Constraints on the time-scales of quasar activity are key to understanding the formation and growth of supermassive black holes (SMBHs), quasar triggering mechanisms, and possible feedback effects on their host galaxies. However, observational estimates of this so-called quasar lifetime are highly uncertain (t_Q~10^4-10^9 yr), because most methods are indirect and involve many model-dependent assumptions. Direct evidence of earlier activity is gained from the higher ionization state of the intergalactic medium (IGM) in the quasar environs, observable as enhanced Ly$alpha$ transmission in the so-called proximity zone. Due to the ~30 Myr equilibration time-scale of HeII in the z~3 IGM, the size of the HeII proximity zone depends on the time the quasar had been active before our observation t_on<t_Q, enabling up to $pm$0.2 dex precise measurements of individual quasar on-times that are comparable to the e-folding time-scale t_S~44 Myr of SMBH growth. Here we present the first statistical sample of 13 quasars whose accurate and precise systemic redshifts allow for measurements of sufficiently precise HeII quasar proximity zone sizes between ~2 and ~15 proper Mpc from science-grade Hubble Space Telescope (HST) spectra. Comparing these sizes to predictions from cosmological hydrodynamical simulations post-processed with one-dimensional radiative transfer, we infer a broad range of quasar on-times from t_on<1 Myr to t_on>30 Myr that does not depend on quasar luminosity, black hole mass, or Eddington ratio. These results point to episodic quasar activity over a long duty cycle, but do not rule out substantial SMBH growth during phases of radiative inefficiency or obscuration.
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