  Although near-term quantum computing devices are still limited by the
quantity and quality of qubits in the so-called NISQ era, quantum computational
advantage has been experimentally demonstrated. Moreover, hybrid architectures
of quantum and classical computing have become the main paradigm for exhibiting
NISQ applications, where low-depth quantum circuits are repeatedly applied. In
order to further scale up the problem size solvable by the NISQ devices, it is
also possible to reduce the number of physical qubits by "cutting" the quantum
circuit into different pieces. In this work, we experimentally demonstrated a
circuit-cutting method for simulating quantum circuits involving many logical
qubits, using only a few physical superconducting qubits. By exploiting the
symmetry of linear-cluster states, we can estimate the effectiveness of
circuit-cutting for simulating up to 33-qubit linear-cluster states, using at
most 4 physical qubits for each subcircuit. Specifically, for the 12-qubit
linear-cluster state, we found that the experimental fidelity bound can reach
as much as 0.734, which is about 19\% higher than a direct simulation {on the
same} 12-qubit superconducting processor. Our results indicate that
circuit-cutting represents a feasible approach of simulating quantum circuits
using much fewer qubits, while achieving a much higher circuit fidelity.
