  Hamiltonian Monte Carlo (HMC) is an efficient method of simulating smooth
distributions and has motivated the widely used No-U-turn Sampler (NUTS) and
software Stan. We build on NUTS and the technique of "unbiased sampling" to
design HMC algorithms that produce perfect simulation of general continuous
distributions that are amenable to HMC. Our methods enable separation of Markov
chain Monte Carlo convergence error from experimental error, and thereby
provide much more powerful MCMC convergence diagnostics than current
state-of-the-art summary statistics which confound these two errors. Objective
comparison of different MCMC algorithms is provided by the number of derivative
evaluations per perfect sample point. We demonstrate the methodology with
applications to normal, $t$ and normal mixture distributions up to 100
dimensions, and a 12-dimensional Bayesian Lasso regression. HMC runs
effectively with a goal of 20 to 30 points per trajectory. Numbers of
derivative evaluations per perfect sample point range from 390 for a univariate
normal distribution to 12,000 for a 100-dimensional mixture of two normal
distributions with modes separated by six standard deviations, and 22,000 for a
100-dimensional $t$-distribution with four degrees of freedom.
