  Fluctuations of quantum spins play a crucial role in the emergence of exotic
magnetic phases and excitations. The lack of the charge degree of freedom in
insulating quantum magnets, however, precludes such fluctuations from mediating
electronic transport. Here we show that the quantum fluctuations of a localized
frustrated magnet induce strong proximitized charge transport of the conduction
electrons in a synthetic heterostructure comprising an epitaxial
$\rm{Bi_{2}Ir_{2}O_{7}}$ ultrathin film on the single crystal of
$\rm{Yb_{2}Ti_{2}O_{7}}$. The proximity effects are evidenced by the scaling
behavior of the $\rm{Bi_{2}Ir_{2}O_{7}}$ resistance in correspondance with the
dynamic scaling of the dynamic spin correlation function of
$\rm{Yb_{2}Ti_{2}O_{7}}$, which is a result of quantum fluctuations near a
multi-phase quantum critical point. The proximitized transport in
$\rm{Bi_{2}Ir_{2}O_{7}}$ can be effectively tuned by magnetic field through
suppressing the quantum spin fluctuations as well as inducing transitions via
magnetic anisotropy in $\rm{Yb_{2}Ti_{2}O_{7}}$. Our work establishes a new
pathway for harnessing quantum spin fluctuations in magnetic insulators with
electric transport, offering exciting prospects for potential applications in
the realm of quantum spintronics.
