The Degree of Quantum Correlation Required to Speed-Up a Computation

TL;DR

This paper investigates the quantum correlations necessary for computational speed-up in the DQC1 model, showing that even minimal entanglement can enable quantum advantage, exemplified by Grover's Search on mixed states.

Contribution

It demonstrates that small quantum correlations suffice for quantum speed-up in DQC1, and refines methods to evaluate entanglement in such models.

Findings

Grover's Search on mixed states shows quantum speed-up with minimal correlations.

Small quantum correlations are sufficient for computational advantage.

Refined techniques for measuring entanglement in DQC1 models.

Abstract

The one clean qubit model of quantum computation (DQC1) efficiently implements a computational task that is not known to have a classical alternative. During the computation, there is never more than a small but finite amount of entanglement present, and it is typically vanishingly small in the system size. In this paper, we demonstrate that there is nothing unexpected hidden within the DQC1 model -- Grover's Search, when acting on a mixed state, provably exhibits a speed-up over classical with guarantees as to the presence of only vanishingly small amounts of quantum correlations (entanglement and quantum discord) -- while arguing that this is not an artefact of the oracle-based construction. We also present some important refinements in the evaluation of how much entanglement may be present in DQC1, and how the typical entanglement of the system must be evaluated.