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Proceedings Paper

Algebra of quantum computations with higher dimensional systems
Author(s): Alexander Yu. Vlasov
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Paper Abstract

Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It is shown next, how for quantum computation with qubits can be used two-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford algebras, and discussed well known applications to product operator formalism in NMR, Jordan-Wigner construction in fermionic quantum computations. It is introduced universal set of quantum gates for higher dimensional system ("qudit"), as some generalization of these models. Finally it is briefly mentioned possible application of such algebraic methods to design of quantum processors (programmable gates arrays) and dsicussed generalization to quantum computation wiht continuous variables.

Paper Details

Date Published: 23 July 2003
PDF: 8 pages
Proc. SPIE 5128, First International Symposium on Quantum Informatics, (23 July 2003); doi: 10.1117/12.517863
Show Author Affiliations
Alexander Yu. Vlasov, Federal Radiological Ctr. (Russia)

Published in SPIE Proceedings Vol. 5128:
First International Symposium on Quantum Informatics
Yuri I. Ozhigov, Editor(s)

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