Abstract
We exactly construct one- and two-qubit holonomic quantum gates in terms of isospectral deformations of an Ising model Hamiltonian. A single logical qubit is constructed out of two spin-$\frac{1}{2}$ particles; the qubit is a dimer. We find that the holonomic gates obtained are discrete but dense in the unitary group. Therefore an approximate gate for a desired one can be constructed with arbitrary accuracy.
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