The Aharonov-Bohm eﬀect results from the phase shift acquired by an electronic excitation in a ring threaded by a magnetic ﬁeld, and is in essence a property of charged particles. However, the eﬀect also occurs for neutral excitons in semiconductor quantum rings if they exhibit a radial polarization. In our case, the polarization of quantum ring excitons can be tuned to the desired degree by a controlled p-type doping of the nanowire core. Moreover, we fabricate rings with nearly ideal interfaces by combining all-binary radial compositional heterostructures with crystal-phase quantum wells along the axis of the nanowires. The exceptionally large coherence length of 200 nm demonstrates that GaAs/AlAs core-shell nanowires are an ideal platform for the study of phase-coherence effects of excitons. Besides the high structural perfection required for preserving spatial phase coherence, these nanostructures also offer a high degree of control over the quantum ring dimensions and the exciton polarization, and thus pave the way toward wavefunction engineering in three dimensions for the experimental study of coherent excitations in semiconductors.