Playing nonlocal games across a topological phase transition on a quantum computer

TL;DR

This paper introduces multiplayer quantum games that leverage topologically ordered phases to demonstrate robust quantum advantage on quantum hardware, and explores how this advantage is affected by a topological phase transition.

Contribution

It presents a family of quantum games utilizing topological phases that maintain quantum advantage under perturbations and experimentally demonstrates this robustness on a quantum computer.

Findings

Quantum advantage persists away from exactly solvable points.

Robustness of quantum advantage is experimentally verified.

Quantum advantage is lost at the topological phase transition.

Abstract

Many-body quantum games provide a natural perspective on phases of matter in quantum hardware, crisply relating the quantum correlations inherent in phases of matter to the securing of quantum advantage at a device-oriented task. In this paper we introduce a family of multiplayer quantum games for which topologically ordered phases of matter are a resource yielding quantum advantage. Unlike previous examples, quantum advantage persists away from the exactly solvable point and is robust to arbitrary local perturbations, irrespective of system size. We demonstrate this robustness experimentally on Quantinuum's H1-1 quantum computer by playing the game with a continuous family of randomly deformed toric code states that can be created with constant-depth circuits leveraging mid-circuit measurements and unitary feedback. We are thus able to tune through a topological phase transition - witnessed by the loss of robust quantum advantage - on currently available quantum hardware. This behavior is contrasted with an analogous family of deformed GHZ states, for which arbitrarily weak local perturbations destroy quantum advantage in the thermodynamic limit. Finally, we discuss a topological interpretation of the game, which leads to a natural generalization involving an arbitrary number of players.