Generalized framework for analyzing decoherence in multi-qubit system using mean-field-based Lindblad master equation 

 

Multi-qubit systems are key for scalable quantum technologies, enabling stable computing, quick error correction, and algorithms such as Shor’s, Grover’s, and variational methods.  However, their performance is limited by strong decoherence due to environmental noise and qubit–qubit interactions. Several studies are investigating fidelity of multi-qubit gates [1], concurrence of multi-qubit states [2], and environmental effects on single qubits [3], However, it is still unclear how qubit-qubit interactions, qubit concentrations, their spatial distributions, or bath temperature, crystal defects affect  qubit relaxation and dephasing times. To address this gap, we propose an analytical framework that analyzes the population dynamics of energy levels and the quantum coherence of a given solid-state qubit interacting with other qubits in a multi-qubit system. Our framework uses the Lindblad master equation approach and includes the inter-qubit interactions within a mean-field approximation. By explicitly incorporating qubit–qubit interactions, we can examine how qubit characteristics such as energy level differences, critical interaction distances, and types of interactions affect the qubit dynamics. Our analysis reveals that increasing qubit concentration leads to shorter relaxation and dephasing times in multi-qubit system. The model successfully explains recent experimental observations in Er³⁺-doped CeO₂, where relaxation times are reported to decrease with increasing dopant concentration [4]. We also observe that qubit relaxation slows down at elevated temperatures, while decoherence is accelerated.  Our framework offers a novel approach to exploring multi-qubit system behavior and provides guidance to design multi-qubit systems with longer coherence and relaxation time under real-world conditions.