Nonlinear Phase Stabilization in Quantum Information Systems: An LA-ODR Framework with Temporal Susceptibility Feedback

Andriy V Lemeshko, Isamu Ohnishi

Published Apr 19, 2026• 0 citations

Abstract

ABSTRACT The scalability of Noisy Intermediate-Scale Quantum (NISQ) devices [21] remains fundamentally limited by decoherence, which conventional dynamical decoupling [25] and quantum error correction [26, 28] only partially mitigate. This paper presents a transition from passive noise suppression to active dynamical stabilization through controlled modulation of the effective state-space metric. Within the Lie-algebraic renormalization (LA-ODR) framework [5, 6, 7], we introduce the Temporal Phase-Locked Loop (TPLL) — an active feedback controller that drives the temporal susceptibility χ_τ toward the globally stable fixed point χ_τ* = λ_nat/(λ_ctrl + λ_nat) via the Kyiv–Ohnishi hybrid flow: dχ_τ/dt = −α · Γ₀ · (χ_τ)^(β+1) − λ_ctrl · χ_τ + λ_nat · (1 − χ_τ) Numerical simulations (illustrative) demonstrate the emergence of metastable coherence plateaus extending coherence times from ~100 µs to ~1.5 ms under realistic hardware benchmarks (FPGA latency Δt < 500 ns). The model predicts two experimentally distinguishable signatures: (i) Phase Inertia — non-exponential initial coherence suppression; and (ii) Avalanche Collapse — a second-order phase transition at χ_τ > χ_crit. These signatures distinguish the TPLL regime from standard Lindblad decay and passive discrete time crystals. Keywords: nonlinear phase stabilization; temporal susceptibility; LA-ODR; Kyiv–Ohnishi flow; TPLL; coherence plateau; Avalanche Collapse; Phase Inertia; NISQ devices; discrete time crystals; Krylov tower invariance

DOI: 10.5281/zenodo.19651032

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