  We report on a universal method to measure the genuine indistinguishability
of n-photons - a crucial parameter that determines the accuracy of optical
quantum computing. Our approach relies on a low-depth cyclic multiport
interferometer with N = 2n modes, leading to a quantum interference fringe
whose visibility is a direct measurement of the genuine n-photon
indistinguishability. We experimentally demonstrate this technique for a 8-mode
integrated interferometer fabricated using femtosecond laser micromachining and
four photons from a quantum dot single-photon source. We measure a four-photon
indistinguishability up to 0.81$\pm$0.03. This value decreases as we
intentionally alter the photon pairwise indistinguishability. The low-depth and
low-loss multiport interferometer design provides an efficient and scalable
path to evaluate the genuine indistinguishability of resource states of
increasing photon number.
