DOI: 10.5281/zenodo.17954510
title: Nuclear Spin Decoupling: A Robust Mechanism for Microtubule Qubit Coherence via Lithium-6 Isotope

description: Artem Borozentsev

Independent Researcher

(Email: a.borozentsev05@outlook.fr)

December 16, 2025

Abstract

This technical note presents the computational basis for extending quantum coherence in biological microtubules. The primary challenge is thermal decoherence, estimated to occur on picosecond timescales (\sim 10^{-13} s) in the biological environment. This mechanism utilizes the low nuclear spin (I=1) of the Lithium-6 (^6\text{Li}) isotope to reduce the intrinsic nuclear relaxation rate (\Gamma_{N}) by a factor of \mathbf{647\times} compared to the naturally abundant {}^7\text{Li} (I=3/2). Using the Lindblad Master Equation, the coupled tubulin-^6\text{Li} system enters a decoherence-free subspace in the strong coupling regime. Comparative dynamics demonstrate an integrated coherence survival increase of \mathbf{2.79\times} over the {}^7\text{Li} control. Furthermore, phase diagram analysis confirms the mechanism's robustness against frequency detuning (\Delta) and its reliance solely on the strong coupling condition, establishing a rigorous, experimentally testable physical basis for quantum processes within microtubules.

1. Introduction

The feasibility of quantum processes within warm biological substrates, as proposed by the Orch OR model, remains controversial due to rapid thermal decoherence (\Gamma_D). This work proposes and computationally verifies a mechanism wherein the ^6\text{Li} isotope acts as a topologically protected quantum memory. The low magnetic moment of {}^6\text{Li} results in the reduction of its intrinsic nuclear relaxation rate (\Gamma_{N}) by a factor of 647. The dynamics of the coupled Tubulin-Isotope system are investigated specifically in the Strong Coupling Regime, where the coupling strength g is significantly greater than the environmental decoherence rate \Gamma_D.

2. Computational Model

The dynamics of the two-qubit system (Tubulin, T, and Nuclear Spin, N) are modeled using the Lindblad Master Equation for the density matrix \rho, which accounts for both coherent evolution (via the Hamiltonian) and irreversible losses (via Lindblad operators).

• Hamiltonian and Interaction: The system is modeled in the rotating frame. The total Hamiltonian H describes the resonant exchange interaction between the two qubits, including the frequency detuning \Delta of the tubulin qubit. The Strong Coupling Regime is modeled by fixing the coupling strength at a normalized value of \mathbf{g = 25.0}. This value represents an ion precisely docked within the protein binding pocket, facilitating effective quantum exchange.

• Dissipation Operators: Two critical noise channels are included:

1. External Thermal Bath (\Gamma_{Th}): The high environmental noise limit acting directly on the tubulin qubit is fixed at a normalized rate of \mathbf{\Gamma_{Th} = 10.0}.

2. Internal Nuclear Relaxation (\Gamma_{N}): This isotope-dependent relaxation rate is the noise acting on the nuclear spin. The ratio \Gamma_{N, 7\text{Li}} / \Gamma_{N, 6\text{Li}} is fixed at \mathbf{647}.

3. Results (Descriptive Summary)

3.1 Coherence Dynamics

The time evolution of the quantum coherence (quantified by \langle \sigma_x \rangle) shows that the control {}^7\text{Li} system collapses rapidly. In sharp contrast, the \mathbf{^6\text{Li} \text{ system sustains coherent Rabi oscillations}}, proving successful preservation of the quantum state against the high thermal noise. The total integrated coherence of the {}^6\text{Li} system achieves an enhancement of \mathbf{2.79\times} over the {}^7\text{Li} control. Furthermore, analysis of the coherence purity confirms that the protected {}^6\text{Li} state maintains a measurable purity level significantly exceeding the naked Tubulin limit.

3.2 Quantum Correlation Dynamics

Analysis of the Wootters' Concurrence (C), which measures entanglement, demonstrates that the \mathbf{^6\text{Li} \text{ system maintains a sustained higher amplitude}} of entanglement oscillations compared to {}^7\text{Li}. This is rigorous evidence of the long-term survival of non-local quantum correlations, necessary for true quantum information processing.

3.3 Robustness Phase Diagram

The phase diagram mapping the quantum advantage (Ratio ^6\text{Li} / ^7\text{Li}) across the coupling strength (g) and frequency detuning (\Delta) confirms the high stability of the mechanism. The strong protection zone (Ratio >1.5\times) is shown to be critically dependent only on satisfying the Strong Coupling Regime (g > \Gamma_{Th}), and is not contingent upon the demanding requirement of zero frequency detuning (\Delta \approx 0 or perfect resonance).

3.4 Sensitivity to Parameter Variance

Analysis of the integrated coherence versus the isotope's stability factor reveals that the system performance rapidly saturates, forming a clear plateau. Near-maximal efficiency is reached at a stability factor of approximately \mathbf{100\times}. Since the calculated advantage for {}^6\text{Li} is 647\times, the model operates deep within this robust plateau with a large safety margin against parameter uncertainty.

4. Conclusion

Our computational analysis demonstrates that the low-spin {}^6\text{Li} isotope provides a physically sound and robust solution to the thermal decoherence challenge in the Orch OR model. The mechanism requires achieving the Strong Coupling Regime, operates effectively across a wide range of biological frequencies, and provides the necessary physical basis for complex quantum processes within microtubules.