the one-dimensional lattice, the cycle.
- OSTI ID:
- 21294516
- Journal Information:
- Journal of Mathematical Physics, Vol. 50, Issue 12; Other Information: DOI: 10.1063/1.3271109; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Alternate two-dimensional quantum walk with a single-qubit coin
Simulating a quantum walk with classical optics