Tri-unitary quantum circuits

TL;DR

This paper introduces tri-unitary quantum circuits with correlations confined to specific spacetime directions, providing exact solutions and revealing rich entanglement dynamics and fracton-like phenomena in higher dimensions.

Contribution

It presents a new class of quantum circuits with tri-unitary gates, extending dual-unitary circuits to three directions, with exact correlation functions and novel entanglement behavior.

Findings

Correlations are confined to three spacetime directions in 1+1 dimensions.

Entanglement grows maximally up to a certain entropy density.

Extension to 2+1 dimensions shows subdimensional information propagation.

Abstract

We introduce a novel class of quantum circuits that are unitary along three distinct "arrows of time". These dynamics share some of the analytical tractability of "dual-unitary" circuits, while exhibiting distinctive and richer phenomenology. We find that two-point correlations in these dynamics are strictly confined to three directions in $(1+1)$-dimensional spacetime -- the two light cone edges, $\delta x=\pm v\delta t$, and the static worldline $\delta x=0$. Along these directions, correlation functions are obtained exactly in terms of quantum channels built from the individual gates that make up the circuit. We prove that, for a class of initial states, entanglement grows at the maximum allowed speed up to an entropy density of at least one half of the thermal value, at which point it becomes model-dependent. Finally, we extend our circuit construction to $2+1$ dimensions, where two-point correlation functions are confined to the one-dimensional edges of a tetrahedral light cone -- a subdimensional propagation of information reminiscent of "fractonic" physics.