  The Bernstein-Vazirani algorithm offers exceptional accuracy in finding a
hidden bit string of a function. We explore how the algorithm performs in
real-world situations where noise can potentially interfere with the
performance. In order to assess the impact of imperfect equipments, we
introduce various forms of glassy disorders into the effect of the Hadamard
gates used in Bernstein-Vazirani circuit. We incorporated disorders of five
different forms, viz. Haar-uniform with finite cutoff, spherical Gaussian,
discrete circular, spherical Cauchy-Lorentz, and squeezed. We find that the
effectiveness of the algorithm decreases with increasing disorder strength in
all cases. Additionally, we demonstrate that as the number of bits in the
secret string increases, the success probability of correctly guessing the
string becomes increasingly insensitive to the type of disorder and instead
depends only on the center and spread of the disorder. We compare our results
with the performance of the analogous classical algorithm in presence of
similar noise. The classical algorithm becomes extremely inefficient for long
secret strings, even in the noiseless scenario. Moreover, we witness that the
Bernstein-Vazirani algorithm performs better than its classical counterpart for
almost all types of disorder under consideration, for all disorder strengths.
An instance where that is not the case is for strong discrete disorder with a
moderate-sized hidden bit string.

Quantum Physics