  We describe a quantum trajectories technique for the unraveling of the
quantum adiabatic master equation in Lindblad form. By evolving a complex state
vector of dimension $N$ instead of a complex density matrix of dimension $N^2$,
simulations of larger system sizes become feasible. The cost of running many
trajectories, which is required to recover the master equation evolution, can
be minimized by running the trajectories in parallel, making this method
suitable for high performance computing clusters. In general, the trajectories
method can provide up to a factor $N$ advantage over directly solving the
master equation. In special cases where only the expectation values of certain
observables are desired, an advantage of up to a factor $N^2$ is possible. We
test the method by demonstrating agreement with direct solution of the quantum
adiabatic master equation for $8$-qubit quantum annealing examples. We also
apply the quantum trajectories method to a $16$-qubit example originally
introduced to demonstrate the role of tunneling in quantum annealing, which is
significantly more time consuming to solve directly using the master equation.
The quantum trajectories method provides insight into individual quantum jump
trajectories and their statistics, thus shedding light on open system quantum
adiabatic evolution beyond the master equation.
