Provable Quantum Advantage in Randomness Processing

TL;DR

This paper demonstrates a provable quantum advantage in randomness processing, showing that quantum computing can solve a strictly larger class of problems than classical physics, with implications for foundational understanding and practical simulations.

Contribution

It provides the first proof of quantum advantage in a specific randomness processing scenario, expanding the known capabilities of quantum computation over classical methods.

Findings

Quantum theory enables solving a larger class of problems in randomness processing.

Quantum advantage is provably demonstrated in this computational scenario.

Potential for developing classically intractable simulations using quantum technologies.

Abstract

Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed, but not proven, that quantum computing provides exponential speed-up for a range of problems, such as factoring. Here we address a computational scenario of "randomness processing" in which quantum theory provably yields, not only resource reduction over classical stochastic physics, but a strictly larger class of problems which can be solved. Beyond new foundational insights into the nature and malleability of randomness, and the distinction between quantum and classical information, these results also offer the potential of developing classically intractable simulations with currently accessible quantum technologies.