We present a biologically inspired quantum neural network that encodes neuronal populations as fully connected qubits governed by the Lipkin-Meshkov-Glick (LMG) quantum Hamiltonian and stabilized by a synaptic-efficacy feedback implementing activity-dependent homeostatic control. The framework links collective quantum many-body modes and attractor structure to population homeostasis and rhythmogenesis, outlining scalable computational primitives -- stable set points, controllable oscillations, and size-dependent robustness -- that position LMG-based architectures as promising blueprints for bio-inspired quantum brains on future quantum hardware.
The study of learning and information processing is a central theme in neuroscience, neural networks theory, and artificial intelligence, drawing the attention of the scientific community for decades. Recently, these topics have extended for quantum systems. For instance, advances in quantum computing motivated the creation of autonomous systems properly designed to try to find the quantum advantage in information processing, giving rise to emerging fields such as quantum machine learning and quantum artificial intelligence [4,15]. Within this context, several proposals have described autonomous quantum devices capable of estimating states or unitaries [17,28], implementing quantum reinforcement learning [5,13,14,27,30,56], and constructing quantum neural networks (QNNs) [12,53]. Also, variational quantum algorithms have been developed recently and used for such tasks [11].
Theoretical models have been proposed for both single quantum neurons [8,22,47], and network architectures, including quantum perceptrons [40,55] and Hopfield networks [45] whose computational properties and storage capacity have been recently reported [51]. Research in this area aims to determine whether such quantum analogues can surpass classical neural networks in pattern recognition and classification and memory storage capacity, while also incorporating biological inspiration [48]. Within this scenario, typically in most of the recent works concerning developing of quantum neural networks, binary neurons are replaced by qubits with simplified interactions. However, most of the classical and biologically inspired neural network models emphasize the crucial role of synapses [3] -nonlinear elements responsible for transmitting information through pair wise processes such as neurotransmitter release and recycling and high-order interactions involving astrocyte’s control of synaptic transmission [33]. Thus, experimental neuroscience has shown that synapses are dynamic, activity-dependent mechanisms whose transmission efficiency can either decrease (synaptic depression) or increase (facilitation) with presynaptic activity [54]. These mechanisms have major computational consequences [50], influencing memory capacity [31,52], dynamic memory formation [39,49], and stochastic resonances during weak-signal processing [32]. Shey can also lead to an imbalance between excitation and inhibition, causing a quick explosive increase of excitatory activity that originates intriguing brain waves [41] with different information content [34].
Building on these previous insights, recently has been proposed a quantum synapse framework incorporating synaptic plasticity, in which a quantum system with biologically inspired activitydependent coupling between qubits was analyzed to study the effects of synaptic depression on qubit interactions and entanglement [48]. However, that model was limited to a small-scale system of only two qubits, which does not adequately represent the behavior of large quantum networks.
Furthermore, the detailed treatment of qubit interactions in that study makes the approach less practical for extending to systems with many qubits, as the dimensionality of the state space increases rapidly with system size.
The Lipkin-Meshkov-Glick (LMG) Hamiltonian is a compact yet highly expressive framework for exploring quantum many-body phenomena. Originating in nuclear physics [24][25][26]43], it provides a controlled setting for analyzing particle-particle and particle-hole correlations among neutrons and protons, as well as for benchmarking approximate many-body techniques. Its applicability extends well beyond that context, e.g. in condensed-matter physics it offers an effective description of Bose-Einstein condensates and Josephson-junction dynamics [23,35,36]. Also in optical physics, it has been used for the metrological quantification of spin-squeezed states and the engineering of multipartite entanglement, both in the presence of an external field and for the quadratic collectivespin Hamiltonian in the absence of a field [18,20,21,42]. Taken together, the LMG model has become a standard tool for modeling collectively interacting two-level quantum systems. Within this framework, the existence of first-, second-, and third-order quantum phase transitions (QPTs) has been demonstrated [10,16]. More recently, it has been established that the associated quantum phase diagrams can be rigorously characterized in terms of phase-space delocalization measures, complemented by entanglement-entropy measures [6,7,9,38,44]. In what follows, we focus on the formulation of the LMG model that arises naturally in one-dimensional lattices of interacting spins -namely, an anisotropic XY (Ising-type) model in a transverse field with all-to-all couplings.
With this in mind, we here propose for the first time a quantum neural system biologically inspired including some level of short-term synaptic plasticity in the system and which is based in this LM
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