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Clifford algebras, noncommutative tori and universal quantum computers

Alexander Yu. Vlasov
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Abstract

Recently author suggested [quant-ph/0010071] an application of Clifford algebras for construction of a "compiler" for universal binary quantum computer together with later development [quant-ph/0012009] of the similar idea for a non-binary base. The non-binary case is related with application of some extension of idea of Clifford algebras. It is noncommutative torus defined by polynomial algebraic relations of order l. For l=2 it coincides with definition of Clifford algebra. Here is presented the joint consideration and comparison of both cases together with some discussion on possible physical consequences.

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Alexander Yu. Vlasov. 2001-09-03. Clifford algebras, noncommutative tori and universal quantum computers. https://arxiv.org/abs/quant-ph/0109010

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