Universal quantum computation using the discrete-time quantum walk
Abstract
A proof that continuous-time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by A. M. Childs [Phys. Rev. Lett. 102, 180501 (2009)]. We present a version based instead on the discrete-time quantum walk. We show that the discrete-time quantum walk is able to implement the same universal gate set and thus both discrete and continuous-time quantum walks are computational primitives. Additionally, we give a set of components on which the discrete-time quantum walk provides perfect state transfer.
- Publication:
-
Physical Review A
- Pub Date:
- April 2010
- DOI:
- 10.1103/PhysRevA.81.042330
- arXiv:
- arXiv:0910.1024
- Bibcode:
- 2010PhRvA..81d2330L
- Keywords:
-
- 03.67.Ac;
- 05.40.Fb;
- Quantum algorithms protocols and simulations;
- Random walks and Levy flights;
- Quantum Physics
- E-Print:
- 9 pages, 10 figures. Updated after referee comments - Section V expanded and minor changes to other parts of the text