  In recent years, due to its formidable potential in computational theory,
quantum computing has become a very popular research topic. However, the
implementation of practical quantum algorithms, which hold the potential to
solve real-world problems, is often hindered by the significant error rates
associated with quantum gates and the limited availability of qubits. In this
study, we propose a practical approach to simulate the dynamics of an open
quantum system on a noisy computer, which encompasses general and valuable
characteristics. Notably, our method leverages gate noises on the IBM-Q real
device, enabling us to perform calculations using only two qubits. The results
generated by our method performed on IBM-Q Jakarta aligned with the those
calculated by hierarchical equations of motion (HEOM), which is a classical
numerically-exact method, while our simulation method runs with a much better
computing complexity. In the last, to deal with the increasing depth of quantum
circuits when doing Trotter expansion, we introduced the transfer tensor
method(TTM) to extend our short-term dynamics simulation. Based on quantum
simulator, we show the extending ability of TTM, which allows us to get a
longer simulation using a relatively short quantum circuits.
