We use continuous weak measurements in conjunction with Bayesian statistics to reconstruct the real-time evolution of the wavefunction describing a two-state system at the level of individual quantum trajectories. Both the case of measurement induced collapse as well as driven unitary evolution are investigated in a cavity coupled superconducting transmon qubit. A variety of statistical metrics are extracted, including the most probable path—analogous to the geodesic in space-time—between two points in Hilbert space. Quantitative agreement with a path integral formalism for the trajectories and their distribution is achieved, opening the door for new quantum control protocols. Furthermore, extensions to many-body quantum systems may promise a route toward more efficient quantum verification and validation of systems with exponentially increasing complexity.