We present a new class of high-order imaginary time propagators forpath-integral Monte Carlo simulations by subtracting lower order propagators.By requiring all terms of the extrapolated propagator be sampled uniformly, thesubtraction only affects the potential part of the path integral. Thenegligible violation of positivity of the resulting path integral at small timesteps has no discernable affect on the accuracy of our method. Thus inprinciple arbitrarily high order algorithms can be devised for path-integralMonte Carlo simulations. We verify this claim is by showing that fourth, sixth,and eighth order convergence can indeed be achieved in solving for the groundstate of strongly interacting quantum many-body systems such as bulk liquid$^4$He.
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