Braiding for the win: Harnessing braiding statistics in topological states to win quantum games

TL;DR

This paper demonstrates that topological and fracton ordered phases of quantum matter can provide robust advantages in nonlocal quantum games by leveraging braiding statistics, with broad implications for quantum information processing.

Contribution

It shows that resource states from topological and fracton phases universally enable quantum advantages in nonlocal games through braiding statistics, extending previous results.

Findings

Robust quantum advantage in nonlocal games from topological phases

Resource states from various topological and fracton phases are effective

Generalized strategies for using quantum error-correcting codes in games

Abstract

Nonlocal quantum games provide proof of principle that quantum resources can confer advantage at certain tasks. They also provide a compelling way to explore the computational utility of phases of matter on quantum hardware. In a recent manuscript [Hart et al., arXiv:2403.04829] we demonstrated that a toric code resource state conferred advantage at a certain nonlocal game, which remained robust to small deformations of the resource state. In this manuscript we demonstrate that this robust advantage is a generic property of resource states drawn from topological or fracton ordered phases of quantum matter. To this end, we illustrate how several other states from paradigmatic topological and fracton ordered phases can function as resources for suitably defined nonlocal games, notably the three-dimensional toric-code phase, the X-cube fracton phase, and the double-semion phase. The key in every case is to design a nonlocal game that harnesses the characteristic braiding processes of a quantum phase as a source of contextuality. We unify the strategies that take advantage of mutual statistics by relating the operators to be measured to order and disorder parameters of an underlying generalized symmetry-breaking phase transition. Finally, we massively generalize the family of games that admit perfect strategies when codewords of homological quantum error-correcting codes are used as resources.