  High-quality random samples of quantum states are needed for a variety of
tasks in quantum information and quantum computation. Searching the
high-dimensional quantum state space for a global maximum of an objective
function with many local maxima or evaluating an integral over a region in the
quantum state space are but two exemplary applications of many. These tasks can
only be performed reliably and efficiently with Monte Carlo methods, which
involve good samplings of the parameter space in accordance with the relevant
target distribution. We show how the Markov-chain Monte Carlo method known as
Hamiltonian Monte Carlo, or hybrid Monte Carlo, can be adapted to this context.
It is applicable when an efficient parameterization of the state space is
available. The resulting random walk is entirely inside the physical parameter
space, and the Hamiltonian dynamics enable us to take big steps, thereby
avoiding strong correlations between successive sample points while enjoying a
high acceptance rate. We use examples of single and double qubit measurements
for illustration.
