Improving dynamical lattice QCD simulations through integrator tuning   using Poisson brackets and a force-gradient integrator
  We show how the integrators used for the molecular dynamics step of the Hybrid Monte Carlo algorithm can be further improved. These integrators not only approximately conserve some Hamiltonian $H$ but conserve exactly a nearby shadow Hamiltonian $\tilde{H}$. This property allows for a new tuning method of the molecular dynamics integrator and also allows for a new class of integrators (force-gradient integrators) which is expected to reduce significantly the computational cost of future large-scale gauge field ensemble generation. 
M. A. Clark, B\'alint Jo\'o, A. D. Kennedy, P. J. Silva
hep-lat