Primitive Quantum Gates for an \(SU(2)\) Discrete Subgroup: Binary Octahedral

We construct a primitive gate set for the digital quantum simulation of the 48-element binary octahedral (\(\mathbb{BO}\)) group. This nonabelian discrete group better approximates \(SU(2)\) lattice gauge theory than previous work on the binary tetrahedral group at the cost of one additional qubit -...

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Bibliographic Details
Published in:arXiv.org 2023-12
Main Authors: Gustafson, Erik J, Lamm, Henry, Lovelace, Felicity
Format: Article
Language:English
Subjects:
Fourier transforms
Gauge theory
Qubits (quantum computing)
Subgroups
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Summary:We construct a primitive gate set for the digital quantum simulation of the 48-element binary octahedral (\(\mathbb{BO}\)) group. This nonabelian discrete group better approximates \(SU(2)\) lattice gauge theory than previous work on the binary tetrahedral group at the cost of one additional qubit -- for a total of six -- per gauge link. The necessary primitives are the inversion gate, the group multiplication gate, the trace gate, and the \(\mathbb{BO}\) Fourier transform.
ISSN:2331-8422