Journal of Applied Mathematics
Volume 2 (2002), Issue 8, Pages 371-405

Introduction to Grassmann manifolds and quantum computation

Kazuyuki Fujii

Department of Mathematical Sciences, Yokohama City University, Yokohama 236-0027, Japan

Received 18 October 2001; Revised 13 June 2002

Copyright © 2002 Kazuyuki Fujii. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Geometrical aspects of quantum computing are reviewed elementarily for nonexperts and/or graduate students who are interested in both geometry and quantum computation. We show how to treat Grassmann manifolds which are very important examples of manifolds in mathematics and physics. Some of their applications to quantum computation and its efficiency problems are shown. An interesting current topic of holonomic quantum computation is also covered. Also, some related advanced topics are discussed.