Quantum gates and quantum algorithms with Clifford algebra technique

Details Quantum gates and quantum algorithms with Clifford algebra technique Quantum gates and quantum algorithms with Clifford algebra technique

2008-01-21

arxiv.org/abs/0801.3201v1

Physics

Quantum Physics

9 pages, revtex

Scientific paper

10.1007/s10773-008-9826-7

We use our Clifford algebra technique, that is nilpotents and projectors which are binomials of the Clifford algebra objects $\gamma^a$ with the property $\{\gamma^a,\gamma^b\}_+ = 2 \eta^{ab}$, for representing quantum gates and quantum algorithms needed in quantum computers in an elegant way. We identify $n$-qubits with spinor representations of the group SO(1,3) for a system of $n$ spinors. Representations are expressed in terms of products of projectors and nilpotents. An algorithm for extracting a particular information out of a general superposition of $2^n$ qubit states is presented. It reproduces for a particular choice of the initial state the Grover's algorithm.

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