Strongly-coupled two harmonics-oscillators CNOT gate under Wigner-parity decoherence in non-equilibrium thermal noise

Abstract We explore how the Wigner-parity operator affects a system of strongly coupled two-harmonic oscillators (SCTHO) interacting with a bosonic bath under thermal non-equilibrium conditions (TNEC). By deforming the Lindblad equation with the Wigner-parity algebra, we model the system’s time evolution, constraining each oscillator to its two lowest energy levels. We use non-Gaussian Tsallis statistics to describe TNEC and examine the time development of concurrence both before and after a CNOT gate operation. Our findings indicate that parity is a strong marker of non-classical behavior in SCTHO exposed to thermal noise. Parity dependent Wigner negativities measure the loss of quantum coherence during CNOT gate operations. This loss is confirmed by Lindblad dynamics. We observe that the parity framework increases concurrence between oscillators after the CNOT, and we analyze how concurrence depends on Wigner parity and system frequency across different Tsallis q -regions. Our analysis reveals that Wigner parity deformation dramatically suppresses decoherence, enhancing concurrence longevity, while Tsallis statistics introduce a distinct hierarchy in thermal resilience. The CNOT gate’s operation induces a frequency dependent entanglement crossover, with parity protection proving most effective at high frequencies. This model offers potential for optimizing thermal solid-state quantum gates (QGs) and provides insights into fault-tolerant encoding in noisy oscillator-based qubits. Furthermore, by extending the analysis to a microscopic model with temperature-dependent decay rates derived from a Tsallis-distributed bath, we demonstrate how non-Gaussian environmental statistics directly shape the decoherence pathways and concurrence dynamics.