Encoding complex-balanced thermalization in quantum circuits

Abstract: We propose a protocol for effectively implementing complex-balanced thermalization via Markovian processes on a quantum-circuit platform that couples the system with engineered reservoir qubits. The non-orthogonality of qubit eigenstates facilitates non-uniform heating through a modified Kubo-Martin-Schwinger relation, while simultaneously supports amplification-dissipation dynamics by violating microscopic time-reversibility. This offers a new approach to realizing out-of-equilibrium states at given temperatures. We show two applications of this platform: temporally-correlated dichromatic emission and Liouvillian exception point protected quantum synchronization at finite temperatures, both of which are challenging to achieve with conventional thermal reservoirs.