  Gravitational collapse into a black hole has been extensively studied with
classical sources. We develop a new formalism to simulate quantum fields
forming a black hole. By choosing a convenient coherent state, this formalism
taps into well-established techniques used for classical collapse and adds on
the evolution of the mode functions of the quantum field operator. Divergences
are regularized with the cosmological constant and Pauli-Villars fields. Using
a massless spherically symmetric scalar field as an example, we demonstrate the
effectiveness of the formalism by reproducing some classical results in
gravitational collapse, and identifying the difference due to the quantum
effects. We also find that Choptuik scaling in critical collapse survives in
the semiclassical simulation, and furthermore the quantum deviation from the
classical Choptuik scaling decreases when the system approaches the critical
point.
