Extreme Quantum Advantage when Simulating Strongly Coupled Classical   Systems
  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. 
C. Aghamohammadi, J. R. Mahoney, and J. P. Crutchfield
quant-ph cond-mat.stat-mech cs.CC cs.IT math.IT