Abstract It has historically proven difficult to explain the relationship between neural activity and representative information content. A new approach focuses on the unique properties of cortical neurons, which allow both upstream signals and random electrical noise to affect the likelihood of reaching action potential threshold. Here, each electron is modeled as an electromagnetic point source, inter-acting in a probabilistic manner with each neuronal membrane. The electron is described as some set of probability amplitudes, distributed across five orthogonal axes: x, y, z, energy state , and time . The membrane potential of each neuron is defined by the probabilistic spatial position and atomic orbital of each local electron, after some time evolution. The mixed sum of all probabilistic component pure states is the physical quantity of information held by the neural network, given by a complex-valued wavefunction. If the probabilistic trajectory of each electron over time t affects the voltage state of multiple computational units, then the system state must be computed as a whole, with the state of each neuron being resolved as every component pure state is resolved. This computational process yields a defined system state at a defined location in time, which immediately becomes the past as a new probability density forms. If the membrane surface of each computational unit is also a charge-detecting polymer substrate that meets the criteria of a holographic recording surface, then this encoding process will generate a holographic projection of representative information content. The constructive and destructive interference of high-dimensional probability amplitudes yields a non-deterministic computational outcome for each neuron. That now-defined system state is paired with a multi-sensory percept, which is exclusively accessed by the encoding structure, with content limited by the range and sensitivity of the sensory apparatus. This model usefully offers a plausible explanation for both perceptual content and non-deterministic computational outcomes emerging from cortical neural network activity.
Abstract It has historically proven difficult to explain the relationship between neural activity and representative information content. A new approach focuses on the unique properties of cortical neurons, which allow both upstream signals and random electrical noise to affect the likelihood of reaching action potential threshold. Here, each electron is modeled as an electromagnetic point source, inter-acting in a probabilistic manner with each neuronal membrane. The electron is described as some set of probability amplitudes, distributed across five orthogonal axes: x, y, z, energy state , and time . The membrane potential of each neuron is defined by the probabilistic spatial position and atomic orbital of each local electron, after some time evolution. The mixed sum of all probabilistic component pure states is the physical quantity of information held by the neural network, given by a complex-valued wavefunction. If the probabilistic trajectory of each electron over time t affects the voltage state of multiple computational units, then the system state must be computed as a whole, with the state of each neuron being resolved as every component pure state is resolved. This computational process yields a defined system state at a defined location in time, which immediately becomes the past as a new probability density forms. If the membrane surface of each computational unit is also a charge-detecting polymer substrate that meets the criteria of a holographic recording surface, then this encoding process will generate a holographic projection of representative information content. The constructive and destructive interference of high-dimensional probability amplitudes yields a non-deterministic computational outcome for each neuron. That now-defined system state is paired with a multi-sensory percept, which is exclusively accessed by the encoding structure, with content limited by the range and sensitivity of the sensory apparatus. This model usefully offers a plausible explanation for both perceptual content and non-deterministic computational outcomes emerging from cortical neural network activity.
In cortical neurons, spontaneous membrane potential fluctuations affect the likelihood of firing an action potential. Yet despite retaining sensitivity to random electrical noise in gating signaling outcomes, these cells achieve highly accurate computations with extraordinary energy efficiency. A new approach models the inherently probabilistic nature of cortical neuron firing as a thermodynamic process of non-deterministic computation. Typically, the cortical neuron is modeled as a binary computational unit, in either an off-state or an on-state, but here, the cortical neuron is modeled as a two-state quantum system, with some probability of switching from an off-state to an on-state. This approach explicitly takes into account the contribution of random electrical noise in gating signaling outcomes, particularly during cortical up-states. In this model, the membrane potential is described as the mixed sum of all component microstates, or the quantity of von Neumann entropy encoded by the computational unit. This distribution of macrostates is given by a density matrix, which undergoes a unitary change of basis as each unit, ‘System A’, interacts with its surrounding environment, ‘System B’. Any linear correlations reduce the number of distinguishable pure states, leading to the selection of an optimal system state in the present context. This process of information compression is shown to be equivalent to the extraction of predictive value from a thermodynamic quantity of information. Calculations demonstrate that estimated coulomb scattering profiles and decoherence timescales in cortical neurons are consistent with a quantum system, with random electrical noise driving signaling outcomes.
