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

Andriy Lemeshko, Isamu Ohnishi

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.29755.99361

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NONLINEAR PHASE STABILIZATION IN QUANTUM INFORMATION SYSTEMS

Andriy Lemeshko, Isamu Ohnishi

•Jul 16, 2026•0 citations

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

Andriy V Lemeshko, Isamu Ohnishi

Abstract: The scalability of Noisy Intermediate-Scale Quantum (NISQ) devices remains fundamentally limited by stochastic decoherence, which traditional passive shielding and resource-heavy quantum error correction (QEC) struggle to overcome. Here, we propose a paradigm shift from passive noise mitigation to active internal phase stabilization. By integrating the Lie-algebraic renormalization (LA-ODR) framework with a dynamic model of temporal susceptibility (χ_τ), we derive a nonlinear control law for quantum coherence. We demonstrate that decoherence can be treated as a deterministic dynamical process governed by the feedback equation dχ_τ / dt = −α · Γ_τ · χ_τ + λ · (1 − χ_τ). Our numerical simulations confirm the formation of metastable coherence plateaus, where the effective qubit lifetime is extended significantly beyond the standard Lindbladian limit (e.g., from 100 µs to 1.5 ms in transmon-based models). We further specify a hardware-ready Temporal Phase-Locked Loop (TPLL) architecture, proving that with control latencies below 500 ns, active synchronization of the temporal metric becomes feasible on modern FPGA-based controllers. This framework provides a path toward fault-tolerant quantum computing by enabling fidelity-by-design at the physical layer, potentially providing a substantial reduction in QEC overhead by maintaining high physical fidelity prior to logical encoding. Keywords nonlinear phase stabilization; temporal susceptibility χτ; Lie-observable-dependent renormalization (LA-ODR); fixed-point Lindbladian; quantum decoherence; active feedback control; temporal phase-locked loop (TPLL); NISQ devices; superconducting qubits; cold atom arrays

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

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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

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Stabilization of Quantum Information: A Unified Dynamical-Algebraic Approach

Paolo Zanardi A

Springer eBooks•Jan 1, 2001•2 citations

NONLINEAR PHASE STABILIZATION IN QUANTUM INFORMATION SYSTEMS: A TEMPORAL PHASE-LOCKED LOOP FRAMEWORK BASED ON LA-ODR TEMPORAL SUSCEPTIBILITY FEEDBACK

Andriy V Lemeshko, Isamu Ohnishi

Abstract: The scalability of Noisy Intermediate-Scale Quantum (NISQ) devices remains fundamentally limited by decoherence, which conventional dynamical decoupling and quantum error correction 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 observable-dependent renormalization (LA-ODR) framework, 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 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). Three operationally distinct zones are characterized by χ_τ thresholds, and two experimentally distinguishable signatures — Phase Inertia and Avalanche Collapse — are predicted. The TPLL is compared with dynamical decoupling, quantum error correction, and discrete time crystals, establishing complementarity rather than competition. The mathematical foundations rest on four global stability theorems via Lyapunov analysis and Chiba renormalization-group flow. Index Terms: Quantum coherence; decoherence control; temporal susceptibility; LA-ODR; Temporal Phase-Locked Loop (TPLL); Kyiv–Ohnishi flow; NISQ devices; open quantum systems; Lyapunov stability; Lie algebra; FPGA quantum control; nonlinear dynamics.

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Dynamical Control of Quantum Information Processing

Gershon Kurizki, Abraham G. Kofman

Cambridge University Press eBooks•Dec 23, 2021•0 citations
Abstract: The scalability of Noisy Intermediate-Scale Quantum (NISQ) devices remains fundamentally limited by stochastic decoherence, which traditional passive shielding and resource-heavy quantum error correction (QEC) struggle to overcome. Here, we propose a paradigm shift from passive noise mitigation to active internal phase stabilization. By integrating the Lie-algebraic renormalization (LA-ODR) framework with a dynamic model of temporal susceptibility (χ_τ), we derive a nonlinear control law for quantum coherence. We demonstrate that decoherence can be treated as a deterministic dynamical process governed by the feedback equation dχ_τ / dt = −α · Γ_τ · χ_τ + λ · (1 − χ_τ). Our numerical simulations confirm the formation of metastable coherence plateaus, where the effective qubit lifetime is extended significantly beyond the standard Lindbladian limit (e.g., from 100 µs to 1.5 ms in transmon-based models). We further specify a hardware-ready Temporal Phase-Locked Loop (TPLL) architecture, proving that with control latencies below 500 ns, active synchronization of the temporal metric becomes feasible on modern FPGA-based controllers. This framework provides a path toward fault-tolerant quantum computing by enabling fidelity-by-design at the physical layer, potentially providing a substantial reduction in QEC overhead by maintaining high physical fidelity prior to logical encoding. Keywords nonlinear phase stabilization; temporal susceptibility χτ; Lie-observable-dependent renormalization (LA-ODR); fixed-point Lindbladian; quantum decoherence; active feedback control; temporal phase-locked loop (TPLL); NISQ devices; superconducting qubits; cold atom arrays
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
Abstract: The scalability of Noisy Intermediate-Scale Quantum (NISQ) devices remains fundamentally limited by decoherence, which conventional dynamical decoupling and quantum error correction 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 observable-dependent renormalization (LA-ODR) framework, 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 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). Three operationally distinct zones are characterized by χ_τ thresholds, and two experimentally distinguishable signatures — Phase Inertia and Avalanche Collapse — are predicted. The TPLL is compared with dynamical decoupling, quantum error correction, and discrete time crystals, establishing complementarity rather than competition. The mathematical foundations rest on four global stability theorems via Lyapunov analysis and Chiba renormalization-group flow. Index Terms: Quantum coherence; decoherence control; temporal susceptibility; LA-ODR; Temporal Phase-Locked Loop (TPLL); Kyiv–Ohnishi flow; NISQ devices; open quantum systems; Lyapunov stability; Lie algebra; FPGA quantum control; nonlinear dynamics.