Quantum computing based on complex Clifford algebras
- URL: http://arxiv.org/abs/2201.02246v2
- Date: Thu, 3 Mar 2022 18:43:00 GMT
- Title: Quantum computing based on complex Clifford algebras
- Authors: Jaroslav Hrdina, Ales Navrat, Petr Vasik
- Abstract summary: We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of $2n.$
We demonstrate its functionality by performing quantum computations with several well known examples of quantum gates.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose to represent both $n$--qubits and quantum gates acting on them as
elements in the complex Clifford algebra defined on a complex vector space of
dimension $2n.$ In this framework, the Dirac formalism can be realized in
straightforward way. We demonstrate its functionality by performing quantum
computations with several well known examples of quantum gates. We also compare
our approach with representations that use real geometric algebras.
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