  Using MCMC to sample from a target distribution, $\pi(x)$ on a
$d$-dimensional state space can be a difficult and computationally expensive
problem. Particularly when the target exhibits multimodality, then the
traditional methods can fail to explore the entire state space and this results
in a bias sample output. Methods to overcome this issue include the parallel
tempering algorithm which utilises an augmented state space approach to help
the Markov chain traverse regions of low probability density and reach other
modes. This method suffers from the curse of dimensionality which dramatically
slows the transfer of mixing information from the auxiliary targets to the
target of interest as $d \rightarrow \infty$. This paper introduces a novel
prototype algorithm, QuanTA, that uses a Gaussian motivated transformation in
an attempt to accelerate the mixing through the temperature schedule of a
parallel tempering algorithm. This new algorithm is accompanied by a
comprehensive theoretical analysis quantifying the improved efficiency and
scalability of the approach; concluding that under weak regularity conditions
the new approach gives accelerated mixing through the temperature schedule.
Empirical evidence of the effectiveness of this new algorithm is illustrated on
canonical examples.
