  A cluster algorithm formulated in continuous (imaginary) time is presented
for Ising models in a transverse field. It works directly with an infinite
number of time-slices in the imaginary time direction, avoiding the necessity
to take this limit explicitly. The algorithm is tested at the zero-temperature
critical point of the pure two-dimensional (2d) transverse Ising model. Then it
is applied to the 2d Ising ferromagnet with random bonds and transverse fields,
for which the phase diagram is determined. Finite size scaling at the quantum
critical point as well as the study of the quantum Griffiths-McCoy phase
indicate that the dynamical critical exponent is infinite as in 1d.