A model of consciousness is proposed, in which the experience attributable to a single neuron is related to its instantaneous firing rate. In that the experience afforded by a sensory neuron can only be quantified within statistical limits from the incidence of spikes across multiple presentations of a stimulus, consciousness remains inaccessible to direct measurement on a single trial. In this way, the model disambiguates subjective experience from objective neural properties. The model adopts a quantum mechanical formalism, in which the state of the neuron is represented as a vector in \nA complex vector space, or as a projector from the space onto that vector. Extension of this formalism to more realistic neural systems merely requires the assimilation of the quantum mechanical principles applicable in this broader context. \nInitially, a mathematical expression for the smooth evolution of a single dimension of perceptual experience will be derived for the single neuron case. \n \nThere follows a description of how the neural state itself might evolve in this \nprocess, utilising the quantum operations formalism of amplitude damping. This approach reveals how smooth evolution of conscious experience might arise from discrete spikes and discontinuous synaptic interaction between neurons. A tensor product formalism will be used to describe the combination of state spaces of individual neurons to form a composite neural space, in which a pure 'mental state' would represent unified conscious experience. The binding of elementary features in this non-local mental state would be reflected in specific patterns of correlated neural firing between remote brain regions. In contrast, the conventional neuron doctrine is classical and local realistic. Local realistic constraints, expressed as Bell Inequalities, limit potential correlations in firing between remote neurons, presenting an opportunity for the experimental test of the scheme in a neurophysiologic thought experiment.
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.
This paper proposes a novel neuron model leveraging the principles of quantum state superposition. Traditional neuron models, based on classical probability, struggle to accurately represent the complex information processing within biological neurons. This model introduces a fundamentally different approach by modeling synaptic connections as quantum states in superposition. The propagation of neural signals is then governed by the quantum mechanical interaction of these superimposed states. We define a mathematical framework incorporating key concepts from quantum mechanics, including superposition, entanglement, and quantum measurement, to describe the dynamics of this model. The core of the model lies in the equation: $ \frac{d| \Psi(t) \rangle}{dt} = \mathcal{H} | \Psi(t) \rangle $ where ∣Ψ(t)⟩ represents the quantum state of the neuron at time *t*, and H is the Hamiltonian operator describing the neuron's dynamics. We explore scenarios involving multiple inputs and their influence on the superposition state. The model demonstrates the potential for enhanced information processing compared to conventional models, particularly in scenarios requiring parallel computation and robust information storage. Furthermore, we discuss the implications of this approach for understanding and potentially mimicking biological neural computation. The model presented offers a theoretical foundation for exploring quantum computation within biological systems.
The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described employing multiple connected electric circuits containing capacitors, voltage sources, and conductances. These conductances depend on previous depolarizing membrane voltages, which can be identified with a memory resistive element called memristor. Inspired by the recent quantization of the memristor, a simplified Hodgkin-Huxley model including a single ion channel has been studied in the quantum regime. Here, we study the quantization of the complete Hodgkin-Huxley model, accounting for all three ion channels, and introduce a quantum source, together with an output waveguide as the connection to a subsequent neuron. Our system consists of two memristors and one resistor, describing potassium, sodium, and chloride ion channel conductances, respectively, and a capacitor to account for the axon's membrane capacitance. We study the behavior of both ion channel conductivities and the circuit voltage, and we compare the results with those of the single channel, for a given quantum state of the source. It is remarkable that, in opposition to the single-channel model, we are able to reproduce the voltage spike in an adiabatic regime. Arguing that the circuit voltage is a quantum variable, we find a purely quantum-mechanical contribution in the system voltage's second moment. This work represents a complete study of the Hodgkin-Huxley model in the quantum regime, establishing a recipe for constructing quantum neuron networks with quantum state inputs. This paves the way for advances in hardware-based neuromorphic quantum computing, as well as quantum machine learning, which might be more efficient resource-wise.
We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites, the axons and the synapses as well as the surrounding glial cells, as a collection of all kinds of oscillating modes arisen from the electric circuital environment of neuronal action potentials. By analyzing the dynamics of this neural model through the master equation approach of open quantum systems, we investigate the collective behavior of neurons. After applying stimulations to the neural network, the neuronal collective state is activated and shows the action potential behavior. We find that this model can generate random neuron-neuron interactions and is proper to describe the process of information transmission in the nervous system physically, which may pave a potential route toward understanding the dynamics of nervous system.