Is Entanglement Sufficient to Enable Quantum Speedup?

TL;DR

The paper clarifies that while the Gottesman-Knill theorem shows certain entangled states are classically simulable, entanglement itself is still a sufficient resource for quantum speedup when fully utilized.

Contribution

It argues that entanglement is fundamentally sufficient for quantum speedup, despite some algorithms with entangled states being classically simulable under restricted operations.

Findings

Gottesman-Knill theorem explains classical simulability of certain entangled states.

Entanglement provides sufficient resources for quantum speedup.

Restricted operations prevent violation of Bell inequalities.

Abstract

According to the Gottesman-Knill theorem, any quantum algorithm utilising operations chosen exclusively from a particular restricted set are efficiently simulable by a classical computer. Since some of these algorithms involve entangled states, it is commonly concluded that entanglement is insufficient to enable quantum speedup. As I explain, however, the operations belonging to this set are precisely those which will never yield a violation of the Bell inequalities. Thus it should be no surprise that entangled quantum states which only undergo operations in this set are efficiently simulable classically. What the Gottesman-Knill theorem shows us is that it is possible to use an entangled state to less than its full potential. Nevertheless, there is a meaningful sense in which entanglement is sufficient for quantum speedup: an entangled quantum state provides sufficient physical resources to enable quantum speedup, whether or not one elects to use these resources fully.