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We propose a quantum Monte Carlo (QMC) algorithm for non-equilibrium dynamicsin a system with a parameter varying as a function of time. The method is basedon successive applications of an evolving Hamiltonian to an initial state anddelivers results for a whole range of the tuning parameter in a single run,allowing for access to both static and dynamic properties of the system. Thisapproach reduces to the standard Schr\"odinger dynamics in imaginary time forquasi-adiabatic evolutions, i.e., including the leading non-adiabaticcorrection to the adiabatic limit. We here demonstrate this quasi-adiabatic QMC(QAQMC) method for linear ramps of the transverse-field Ising model across itsquantum-critical point in one and two dimensions. The critical behavior can bedescribed by generalized dynamic scaling. For the two-dimensionalsquare-lattice system we use the method to obtain a high-precision estimate ofthe quantum-critical point $(h/J)_c=3.04463(12)$, where $h$ is the transversemagnetic field and $J$ the nearest-neighbor Ising coupling. The QAQMC methodcan also be used to extract the Berry curvature and the metric tensor.

Quasi-adiabatic quantum Monte Carlo algorithm for quantum evolution in imaginary time