The quantum calculus provides an extra degree of freedom to search the local and global minima by inducing a q-parameter. Motivated by this fact, a quantum calculus-based noisy links incremental least mean squares (NL-qILMS) algorithm is proposed. Moreover, for the proposed NL-qILMS, we also devised various time-varying techniques for the selection of the optimal q-parameter to improve the performance. Furthermore, the closed-form solutions for the steady-state mean square deviation, excess mean square deviation and mean square error are derived. The analytical results are validated through simulation. Finally, extensive simulations have been done to evaluate the performance of the proposed algorithm for various choices of optimal q-values. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.