  Fault-tolerant quantum computation (FTQC) is essential to implement quantum
algorithms in a noise-resilient way, and thus to enjoy advantages of quantum
computers even with presence of noise. In FTQC, a quantum circuit is decomposed
into universal gates that can be fault-tolerantly implemented, for example,
Clifford+$T$ gates. Here, $T$ gate is usually regarded as an essential resource
for quantum computation because its action cannot be simulated efficiently on
classical computers and it is experimentally difficult to implement
fault-tolerantly. Practically, it is highly likely that only a limited number
of $T$ gates are available in the near future. Pre-FTQC era, due to the
constraint on available resources, it is vital to precisely estimate the
decomposition error of a whole circuit. In this paper, we propose that the
Clifford+$T$ decomposition error for a given quantum circuit containing a large
number of quantum gates can be modeled as the depolarizing noise by averaging
the decomposition error for each quantum gate in the circuit, and our model
provides more accurate error estimation than the naive estimation. We exemplify
this by taking unitary coupled-cluster (UCC) ansatz used in the applications of
quantum computers to quantum chemistry as an example. We theoretically evaluate
the approximation error of UCC ansatz when decomposed into Clifford+$T$ gates,
and the numerical simulation for a wide variety of molecules verified that our
model well explains the total decomposition error of the ansatz. Our results
enable the precise and efficient usage of quantum resources in the early-stage
applications of quantum computers and fuel further research towards what
quantum computation can achieve in the upcoming future.
