Circuits of space and time quantum channels

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