Quantum Synchronization in Nonconservative Electrical Circuits

Quantum synchronization has garnered significant attention due to its applications in neuromorphic computing, metrology, and as an entanglement witness. Given the numerous theoretical circuit designs that leverage dissipative environments to demonstrate quantum synchronization, circuit QED provides an ideal platform for realizing this phenomenon. However, the standard Lindblad master equation methodology used to describe these circuits has limitations, as it may not fully capture the original circuit’s topological and electrical properties. In contrast, our research introduces the Maxwell-Heisenberg equations as a native circuital approach. These Maxwell-Heisenberg equations replace the use of Lindbladians to describe open system dynamics by incorporating loss via a Rayleigh dissipation function. Using the Maxwell-Heisenberg equations, we explore the use of nonconservative elements as a valuable resource to robustly induce synchronization in coupled circuits without the use of noise. The qubit and resonator systems we analyze employ a common resistive element to passively induce synchronization between bipartite quantum systems. Notably, our approach can be extended to study singular circuits, where we explicitly demonstrate the persistence of quantum synchronization in the circuit used to resolve the singularity. These findings provide a foundation for the experimental validation of our approach in superconducting quantum circuits.