  Quantum algorithms have the ability to reduce runtime for executing tasks
beyond the capabilities of classical algorithms. Therefore, identifying the
resources responsible for quantum advantages is an interesting endeavour. We
prove that nonvanishing quantum correlations, both bipartite and genuine
multipartite entanglement, are required for solving nontrivial linear systems
of equations in the Harrow-Hassidim-Lloyd (HHL) algorithm. Moreover, we find a
nonvanishing l1-norm quantum coherence of the entire system and the register
qubit which turns out to be related to the success probability of the
algorithm. Quantitative analysis of the quantum resources reveals that while a
significant amount of bipartite entanglement is generated in each step and
required for this algorithm, multipartite entanglement content is inversely
proportional to the performance indicator. In addition, we report that when
imperfections chosen from Gaussian distribution are incorporated in controlled
rotations, multipartite entanglement increases with the strength of the
disorder, albeit error also increases while bipartite entanglement and
coherence decreases, confirming the beneficial role of bipartite entanglement
and coherence in this algorithm.
