Experimental realization of direct entangling gates between dual-type qubits

Abstract: Dual-type qubits have become a promising way to suppress the crosstalk error of auxiliary operations in large-scale ion trap quantum computation. Here we demonstrate a direct entangling gate between dual-type qubits encoded in the $S_{1/2}$ and $D_{5/2}$ hyperfine manifolds of $^{137}\mathrm{Ba}^{+}$ ions. Our scheme is economic in the hardware, requiring only a single $532\,$nm laser system to entangle both qubit types by driving their Raman transitions. We achieve a Bell state fidelity of $96.3(4)\%$ for the dual-type Molmer-Sorensen gate between an $S$-$D$ ion pair, comparable to that for the same-type $S$-$S$ or $D$-$D$ gates. This technique can reduce the overhead for back-and-forth conversions between dual-type qubits in the quantum circuit with wide applications in quantum error correction and ion-photon quantum networks.