Circuits of space-time quantum channels

Pavel Kos, Georgios Styliaris

Published 2022-06-24Version 1

Exact solutions in interacting many-body systems are scarce and very valuable since they provide crucial insights into the dynamics. This is true for both closed and open quantum systems. Recently introduced dual-unitary models are one example where this is possible. These brick-wall quantum circuits consist of local gates, which are unitary in both time and space directions. In this work we generalise these ideas to obtain exact solutions in open quantum circuits, where each gate is substituted by a local quantum channel. Exact solutions are enabled by demanding additional unitality directions for local quantum channels. That is, local channels preserve the identity operator also in (at least one) space direction. We introduce new families of models, which obey different combinations of unitality conditions, and study their structure. Moreover, we prove that any 4-way unital channel can be written as an affine combination of a particular class of dual-unitary gates. Next, we use these families to provide exact solutions of spatio-temporal correlation functions, spatial correlations after a quantum quench, and study their steady states. For solvable quenches, we define initial solvable matrix product density operators (MPDO). In addition, we prove that solvable MPDO in the local purification form are in one-to-one correspondence with quantum channels.