  Markov chain Monte Carlo (MCMC) is a powerful methodology for the
approximation of posterior distributions. However, the iterative nature of MCMC
does not naturally facilitate its use with modern highly parallelisable
computation on HPC and cloud environments. Another concern is the
identification of the bias and Monte Carlo error of produced averages. The
above have prompted the recent development of fully (`embarrassingly')
parallelisable unbiased Monte Carlo methodology based on couplings of MCMC
algorithms. A caveat is that formulation of effective couplings is typically
not trivial and requires model-specific technical effort. We propose couplings
of sequential Monte Carlo (SMC) by considering adaptive SMC to approximate
complex, high-dimensional posteriors combined with recent advances in unbiased
estimation for state-space models. Coupling is then achieved at the SMC level
and is, in general, not problem-specific. The resulting methodology enjoys
desirable theoretical properties. We illustrate the effectiveness of the
algorithm via application to two statistical models in high dimensions: (i)
horseshoe regression; (ii) Gaussian graphical models.
