Quantum annealing (QA) provides us with a way to solve combinatorial
optimization problems. In the previous demonstration of the QA, a
superconducting flux qubit (FQ) was used. However, the flux qubits in these
demonstrations have a short coherence time such as tens of nano seconds. For
the purpose to utilize quantum properties, it is necessary to use another qubit
with a better coherence time. Here, we propose to use a capacitive-shunted flux
qubit (CSFQ) for the implementation of the QA. The CSFQ has a few order of
magnitude better coherence time than the FQ used in the QA. We theoretically
show that, although it is difficult to perform the conventional QA with the
CSFQ due to the form and strength of the interaction between the CSFQs, a
spin-lock based QA can be implemented with the CSFQ even with the current
technology. Our results pave the way for the realization of the practical QA
that exploits quantum advantage with long-lived qubits.