Unbounded memory advantage in stochastic simulation using quantum mechanics

TL;DR

This paper demonstrates that quantum processors can simulate stochastic processes with arbitrary precision using fixed finite memory, revealing an unbounded memory advantage over classical simulators.

Contribution

It introduces a method showing quantum simulators can achieve arbitrarily high precision with fixed memory, surpassing classical limitations.

Findings

Quantum processors can simulate stochastic processes with arbitrary precision.

Quantum simulators exhibit an unbounded memory advantage over classical ones.

The approach leverages tools from computational mechanics.

Abstract

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. Here, using tools from computational mechanics, we show that quantum processors with a fixed finite memory can simulate stochastic processes of real variables to arbitrarily high precision. This demonstrates a provable, unbounded memory advantage that a quantum simulator can exhibit over its best possible classical counterpart.