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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.
This brief article gives an overview of quantum mechanics as a {em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum stochastic
Coherently manipulating multipartite quantum correlations leads to remarkable advantages in quantum information processing. A fundamental question is whether such quantum advantages persist only by exploiting multipartite correlations, such as entang
A growing body of work has established the modelling of stochastic processes as a promising area of application for quantum techologies; it has been shown that quantum models are able to replicate the future statistics of a stochastic process whilst
Atomic ions trapped in ultra-high vacuum form an especially well-understood and useful physical system for quantum information processing. They provide excellent shielding of quantum information from environmental noise, while strong, well-controlled
In quantum communication networks, wires represent well-defined trajectories along which quantum systems are transmitted. In spite of this, trajectories can be used as a quantum control to govern the order of different noisy communication channels, a