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This manuscript aims to illustrate a quantum-classical dissipative theory (suited to be converted to effective algorithms for numerical simulations) within the long-term project of studying molecular processes in the brain. Other…
We develop the statistical mechanics of the Hopfield model in a transverse field to investigate how quantum fluctuations affect the macroscopic behavior of neural networks. When the number of embedded patterns is finite, the Trotter…
Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the…
Artificial intelligence (AI) has drawn significant inspiration from neuroscience to develop artificial neural network (ANN) models. However, these models remain constrained by the Von Neumann architecture and struggle to capture the…
The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…
We consider continuous time Hopfield-like recurrent networks as dynamical models for gene regulation and neural networks. We are interested in networks that contain n high-degree nodes preferably connected to a large number of Ns weakly…
I start from the fundamental principles of non-relativistic quantum mechanics, without probability, and interpret them using the notion of coexistence: a quantum state can be read, not uniquely, as a coexistence of other quantum states,…
Motivated by the potential similarities between the underlying mechanisms of the enhanced memory storage capacity in black holes and in brain networks, we construct an artificial quantum neural network based on gravity-like synaptic…
We present a contextualist statistical realistic model for quantum-like representations in physics, cognitive science and psychology. We apply this model to describe cognitive experiments to check quantum-like structures of mental…
Classical shallow networks are universal approximators. Given a sufficient number of neurons, they can reproduce any continuous function to arbitrary precision, with a resource cost that scales linearly in both the input size and the number…
An important difference between brains and deep neural networks is the way they learn. Nervous systems learn online where a stream of noisy data points are presented in a non-independent, identically distributed (non-i.i.d.) way. Further,…
Quantum mechanics traditionally places the observer outside of the system being studied and employs the Born interpretation. In this and related papers the observer is placed inside the system. To accomplish this, special rules are required…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
Quantum neuromorphic computing physically implements neural networks in brain-inspired quantum hardware to speed up their computation. In this perspective article, we show that this emerging paradigm could make the best use of the existing…
Understanding of how biological neural networks process information is one of the biggest open scientific questions of our time. Advances in machine learning and artificial neural networks have enabled the modeling of neuronal behavior, but…
This paper combines quantum computation with classical neural network theory to produce a quantum computational learning algorithm. Quantum computation uses microscopic quantum level effects to perform computational tasks and has produced…
We consider a system of two-level quantum quasi-spins and gauge bosons put on a 3+1D lattice. As a model of neural network of the brain functions, these spins describe neurons quantum-mechanically, and the gauge bosons describes weights of…
Algorithms for associative memory typically rely on a network of many connected units. The prototypical example is the Hopfield model, whose generalizations to the quantum realm are mainly based on open quantum Ising models. We propose a…
I present a quantum-tunnelling oscillator model as a universal dynamical engine for two paradigmatic problems in quantum cognition theory -- optical illusion perception and group decision making -- where individuals are treated as…
In this paper we propose the use of neural interference as the origin of quantum-like effects in the brain. We do so by using a neural oscillator model consistent with neurophysiological data. The model used was shown to reproduce well the…