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DOE OSTI · 1831839

Primitive quantum gates for dihedral gauge theories

Alam, M. Sohaib·Hadfield, Stuart·Lamm, Henry·Li, Andy C.Y.
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Abstract

We describe the simulation of dihedral gauge theories on digital quantum computers. The nonabelian discrete gauge group $D_N$-- the dihedral group -- serves as an approximation to $U(1)\times\mathbb{Z}_2$ lattice gauge theory. In order to carry out such a lattice simulation, we detail the construction of efficient quantum circuits to realize basic primitives including the nonabelian Fourier transform over $D_N$, the trace operation, and the group multiplication and inversion operations. For each case the required quantum resources scale linearly or as low-degree polynomials in $n=\log N$. We experimentally benchmark our gates on the Rigetti Aspen-9 quantum processor for the case of $D_4$. The fidelity of all $D_4$ gates was found to exceed $80\%$.

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Alam, M. Sohaib, Hadfield, Stuart, Lamm, Henry, Li, Andy C.Y.. 2022-06-02. Primitive quantum gates for dihedral gauge theories. https://doi.org/10.1103/physrevd.105.114501

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