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

Richard M Milbradt1, Lisa Scheller1, Christopher Aßmus1

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We introduce ternary unitary gates for quantum lattice models in 2+1 dimensions, revealing a light ray structure in dynamical correlations. Solvable projected entangled pair states are identified with matrix product unitaries, simplifying correlation function calculations.

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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.