  Sampling occupies an important position in theories of various scientific
fields, and Markov chain Monte Carlo (MCMC) provides the most common technique
of sampling. In the progress of MCMC, a huge number of studies have aimed the
acceleration of convergence to the target distribution. Hamiltonian Monte Carlo
(HMC) is such a variant of MCMC. In the recent development of MCMC, another
approach based on the violation of the detailed balance condition has attracted
much attention. Historically, these two approaches have been proposed
independently, and their relationship has not been clearly understood. In this
paper, the two approaches are seamlessly understood in the framework of
generalized Monte Carlo method that violates the detailed balance condition.
Furthermore we propose an efficient Monte Carlo method based on our framework.
