  The variational quantum imaginary time evolution algorithm is efficient in
finding the ground state of a quantum Hamiltonian. This algorithm involves
solving a system of linear equations in a classical computer and the solution
is then used to propagate a quantum wavefunction. Here, we show that owing to
the noisy nature of current quantum processors, such a quantum algorithm or the
family of quantum algorithms will require single- and two-qubit gates with very
low error probability to produce reliable results. Failure to meet such
condition will result in erroneous quantum data propagation even for a
relatively small quantum circuit ansatz. Specifically, we provide the upper
bounds on how the relative error in variational parameters' propagation scales
with the probability of noise in quantum hardware. We also present an exact
expression of how the relative error in variational parameter propagation
scales with the probability of partially depolarizing noise.
