Almost-Everywhere Superiority for Quantum Computing

TL;DR

This paper demonstrates that quantum computers can outperform classical computers almost everywhere for certain tasks, extending previous results of exponential speedup to a broader context.

Contribution

It introduces the concept that quantum advantage can be achieved almost everywhere, not just infinitely often, for specific computational tasks.

Findings

Quantum computers are exponentially faster than classical ones almost everywhere.

Extends previous results of exponential speedup from infinitely often to almost everywhere.

Highlights the broad applicability of quantum advantage in computational tasks.

Abstract

Simon as extended by Brassard and H{\o}yer shows that there are tasks on which polynomial-time quantum machines are exponentially faster than each classical machine infinitely often. The present paper shows that there are tasks on which polynomial-time quantum machines are exponentially faster than each classical machine almost everywhere.