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Journal Club for Condensed Matter Physics

Many body quantum games and phases of matter

Rahul Nandkishore

Published Nov 30, 2023• 0 citations
Publisher

Abstract

1. A multiplayer multiteam nonlocal game for the toric code Authors: Vir B. Bulchandani, Fiona J. Burnell, and S.L.Sondhi Phys. Rev. B 107, 035409 (2023); DOI: 10.1103/PhysRevB.107.035409 2. Playing nonlocal games with phases of matter Authors: Vir B. Bulchandani, Fiona J. Burnell, and S.L.Sondhi Phys. Rev. B 107, 045412 (2023); DOI: 10.1103/PhysRevB.107.045412 Recommended with a […]

DOI
10.36471/jccm_november_2023_02

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  1. A multiplayer multiteam nonlocal game for the toric code Authors: Vir B. Bulchandani, Fiona J. Burnell, and S.L.Sondhi Phys. Rev. B 107, 035409 (2023); DOI: 10.1103/PhysRevB.107.035409 2. Playing nonlocal games with phases of matter Authors: Vir B. Bulchandani, Fiona J. Burnell, and S.L.Sondhi Phys. Rev. B 107, 045412 (2023); DOI: 10.1103/PhysRevB.107.045412 Recommended with a […]
Nonlocal games yield an unusual perspective on entangled quantum states. The defining property of such games is that a set of players in joint possession of an entangled state can win the game with higher probability than is allowed by classical physics. Here we construct a nonlocal game that can be won with certainty by 2N2N2N players if they have access to the ground state of the toric code on as many qubits. By contrast, the game cannot be won by classical players more than half the time in the large NNN limit. Our game differs from previous examples because it arranges the players on a lattice and allows them to carry out quantum operations in teams, whose composition is dynamically specified. This is natural when seeking to characterize the degree of quantumness of nontrivial many-body states, which potentially include states in much more varied phases of matter than the toric code. We present generalizations of the toric code game to states with ZM{\mathbb{Z}}_{M}ZM​ topological order.
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 Letter, 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 midcircuit 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 Greenberger-Horne-Zeilinger 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.