Ternary Unitary Quantum Lattice Models and Circuits in 2+1 Dimensions

Area of Science:

• Quantum Information Theory
• Condensed Matter Physics
• Quantum Computing

Background:

• Extends the concept of dual unitary quantum gates to higher dimensions.
• Builds upon previous work on solvable matrix product states.

Purpose of the Study:

• Introduce and study ternary unitary four-particle gates in 2+1 dimensions.
• Investigate dynamical correlation functions in lattice models.
• Generalize solvable matrix product states to two spatial dimensions.

Main Methods:

• Utilizing ternary unitary gates as building blocks for lattice models.
• Applying periodic boundary conditions in time and space.
• Generalizing matrix product states to projected entangled pair states in 2D.
• Employing tensor network contractions for correlation function evaluation.

Main Results:

• Dynamical correlation functions exhibit a light ray structure.
• Solvable projected entangled pair states are identified with matrix product unitaries.
• Bulk ternary unitary gates cancel out in tensor networks for equal-time correlations.

Conclusions:

• Ternary unitary gates offer a new framework for quantum lattice models.
• The identified structure simplifies the computation of correlation functions.
• This work provides a numerical algorithm for computing these correlations efficiently.