Minimal and Robust Composite Two-Qubit Gates with Ising-Type Interaction

We construct a minimal robust controlled-NOT gate with an Ising-type interaction by which elementary two-qubit gates are implemented. It is robust against inaccuracy of the coupling strength and the obtained quantum circuits are constructed with the minimal number (N=3) of elementary two-qubit gates and several one-qubit gates. It is noteworthy that all the robust circuits can be mapped to one-qubit circuits robust against a pulse length error. We also prove that a minimal robust SWAP gate cannot be constructed with N=3, but requires N=6 elementary two-qubit gates.