Quasi-Clifford to qubit mappings
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912516653711360 |
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| author | Huber, Felix |
| author_facet | Huber, Felix |
| contents | Algebras with given (anti-)commutativity structure are widespread in quantum mechanics. This structure is captured by quasi-Clifford algebras (QCA): a QCA generated by $α_1, \dots, α_n$ is is given by the relations $α_i^2 = k_i$ and $α_j α_i = (-1)^{χ_{ij}} α_i α_j$, where $k_i \in \mathbb{C}$ and $χ_{ij} \in \{0, 1\}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-Clifford to qubit mappings Huber, Felix Quantum Physics Mathematical Physics Algebras with given (anti-)commutativity structure are widespread in quantum mechanics. This structure is captured by quasi-Clifford algebras (QCA): a QCA generated by $α_1, \dots, α_n$ is is given by the relations $α_i^2 = k_i$ and $α_j α_i = (-1)^{χ_{ij}} α_i α_j$, where $k_i \in \mathbb{C}$ and $χ_{ij} \in \{0, 1\}$. 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. |
| title | Quasi-Clifford to qubit mappings |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2508.01470 |