Exact nonequilibrium steady states of boundary driven circuit with XYZ gates

TL;DR

This paper derives exact nonequilibrium steady states for a boundary-driven quantum circuit with XYZ gates using a complex matrix product Ansatz, revealing robust states with potential experimental relevance.

Contribution

It generalizes previous XXZ circuit solutions to XYZ interactions and introduces a family of experimentally attractive, separable chiral NESS.

Findings

Exact density operator obtained via inhomogeneous matrix product Ansatz.

Discovery of a family of robust, separable chiral NESS.

Relevance for experimental realization of quantum circuits.

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.