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

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Computational Complexity Theory

Background:

• Nonlocal games showcase quantum resource advantages over classical ones.
• Multiplayer nonlocal games have recently proven computational complexity class separations.
• Symmetry-Protected Topological Orders (SPTOs) are a key area in condensed matter physics.

Purpose of the Study:

• To demonstrate advantageous quantum strategies for nonlocal games using SPTOs.
• To establish a link between SPTO properties and computational separations.
• To explore the potential of quantum correlations in computational tasks.

Main Methods:

• Utilizing generic ground states of one-dimensional SPTOs.
• Leveraging the twist phase invariant of SPTOs.
• Analyzing string order parameters to identify global correlations.

Main Results:

• Advantageous nonlocal game strategies were found for SPTOs with a nontrivial, -1 twist phase.
• The study shows that large string order parameters in SPTOs indicate useful global correlations.
• These correlations are effective for achieving unconditional computational separations.

Conclusions:

• SPTOs with specific twist phases provide a resource for advantageous quantum strategies in nonlocal games.
• String order parameters serve as indicators of globally constrained correlations relevant to computational complexity.
• This work bridges quantum information, condensed matter, and computational complexity theory.