Introduction to Grassmann Manifolds and Quantum Computation
arXiv:quant-ph/0103011
Abstract
Geometrical aspects of quantum computing are reviewed elementarily for non-experts and/or graduate students who are interested in both Geometry and Quantum Computation. In the first half 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 in the second half. An interesting current topic of Holonomic Quantum Computation is also covered. In the Appendix some related advanced topics are discussed.
Latex File, 28 pages, corrected considerably in the process of refereeing. to appear in Journal of Applied Mathematics
References in corpus (7)
- Elementary gates for quantum computation
- Self-Dual Chern-Simons Theories
- Non-Abelian Berry connections for quantum computation
- Quantum factoring, discrete logarithms and the hidden subgroup problem
- Coherent states over Grassmann manifolds and the WKB-exactness in path integral
- An Exponentially Fast Quantum Search Algorithm
- A Lecture on Quantum Logic Gates