The antiferromagnetic Ising model on the pyrochlore lattice exhibits a quantum phase transition in an applied transverse field from the low-field quantum spin-ice phase to the high-field polarized regime. Recent field-theoretical analysis and series expansion results indicate this to be a discontinuous, first-order transition. Here, we explore this transition using quantum Monte Carlo simulations in order to assess this scenario and study the thermodynamic properties in the vicinity of the quantum phase transition. For this purpose, we also consider several variants of extended cluster-update schemes for the transverse-field Ising antiferromagnet on frustrated lattices and compare their performance to the conventional bond-based algorithm for the transverse-field Ising model on the pyrochlore lattice.