  Simulation of quantum computing on supercomputers is a significant research
topic, which plays a vital role in quantum algorithm verification,
error-tolerant verification and other applications. Tensor network contraction
based on density matrix is an important single-amplitude simulation strategy,
but it is hard to execute on the distributed computing systems currently. In
this paper, we dive deep into this problem, and propose a scheme based on
cutting edges of undirected graphs. This scheme cuts edges of undirected graphs
with large tree width to obtain many undirected subgraphs with small tree
width, and these subgraphs contracted on different computing cores. The
contraction results of slave cores are summarized in the master node, which is
consistent with the original tensor network contraction. Thus, we can simulate
the larger scale quantum circuit than single core. Moreover, it's an NP-hard
problem to find the global optimum cutting edges, and we propose a search
strategy based on a heuristic algorithm to approach it. In order to verify the
effectiveness of our scheme, we conduct tests based on QAOA algorithm, and it
can simulate 120-qubit 3-regular QAOA algorithm on 4096-core supercomputer,
which greatly exceeds the simulation scale on a single core of 100-qubit.
