Synaptic Algebras as Models for Quantum Mechanics

Steven J. Burden, Ronald D.G. McKay

Kayra Ügümü

Synaptic plasticity—the capacity of neural circuits to strengthen, weaken, or reconfigure connections in response to activity—is fundamental to learning, memory formation, and adaptive behavior. Classical computational models have advanced the understanding of plasticity, but they struggle to fully capture the high-dimensional, nonlinear, and quantum-biophysical processes that shape synaptic dynamics at molecular and network scales. This study explores a quantum simulation framework for modeling synaptic plasticity mechanisms by leveraging variational quantum circuits, Hamiltonian-based learning rules, and quantum state representations of neuronal interactions. The proposed approach encodes synaptic weight updates, spike-timing–dependent plasticity (STDP), and Hebbian/anti-Hebbian processes within quantum operators capable of expressing richer correlation structures than classical models. Preliminary results demonstrate that quantum simulations can represent multi-synapse entanglement, non-Markovian memory traces, and complex attractor transitions that approximate biological synaptic behaviors with enhanced precision. These findings highlight the emerging role of quantum computational tools in uncovering new aspects of neural adaptability and advancing next-generation computational neuroscience.

In this study, we explore the impact of quantum effects on synaptic activity and their implications for the deterministic model of neural processes. By simulating synaptic events in a large-scale neural network, we demonstrate how small probabilistic quantum events can accumulate and introduce variability in neural behavior. Our model incorporates Dirac delta functions to simulate sudden changes in synaptic probabilities, creating a non-linear, seesaw effect in the cumulative synaptic activity curve. The results reveal that even minimal quantum effects, when scaled to the vast number of synapses in the human brain, can lead to significant dissociations in neural activity. These findings challenge the traditional deterministic view, suggesting that neural processes—and by extension, decision-making and movements—may inherently incorporate elements of randomness. This probabilistic perspective aligns with theories of free will and underscores the need for further empirical research to validate the role of quantum mechanics in neuroscience. Our study provides a theoretical framework for understanding the complex interplay between quantum effects and neural dynamics, opening new avenues for exploring the nature of consciousness and the fundamental principles governing reality.

John C. Inkson

Yuichiro Kitajima

F. Beck

In the struggle about the role of monism and dualism as basic concepts of the mind-brain relation the indeterminacy of quantum events has led an increasing number of authors to postulate quantum brain dynamics as the key towards a scientific understanding of consciousness. In most cases some specific form of macroscopic quantum states in the brain are invoked without giving details for their occurrence or persistence. This raises immediately the question how such states could survive thermal fluctuations in the hot and wet brain environment. In this paper we present a model for a quantum mechanical trigger which regulates synaptic exocytosis, the regulator for ordered brain activity. The model is based on a quantum mechanical tunnelling process which is stable against thermal fluctuations and consistent with the physiological conditions of the synaptic membrane.