Ternary unitary quantum lattice models and circuits in $2+1$ dimensions

Abstract

We extend the concept of dual unitary quantum gates to quantum lattice models in $2+1$ dimensions, by introducing and studying ternary unitary four-particle gates, which are unitary in time and both spatial dimensions. When used as building blocks of lattice models with periodic boundary conditions in time and space (corresponding to infinite temperature states), dynamical correlation functions exhibit a light-ray structure. We also generalize solvable MPS to two spatial dimensions with cylindrical boundary conditions, by showing that the analogous solvable PEPS can be identified with matrix product unitaries. In the resulting tensor network for evaluating equal-time correlation functions, the bulk ternary unitary gates cancel out. We delineate and implement a numerical algorithm for computing such correlations by contracting the remaining tensors.

16 pages, 6 figures

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Cited by in corpus (13)

• Growth of entanglement of generic states under dual-unitary dynamics
• Hierarchical generalization of dual unitarity
• Crystalline Quantum Circuits
• Circuits of space and time quantum channels
• Zero-temperature entanglement membranes in quantum circuits
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Exactly solvable many-body dynamics from space-time duality
• Exact Hidden Markovian Dynamics in Quantum Circuits
• Tensor network decompositions for absolutely maximally entangled states
• Fundamental charges for dual-unitary circuits
• Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
• Solvable Quantum Circuits in Tree+1 Dimensions
• Logarithmic growth of operator entanglement in a clean non-integrable circuit