Benchmarking of two-qubit gates for singlet-triplet qubits*

We perform benchmarking to evaluate the performance of two-qubit dynamically corrected gates (DCGs) in the singlet-triplet spin qubit system. We execute two types of circuits, i.e. the Deutsch-Jozsa algorithm and Grover algorithm, each of which is carried out with DCGs and gates not immune to noise. The benchmarking process is performed by repeating 100 times of the respective circuit under 1/f noises with different noise exponents ($\alpha$). The average error per execution of one algorithm is compared between DCGs and non-noise-correcting ones, and whether DCGs offer improvement depends on the noise exponent, $\alpha$. We have found that when $\alpha<0.8$ the DCGs would not offer improvements, but DCGs can outperform the non-correcting ones otherwise. The fact that DCGs can offer improvement for a wide range of $\alpha$, on one hand, suggests using DCGs on two-qubit gates can reduce the error, but on the other hand also indicates that quantum algorithms involving two-qubit gates suffer more heavily from noises than those only involving single-qubit gates if no correction to noise is performed.