  We analyze the robustness of Grover's quantum search algorithm performed by a
quantum register under a possibly time-correlated noise acting locally on the
qubits. We model the noise as originating from an arbitrary but fixed unitary
evolution, $U$, of some noisy qubits. The noise can occur with some probability
in the interval between any pair of consecutive noiseless Grover evolutions.
Although each run of the algorithm is a unitary process, the noise model leads
to decoherence when all possible runs are considered. We derive a set of
unitary $U$'s, called the 'good noises,' for which the success probability of
the algorithm at any given time remains unchanged with varying the non-trivial
total number ($m$) of noisy qubits in the register. The result holds
irrespective of the presence of any time-correlations in the noise. We show
that only when $U$ is either of the Pauli matrices $\sigma_x$ and $\sigma_z$
(which give rise to $m$-qubit bit-flip and phase-damping channels respectively
in the time-correlation-less case), the algorithm's success probability stays
unchanged when increasing or decreasing $m$. In contrast, when $U$ is the Pauli
matrix $\sigma_y$ (giving rise to $m$-qubit bit-phase flip channel in the
time-correlation-less case), the success probability at all times stays
unaltered as long as the parity (even or odd) of the total number $m$ remains
the same. This asymmetry between the Pauli operators stems from the inherent
symmetry-breaking existing within the Grover circuit. We further show that the
positions of the noisy sites are irrelevant in case of any of the Pauli noises.
The results are illustrated in the cases of time-correlated and
time-correlation-less noise. We find that the former case leads to a better
performance of the noisy algorithm. We also discuss physical scenarios where
our chosen noise model is of relevance.
