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We take a different approach by utilizing quantum computing based on complex Clifford algebra with split signatures, rather than the classical Euclidean signature \(\mathbb {C} \mathbb {G}(2n)\) . This results in a different representation of gates. We demonstrate how Dirac calculus is applied in this context and provide examples to illustrate the process. Additionally, we highlight the advantages of using split signatures for implementation through Bott periodicity. We show that the use of split signature enables an efficient matrix representation.

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Notes on Quantum Computing over Complex Geometric Algebras with Split Signature

  • 会议论文

  • 发表日期：

    2026年

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  • Jaroslav Hrdina

摘要

We take a different approach by utilizing quantum computing based on complex Clifford algebra with split signatures, rather than the classical Euclidean signature \(\mathbb {C} \mathbb {G}(2n)\) . This results in a different representation of gates. We demonstrate how Dirac calculus is applied in this context and provide examples to illustrate the process. Additionally, we highlight the advantages of using split signatures for implementation through Bott periodicity. We show that the use of split signature enables an efficient matrix representation.