Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the simulation is thus generally limited by the internal memory available to the simulator. In this presentation, using tools from computational mechanics, I shall show that quantum information processing allows the simulation of stochastic processes to arbitrarily high precision at a finite memory cost. This demonstrates the unbounded memory advantage that a quantum computer can exhibit over its best possible classical counterpart when used for stochastic simulations.
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