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== Method ==
[[File:Master equation unravelings.svg|thumb|An example of the quantum jump method being used to approximate the density matrix of a two-level atom undergoing damped [[Rabi oscillation|Rabi oscillations]]. The random jumps can clearly be seen in the top subplot, and the bottom subplot compares the fully simulated density matrix to the approximation obtained using the quantum jump method.]]
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. 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 doi|10.1364/JOSAB.10.000524}}</ref>▼
▲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 wave function 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 doi|10.1364/JOSAB.10.000524}}</ref>
<!-- Sections to be written: Algorithm; Equivalence to master equation treatment (maybe); Applications -->
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