  Classical stochastic processes can be generated by quantum simulators instead
of the more standard classical ones, such as hidden Markov models. One reason
for using quantum simulators is that they generally require less memory than
their classical counterparts. Here, we examine this quantum advantage for
strongly coupled spin systems---the Dyson-like one-dimensional Ising spin chain
with variable interaction length. We find that the advantage scales with both
interaction range and temperature, growing without bound as interaction
increases. Thus, quantum systems can very efficiently simulate strongly coupled
classical systems.
