  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.
