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Continuous-time quantum Monte Carlo refers to a class of algorithms designedto sample the thermal distribution of a quantum Hamiltonian through exactexpansions of the Boltzmann exponential in terms of stochastic trajectorieswhich are periodic in imaginary time. Here, we show that for(sign-problem-free) quantum many-body systems with discrete degrees of freedom-- such as spins on a lattice -- this sampling can be done in a rejection-freemanner using transition path sampling (TPS). The key idea is to converge thetrajectory ensemble through updates where one individual degree of freedom ismodified across all time while the remaining unaltered ones provide atime-dependent background. The ensuing single-body dynamics provides a way togenerate trajectory updates exactly, allowing one to obtain the target ensembleefficiently via rejection-free TPS. We demonstrate our method on the transversefield Ising model in one and two dimensions, and on the quantum triangularplaquette (or Newman-Moore) model. We show that despite large autocorrelationtimes, our method is able to efficiently recover the respective quantum phasetransition of each model. We also discuss the connection to rare event samplingin continuous-time Markov dynamics.

Rejection-free quantum Monte Carlo in continuous time from transition path sampling