[[File:MC-ensemble average.gif|thumb|Animation of the Monte Carlo prediction (blue) for the population of a coherently-driven, damped two-level system as more trajectories are added to the ensemble average, compared to the master equation prediction (red).]]
The quantum jump method is an approach which is much like the [[Lindblad equation|master-equation treatment]] except that it operates on the wave function rather than using a [[density matrix]] approach. The main component of the method is evolving the system's wave function in time with a pseudo-Hamiltonian; where at each [[time step]], a quantum jump (discontinuous change) may take place with some probability. The calculated system state as a function of time is known as a [[Quantum stochastic calculus#Quantum trajectories|quantum trajectory]], and the desired [[density matrix]] as a function of time may be calculated by averaging over many simulated trajectories. For a Hilbert space of dimension N, the number of wave function components is equal to N while the number of density matrix components is equal to N<sup>2</sup>. Consequently, for certain problems the quantum jump method offers a performance advantage over direct master-equation approaches.<ref name=MCD1993>{{Cite journal | last1 = Mølmer | first1 = K. | last2 = Castin | first2 = Y. | last3 = Dalibard | first3 = J. | doi = 10.1364/JOSAB.10.000524 | title = Monte Carlo wave-function method in quantum optics | journal = Journal of the Optical Society of America B | volume = 10 | issue = 3 | pages = 524 | year = 1993 |bibcode = 1993JOSAB..10..524M }}</ref>
<!-- Sections to be written: Algorithm; Equivalence to master equation treatment (maybe); Applications -->
