  The three key elements of a quantum simulation are state preparation, time
evolution, and measurement. While the complexity scaling of dynamics and
measurements are well known, many state preparation methods are strongly
system-dependent and require prior knowledge of the system's eigenvalue
spectrum. Here, we report on a quantum-classical implementation of the
coupled-cluster Green's function (CCGF) method, which replaces explicit ground
state preparation with the task of applying unitary operators to a simple
product state. While our approach is broadly applicable to a wide range of
models, we demonstrate it here for the Anderson impurity model (AIM). The
method requires a number of T gates that grows as $ \mathcal{O} \left(N^5
\right)$ per time step to calculate the impurity Green's function in the time
domain, where $N$ is the total number of energy levels in the AIM. For
comparison, a classical CCGF calculation of the same order would require
computational resources that grow as $ \mathcal{O} \left(N^6 \right)$ per time
step.
