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.

Figure 1

Schematic of the quantum circuit, (2), for $N=3$. $R({\theta }_i,{\varphi }_i)$ and $S\left({\Theta }_i\right)$ are defined by Eq. (1).

Figure 2

Schematic of the minimal robust circuit ($N=3$; $\alpha =-1$, $\beta =-\gamma$).