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 algorithms 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.
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