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arXiv:2411.12362 · Physical Review Research

Active quantum memory: Exploring the quantum dynamical process of voltage-gated ion channel

Yu-Juan Sun, Wei-Min Zhang

Published Jul 10, 2026• 0 citations

Abstract

It is known that the opening or closing mechanism of a voltage-gated ion channel is triggered by the potential difference across the cell membrane in the nervous system. Based on this picture, we model the ion channel as a nanoscale two-terminal ionic tunneling junction. We apply an external time-varying voltage on the junction to mimic the membrane potential difference in the stimulation of neurons. We derive the non-Markovian quantum Langevin equation from the first principle of quantum mechanics for the ion transport in ion channels, and obtain the ion transport current in terms of quantum tunnelings of ions controlled by the time-varying voltage. We find that the time-varying voltage induces an effective magnetic flux, which causes quantum coherence in ion tunnelings. This effective magnetic flux induces further an oscillatory component to the spectral structure of the ion system, forming a time-dependent quantum memory. Such voltage-induced memory is defined as the active quantum memory, which manifests in the system with a regular oscillatory sideband structure in the ion transport current. The sideband structure demonstrates a multicrossing hysteresis in the current-voltage ( I − V ) curve, responding to the variation of the time-varying voltage (membrane potential difference). We also find that the strength of active quantum memory can be described by the ratio of amplitude and frequency of the time-varying voltage, and can be quantitatively measured through the number of nonzero cross points in the I − V hysteresis and conductance-voltage diagram. Additionally, we explore the temperature dependence of the active quantum memory in such a system. Further, we apply this model to the ion channel system on the biological energy scale. The description of these active quantum memory characteristics provides a quantum mechanical understanding to the underlying mechanism of ion channel dynamics.

DOI: 10.1103/ll5d-t22x

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It is known that the opening or closing mechanism of a voltage-gated ion channel is triggered by the potential difference across the cell membrane in the nervous system. Based on this picture, we model the ion channel as a nanoscale two-terminal ionic tunneling junction. We apply an external time-varying voltage on the junction to mimic the membrane potential difference in the stimulation of neurons. We derive the non-Markovian quantum Langevin equation from the first principle of quantum mechanics for the ion transport in ion channels, and obtain the ion transport current in terms of quantum tunnelings of ions controlled by the time-varying voltage. We find that the time-varying voltage induces an effective magnetic flux, which causes quantum coherence in ion tunnelings. This effective magnetic flux induces further an oscillatory component to the spectral structure of the ion system, forming a time-dependent quantum memory. Such voltage-induced memory is defined as the active quantum memory, which manifests in the system with a regular oscillatory sideband structure in the ion transport current. The sideband structure demonstrates a multicrossing hysteresis in the current-voltage ( I − V ) curve, responding to the variation of the time-varying voltage (membrane potential difference). We also find that the strength of active quantum memory can be described by the ratio of amplitude and frequency of the time-varying voltage, and can be quantitatively measured through the number of nonzero cross points in the I − V hysteresis and conductance-voltage diagram. Additionally, we explore the temperature dependence of the active quantum memory in such a system. Further, we apply this model to the ion channel system on the biological energy scale. The description of these active quantum memory characteristics provides a quantum mechanical understanding to the underlying mechanism of ion channel dynamics.

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The resting membrane voltage of excitable cells such as neurons and muscle cells is determined by the electrochemical equilibrium of potassium and sodium ions. This voltage is calculated by using the Goldman–Hodgkin–Katz equation. However, from the quantum perspective, ions with significant quantum tunneling through closed channels can interfere with the electrochemical equilibrium and affect the value of the membrane voltage. Hence, in this case the equilibrium becomes quantum electrochemical. Therefore, the model of quantum tunneling of ions is used in this study to modify the Goldman–Hodgkin–Katz equation in such a way to calculate the resting membrane voltage at the point of equilibrium. According to the present calculations, it is found that lithium—with its lower mass—shows a significant depolarizing shift in membrane voltage. In addition to this, when the free gating energy of the closed channels decreases, even sodium and potassium ions depolarize the resting membrane voltage via quantum tunneling. This study proposes the concept of quantum electrochemical equilibrium, at which the electrical potential gradient, the concentration gradient and the quantum gradient (due to quantum tunneling) are balanced. Additionally, this concept may be used to solve many issues and problems in which the quantum behavior becomes more influential.

We investigate the effects of a quantum entanglement regime within an ion conducting molecule (ion channel) of the neuronal plasma membrane on the onset dynamics of propagating nerve pulses (action potentials). In particular, we model the onset parameters of the sodium current in the Hodgkin Huxley equation as three similar but independent probabilistic mechanisms which become quantum entangled. The underlying physics is general and can involve entanglement between various degrees of freedom underlaying ion transition states or 'gating states' during conduction, e.g. Na

^+

ions in different channel locations, or different 'affinity' states of ions with atoms lining the sub-regions of the channel protein ('filter-states'). We find that the 'quantum corrected' Hodgkin Huxley equation incorporating entangled systems states can reproduce action potential pulses with the critical onset dynamics observed recently in neocortical neurons in vivo by Naundorf et al. [Nature {\bf 440}, 1060 (20 April 2006)]. Interestingly, the suggested entanglement term can also slow down action potential initiation.

Understanding neural excitability and action potential generation is a cornerstone of neuroscience, relying on the complex interplay of biophysical mechanisms governed by ion channels in neuronal membranes. Traditional approaches, such as the Hodgkin-Huxley model, have provided a robust framework for simulating these processes using classical computational techniques. However, the advent of quantum computing opens new avenues for exploring neuronal dynamics, particularly due to ion movement's inherently quantum mechanical properties at atomic scales. In this study, I investigated the intersection of quantum computing and membrane biophysics, evaluating how quantum algorithms could revolutionize simulations of ion channel behavior and neuronal signaling. I began by analyzing the limitations of classical methods in handling high-dimensional, nonlinear systems. Next, I introduced key quantum computing principles, including qubits, superposition, and entanglement, and their potential applications in solving molecular dynamics and differential equations relevant to neuronal activity. Despite promising theoretical advantages, practical challenges such as qubit coherence, error rates, and hardware scalability must be addressed before quantum models can outperform classical simulations. I also discussed hybrid classical-quantum approaches as a transitional strategy, leveraging the strengths of both paradigms. By bridging neuroscience, biophysics, and quantum information science, I aimed to stimulate interdisciplinary research toward more efficient and accurate models of neural excitability.

A new class of formal latent-variable stochastic processes called hidden quantum models (HQM's) is defined in order to clarify the theoretical foundations of ion channel signal processing. HQM's are based on quantum stochastic processes which formalize time-dependent observation. They allow the calculation of autocovariance functions which are essential for frequency-domain signal processing. HQM's based on a particular type of observation protocol called independent activated measurements are shown to to be distributionally equivalent to hidden Markov models yet without an underlying physical Markov process. Since the formal Markov processes are non-physical, the theory of activated measurement allows merging energy-based Eyring rate theories of ion channel behavior with the more common phenomenological Markov kinetic schemes to form energy-modulated quantum channels. Using the simplest quantum channel model consistent with neuronal membrane voltage-clamp experiments, activation eigenenergies are calculated for the Hodgkin-Huxley K+ and Na+ ion channels. It is also shown that maximizing entropy under constrained activation energy yields noise spectral densities approximating

S(f) \sim 1/f^α

, thus offering a biophysical explanation for the ubiquitous

1/f

-type in neurological signals.