Quasi-Clifford to qubit mappings

• URL: http://arxiv.org/abs/2508.01470v1
• Date: Sat, 02 Aug 2025 19:40:44 GMT
• Title: Quasi-Clifford to qubit mappings
• Authors: Felix Huber,
• Abstract summary: Algebras with given (anti-)commutativity structure are widespread in quantum mechanics.<n>We present a mapping from QCA to Pauli algebras and discuss its use in quantum information and computation.
• Score: 3.626013617212667
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Algebras with given (anti-)commutativity structure are widespread in quantum mechanics. This structure is captured by quasi-Clifford algebras (QCA): a QCA generated by $\alpha_1, \dots, \alpha_n$ is is given by the relations $\alpha_i^2 = k_i$ and $\alpha_j \alpha_i = (-1)^{\chi_{ij}} \alpha_i \alpha_j$, where $k_i \in \mathbb{C}$ and $\chi_{ij} \in \{0, 1\}$. We present a mapping from QCA to Pauli algebras and discuss its use in quantum information and computation. The mapping also provides a Wedderburn decomposition of matrix groups with quasi-Clifford structure. This provides a block-diagonalization for e.g. Pauli groups, while for Majorana operators the Jordan-Wigner transform is recovered. Applications to the symmetry reduction of semidefinite programs and for constructing maximal anti-commuting subsets are discussed.

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