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Efficient classical simulation of slightly entangled quantum computations

Guifre Vidal
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Abstract

We present a scheme to efficiently simulate, with a classical computer, the dynamics of multipartite quantum systems on which the amount of entanglement (or of correlations in the case of mixed-state dynamics) is conveniently restricted. The evolution of a pure state of n qubits can be simulated by using computational resources that grow linearly in n and exponentially in the entanglement. We show that a pure-state quantum computation can only yield an exponential speed-up with respect to classical computations if the entanglement increases with the size n of the computation, and gives a lower bound on the required growth.

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Guifre Vidal. 2003-02-26. Efficient classical simulation of slightly entangled quantum computations. https://doi.org/10.1103/physrevlett.91.147902

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