We investigate coherent quantum transport on multilayer complex networks composed of treelike scale-free layers. The general principles governing transport efficiency are uncovered under continuous-time quantum walks by tuning the degree distribution exponent $\gamma$, which interpolates between starlike and chainlike structures, and the interlink probability $q$. We show that global transport efficiency improves with increasing $\gamma$, increasing the number of layers, and increasing interlayer connectivity. The symmetry breaking and the decrease of spectral degeneracy of Laplacian maximally enhance transport efficiency when exactly one interlink between any pair of adjacent layers is removed. Notably, due to reduced structural symmetries nonidentical layers yield better transport than identical ones.

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• Degree distributions
• Network formation & growth
• Network searches
• Quantum coherence & coherence measures
• Spreading
• Transport in networks
• Multilayer & multiplex networks
• Quantum complex networks
• Scale free & inhomogeneous networks
• Tree network
• Evolving network models