  Along their long propagation from production to detection, neutrino states
undergo quantum interference which converts their types, or flavours.
High-energy astrophysical neutrinos, first observed by the IceCube Neutrino
Observatory, are known to propagate unperturbed over a billion light years in
vacuum. These neutrinos act as the largest quantum interferometer and are
sensitive to the smallest effects in vacuum due to new physics. Quantum gravity
(QG) aims to describe gravity in a quantum mechanical framework, unifying
matter, forces and space-time. QG effects are expected to appear at the
ultra-high-energy scale known as the Planck energy, $E_{P}\equiv 1.22\times
10^{19}$~giga-electronvolts (GeV). Such a high-energy universe would have
existed only right after the Big Bang and it is inaccessible by human
technologies. On the other hand, it is speculated that the effects of QG may
exist in our low-energy vacuum, but are suppressed by the Planck energy as
$E_{P}^{-1}$ ($\sim 10^{-19}$~GeV$^{-1}$), $E_{P}^{-2}$ ($\sim
10^{-38}$~GeV$^{-2}$), or its higher powers. The coupling of particles to these
effects is too small to measure in kinematic observables, but the phase shift
of neutrino waves could cause observable flavour conversions. Here, we report
the first result of neutrino interferometry~\cite{Aartsen:2017ibm} using
astrophysical neutrino flavours to search for new space-time structure. We did
not find any evidence of anomalous flavour conversion in IceCube astrophysical
neutrino flavour data. We place the most stringent limits of any known
technologies, down to $10^{-42}$~GeV$^{-2}$, on the dimension-six operators
that parameterize the space-time defects for preferred astrophysical production
scenarios. For the first time, we unambiguously reach the signal region of
quantum-gravity-motivated physics.
