Universal quantum computation with little entanglement

TL;DR

This paper demonstrates that universal quantum computation is possible with minimal entanglement, challenging the notion that high entanglement is essential for quantum speed-ups.

Contribution

It proves that quantum computers can be universal even when entanglement entropy remains very low, broadening understanding of entanglement's role in quantum computation.

Findings

Universal quantum computation can occur with small or vanishing entanglement.

Many continuous entanglement measures also do not need high entanglement for universality.

Implications question the necessity of entanglement as a key resource for quantum speed-ups.

Abstract

We show that universal quantum computation can be achieved in the standard pure-state circuit model while, at any time, the entanglement entropy of all bipartitions is small---even tending to zero with growing system size. The result is obtained by showing that a quantum computer operating within a small region around the set of unentangled states still has universal computational power, and by using continuity of entanglement entropy. In fact an analogous conclusion applies to every entanglement measure which is continuous in a certain natural sense, which amounts to a large class. Other examples include the geometric measure, localizable entanglement, smooth epsilon-measures, multipartite concurrence, squashed entanglement, and several others. We discuss implications of these results for the believed role of entanglement as a key necessary resource for quantum speed-ups.