Quantum computational advantage with string order parameters of 1D symmetry-protected topological order

TL;DR

This paper demonstrates that large string order parameters in 1D symmetry-protected topological orders enable advantageous quantum strategies in nonlocal games, highlighting their potential for demonstrating quantum computational advantages.

Contribution

It introduces a method to use string order parameters of 1D SPTOs to achieve advantageous strategies in nonlocal games, establishing a link between topological order and quantum computational advantage.

Findings

Advantageous quantum strategies are possible for ground states of 1D SPTOs with nontrivial twist phases.

Large string order parameters correlate with globally constrained quantum correlations.

The approach provides a new way to demonstrate quantum computational separation using topological order.

Abstract

Nonlocal games with advantageous quantum strategies give arguably the most fundamental demonstration of the power of quantum resources over their classical counterparts. Recently, certain multiplayer generalizations of nonlocal games have been used to prove unconditional separations between small computational complexity classes of shallow-depth circuits. Here, we show advantageous strategies for these nonlocal games for generic ground states of one-dimensional symmetry-protected topological orders (SPTOs), when a discrete invariant of a SPTO known as a twist phase is nontrivial and -1. Our construction demonstrates that sufficiently large string order parameters of such SPTOs are indicative of globally constrained correlations useful for the unconditional computational separation.