  For spin rotational symmetric models with a positive-definite
high-temperature expansion of the partition function, a stochastic sampling of
the series expansion upon partial resummation becomes logically equivalent to
sampling an uncoloured closely-packed loop-gas model in one higher dimension.
We devise quantum Monte Carlo updates based on this for general $SU(N)$ in
fundamental and higher-symmetric representations. The algorithmic performance
systematically improves with increase in (continuous) $N$ allowing efficient
simulation of short-loop phases like valence bond solids. The above gives a
connection between Sandvik's $JQ$ model class and classical loop-gas models in
the deconfined universality class.
