Circuits of space and time quantum channels

TL;DR

This paper extends dual-unitary quantum circuits to noisy environments by introducing local quantum channels, providing exact solutions for correlation functions, steady states, and initial states, even with significant violations of dual-unitarity.

Contribution

It generalizes dual-unitary models to include noise via quantum channels, offering exact solutions and classifications in non-ideal, realistic quantum systems.

Findings

Exact solutions for spatio-temporal correlations

Noise unbiased around dual-unitary models remains solvable

Channels unital in space and time can be expressed as affine combinations

Abstract

Exact solutions in interacting many-body systems are scarce but extremely valuable since they provide insights into the dynamics. Dual-unitary models are examples in one spatial dimension where this is possible. These brick-wall quantum circuits consist of local gates, which remain unitary not only in time, but also when interpreted as evolutions along the spatial directions. However, this setting of unitary dynamics does not directly apply to real-world systems due to their imperfect isolation, and it is thus imperative to consider the impact of noise to dual-unitary dynamics and its exact solvability. In this work we generalise the ideas of dual-unitarity to obtain exact solutions in noisy quantum circuits, where each unitary gate is substituted by a local quantum channel. Exact solutions are obtained by demanding that the noisy gates yield a valid quantum channel not only in time, but also when interpreted as evolutions along one or both of the spatial directions and possibly backwards in time. This gives rise to new families of models that satisfy different combinations of unitality constraints along the space and time directions. We provide exact solutions for the spatio-temporal correlation functions, spatial correlations after a quantum quench, and the structure of steady states for these families of models. We show that noise unbiased around the dual-unitary family leads to exactly solvable models, even if dual-unitarity is strongly violated. We prove that any channel unital in both space and time directions can be written as an affine combination of a particular class of dual-unitary gates. Finally, we extend the definition of solvable initial states to matrix-product density operators. We completely classify them when their tensor admits a local purification.