Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. Yet the most interesting systems are often complex, such that simulating their future behaviour demands storing immense amounts of information regarding how they have behaved in the past. For increasingly complex systems, simulation becomes increasingly difficult and is ultimately constrained by resources such as computer memory. Recent theoretical work shows quantum theory can reduce this memory requirement beyond ultimate classical limits (as measured by a process statistical complexity, C). Here we experimentally demonstrate this quantum advantage in simulating stochastic processes. Our quantum implementation observes a memory requirement of C_q = 0.05 $pm$ 0.01, far below the ultimate classical limit of C = 1. Scaling up this technique would substantially reduce the memory required in simulation of more complex systems.
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