International Journal of Theoretical Physics

, Volume 48, Issue 2, pp 507–515 | Cite as

Quantum Gates and Quantum Algorithms with Clifford Algebra Technique

  • M. Gregorič
  • N. S. Mankoč Borštnik


We use the Clifford algebra technique (J. Math. Phys. 43:5782, 2002; J. Math. Phys. 44:4817, 2003), that is nilpotents and projectors which are binomials of the Clifford algebra objects γ a with the property {γ a ,γ b }+=2η ab , for representing quantum gates and quantum algorithms needed in quantum computers in a simple and an elegant way. We identify n-qubits with the 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; we pay attention also on the nonrelativistic limit. 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 (Proc. 28th Annual ACM Symp. Theory Comput. 212, 1996).


Clifford algebra Quantum gates Quantum algorithms Group SO(1,3) 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of LjubljanaLjubljanaSlovenia

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