Exact nonequilibrium steady state of $XXZ$ circuits boundary driven with arbitrary resets or fields

We propose a spatially inhomogeneous matrix product Ansatz for an exact many-body density operator of a boundary-driven $XXZ$ quantum circuit. The Ansatz has formally infinite bond dimension and is fundamentally different from previous constructions. The circuit is driven by a pair of reset quantum channels applied on the boundary qubits, which polarize the qubits to arbitrary pure target states. Moreover, one of the reset channels can be replaced by an arbitrary local unitary gate, thus representing a hybrid case with coherent and incoherent driving. Analyzing the Ansatz, we obtain a family of relatively robust separable nonequilibrium steady states, which can be viewed as a circuit extension of spin-helix states and are particularly suited for experimental investigations.