Quantum Computational Advantage with String Order Parameters of One-Dimensional Symmetry-Protected Topological Order

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