  The coalescence of binary neutron stars are one of the main sources of
gravitational waves for ground-based gravitational wave detectors. As Bayesian
inference for binary neutron stars is computationally expensive, more efficient
and faster converging algorithms are always needed. In this work, we conduct a
feasibility study using a Hamiltonian Monte Carlo algorithm (HMC). The HMC is a
sampling algorithm that takes advantage of gradient information from the
geometry of the parameter space to efficiently sample from the posterior
distribution, allowing the algorithm to avoid the random-walk behaviour
commonly associated with stochastic samplers. As well as tuning the algorithm's
free parameters specifically for gravitational wave astronomy, we introduce a
method for approximating the gradients of the log-likelihood that reduces the
runtime for a $10^6$ trajectory run from ten weeks, using numerical derivatives
along the Hamiltonian trajectories, to one day, in the case of non-spinning
neutron stars. Testing our algorithm against a set of neutron star binaries
using a detector network composed of Advanced LIGO and Advanced Virgo at
optimal design, we demonstrate that not only is our algorithm more efficient
than a standard sampler, but a $10^6$ trajectory HMC produces an effective
sample size on the order of $10^4 - 10^5$ statistically independent samples.
