Holonomic quantum gates in an isospectral deformation of Ising model

　We construct one- and two- qubit holonomic quantum gates in anisospectral deformation of Ising-type dimer-chain model.
　The singlequbit is represented by two particles with spin $\frac{1}{2}$; the logicalqubit is made of a dimer. We adopt the interaction between thoseparticles as the Ising-type interaction, taking a liquid-state NMRquantum computer into consideration. As for the one-qubit gates,we construct the Hadamard gate and gates producing rotationsaround $x$-axis and $y$-axis. In addition, we construct the controlled-Zgate. Explicitly imposing the condition for the closure of a loop in theparameter space, the set of the attainable rotation angles in a quantumgate is discrete. However, we show such a set is dense and anapproximate gate for the desired one can be found with arbitraryaccuracy.