Channel-state correspondence and no-go theorem for two-dimensional sequential circuit

In this work, we discuss the capability of 2D local sequential circuit by leveraging on the triality between the sequential circuit, isoTNS and 1D quantum channel dynamics. Specifically, we examine the possibility of preparing chiral states using the sequential circuit. For free-fermion systems, we prove that any one-dimensional translation-invariant local Gaussian fermion channel has at least one steady state with exponentially decaying correlation functions, which henceforth implies any two-dimensional state prepared by a Gaussian fermion sequential circuit has a trivial entanglement spectrum, forbidding chirality. We also provide some comments on the no-go theorem in the interacting case.