Primitive Quantum Gates for Dihedral Gauge Theories
- URL: http://arxiv.org/abs/2108.13305v2
- Date: Thu, 30 Jun 2022 18:59:56 GMT
- Title: Primitive Quantum Gates for Dihedral Gauge Theories
- Authors: M. Sohaib Alam, Stuart Hadfield, Henry Lamm, Andy C. Y. Li
- Abstract summary: We describe the simulation of dihedral gauge theories on digital quantum computers.
The nonabelian discrete gauge group $D_N$ serves as an approximation to $U(1)timesbbZ$ lattice gauge theory.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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