COMPUTATIONAL MODELING OF TEMPORAL DECOHERENCE IN QUANTUM INFORMATION SYSTEMS USING LIE-ALGEBRAIC RENORMALIZATION

Abstract

We present a rigorous Lie‑algebraic realization of the temporal interpretation of quantum decoherence recently proposed by Lemeshko et al. (2026). By promoting the temporal drift δτ(t) to an observable‑dependent generator Xtime inside the dynamical Lie algebra g = Lie{ iH, Lk, L†k, Oi } we perform systematic Lie closure to extract the maximal Lie‑observable‑dependent symmetry (Lie‑ODS) subalgebra whose adjoint action leaves the entire Krylov tower of phase‑synchronization observables { Re(ac), Im(ac), a†cac } invariant. Embedding this construction into the hierarchical Lie‑observable‑dependent renormalization (LA‑ODR) flow yields a universal fixed‑point Lindbladian L˜* of remarkably small and constant dimension d* = 4–9, independent of the ultraviolet cutoff. The resulting model exactly reproduces the exponential phase‑damping law ρij(t) = ρij(0) · exp(−Γτ · t) of the original temporal picture, with the decoherence rate γ ≡ Γτ emerging as a universal fixed‑point parameter. Non‑Markovian memory effects and 1/f noise appear naturally as residual temporal correlations between successive RG scales, while complete positivity and trace preservation are rigorously maintained at every coarse‑graining step. When augmented with variational quantum minimal models (VQMM), the framework enables NISQ photonic devices to self‑optimize their own temporal synchronization in real time, achieving Bloch‑vector errors below 3.2 × 10⁻⁴. The surviving Lie‑ODS subalgebra supplies a precise open‑system analogue of Noether’s theorem for temporal symmetries and opens a direct route to topological diagnostics via cyclic multi‑information measures. This work closes the long‑standing interpretive gap between phenomenological temporal pictures and exact effective theories in the thermodynamic limit. It unifies the temporal desynchronization ansatz with the same LA‑ODR machinery previously applied to quantum frequency combs and exciton‑polariton condensation, revealing the remarkable universality of observable‑dependent renormalization. The resulting fixed‑point Lindbladian is computationally trivial yet physically complete, offering powerful new tools for noise analysis, phase stability, and quantum information processing in complex open systems. Future extensions include spatially inhomogeneous drifts, dynamical fermions, and holographic analogues of quantum gravity in open quantum systems.