Exact nonequilibrium steady states of boundary driven circuit with XYZ gates

Abstract

We obtain the exact many-body density operator of a boundary-driven XXZ quantum circuit via a spatially inhomogeneous matrix product Ansatz. The Ansatz has formally infinite bond-dimension and generalizes authors' previous construction \cite{2025XXZcircuit} for the XXZ interactions. The boundary qubits are coupled to reset quantum channels that project them toward arbitrary pure target states. We find and describe a family of relatively robust separable chiral nonequilibrium steady states (NESS), which are elliptic analogs of spin helices for the circuit, and which are particularly attractive from an experimental perspective.