  We investigate the response to noise, in the form of glassy disorder present
in circuit elements, in the success probability of the quantum phase estimation
algorithm, a subroutine used to determine the eigenvalue - a phase -
corresponding to an eigenvector of a unitary gate. We prove that when a large
number of auxiliary qubits are involved in the circuit, the probability does
not depend on the actual type of disorder but only on the mean and strength of
the disorder. For further analysis, we consider three types of disorder
distributions: Haar-uniform with a circular cut-off, Haar-uniform with an
elliptical or squeezed cut-off, and spherical normal. There is generally a
depreciation of the disorder-averaged success probability in response to the
disorder incorporation. Even in the presence of the disorder, increasing the
number of auxiliary qubits helps to get a better precision of the phase, albeit
to a lesser extent (probability) than that in the clean case. We find a concave
to convex transition in the dependence of probability on the strength of
disorder, and a log-log dependence is witnessed between the point of inflection
and the number of auxiliary qubits used.
