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Quantum computing based on complex Clifford algebras

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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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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic

    Jaroslav Hrdina, Aleš Návrat & Petr Vašík

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  1. Jaroslav Hrdina
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  2. Aleš Návrat
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  3. Petr Vašík
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Correspondence to Aleš Návrat.

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The authors was supported by the Grant No. FSI-S-20-6187.

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Hrdina, J., Návrat, A. & Vašík, P. Quantum computing based on complex Clifford algebras. Quantum Inf Process 21, 310 (2022). https://doi.org/10.1007/s11128-022-03648-w

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