It is unclear whether quantum phenomena can be observed in brain recordings because of thermal noise causing decoherence, that is, quantum superpositions and entanglement quickly collapsing into classical, i.e. non-quantum states. This paper first demonstrates that neuronal noise of the Brownian motion type is mathematically equivalent to a wave-particle description of the kind predicted by a fundamental equation in quantum mechanics known as the Schrödinger equation. It then extends the considerations to the more realistic FitzHugh-Nagumo model which has been widely used to describe neuronal dynamics. This approach could provide new insights into the underlying mechanisms of brain function.
It is unclear whether quantum phenomena can be observed in brain recordings because of thermal noise causing decoherence, that is, quantum superpositions and entanglement quickly collapsing into classical, i.e. non-quantum states. This paper first demonstrates that neuronal noise of the Brownian motion type is mathematically equivalent to a wave-particle description of the kind predicted by a fundamental equation in quantum mechanics known as the Schrödinger equation. It then extends the considerations to the more realistic FitzHugh-Nagumo model which has been widely used to describe neuronal dynamics. This approach could provide new insights into the underlying mechanisms of brain function.
Despite the prevalent view that quantum mechanics is irrelevant to macroscopic biological systems because of inherent noise and decoherence, this paper demonstrates that the electrical noise (Brownian motion) in neuron membranes gives rise to an `emergent' Schrödinger equation involving a new neuronal constant ℏ^, fundamentally challenging the standard view of neuronal behaviour. This result could provide new insights into the underlying mechanisms of brain function, thus challenging existing paradigms in both quantum physics and neuroscience. A possible empirical test of this emergent quantum behaviour would be to look for quantum fluctuations in subthreshold neural oscillations.
Traditional brain emulation approaches often rely on classical computational models that inadequately capture the stochastic, nonlinear, and potentially coherent features of biological neural systems. In this position paper, we introduce NeuroQ a quantum-inspired framework grounded in stochastic mechanics, particularly Nelson's formulation. By reformulating the FitzHugh-Nagumo neuron model with structured noise, we derive a Schrödinger-like equation that encodes membrane dynamics in a quantum-like formalism. This formulation enables the use of quantum simulation strategies-including Hamiltonian encoding, variational eigensolvers, and continuous-variable models-for neural emulation. We outline a conceptual roadmap for implementing NeuroQ on near-term quantum platforms and discuss its broader implications for neuromorphic quantum hardware, artificial consciousness, and time-symmetric cognitive architectures. Rather than demonstrating a working prototype, this work aims to establish a coherent theoretical foundation for future research in quantum brain emulation.
We first point out that nonrelativistic quantum mechanics formulated at imaginary time s = it can formally be recognized as the Fokker-Planck description of a classical Brownian motion, which occurs (in general) in a medium where particles are absorbed and emitted. We next offer a new formulation of quantum dynamics, which is basically the Langevin treatment of that Brownian motion. More explicitly, we derive a noise average representation of the transition probability W ( X", s"|X', s' ) in terms of the solutions to a Langevin equation with a Gaussian white noise. Upon analytic continuation back to real time W ( X", s"|X', s' ) becomes the propagator of the original Schrödinger equation, namely we have ⟨ X", t"|X', t' ⟩ = W ( X", it"|X', it' ). The main advantage of this approach is to permit a systematic application to quantum-dynamical problems of the mathematical techniques developed in the theory of classical stochastic processes, even when vector potentials and/or time-dependent potentials are present.
Introduction This chapter gives the physical and mathematical basis of decoherence in quantum systems, with particular emphasis on its importance in quantum information theory and quantum computation. We assume that the reader is already familiar with the basics of quantum mechanics, such as wave functions, the Schrödinger equation, and Hilbert spaces, which are covered in standard textbooks. Nevertheless, all basic concepts will be at least briefly defined and described. A working knowledge of graduate-level linear algebra and calculus is also assumed. In quantum information processing, the term decoherence is often used loosely to describe any kind of noise that can affect a quantum system. This can include sources of noise that seem, qualitatively, to be quite different from each other. These noise sources include: (i) Random driving forces from the environment (e.g., Brownian motion). (ii) Interactions that produce entanglement between the system and the environment. (iii) Statistical imprecision in the experimental controls on the system (e.g., timing errors, frequency fluctuations, etc.). Remarkably, all of these sources of noise can be described by an almost identical mathematical framework, in which pure quantum states can evolve into mixed quantum states, and the quantum effects necessary for information processing – interference, entanglement, and reversible evolution – are disrupted. The chapter begins by examining a highly schematic model of decoherence, involving systems of qubits, but uses this model to present the mathematical formalism used in describing more realistic systems as well.
In recent decades, progress in the field of neurosciences has triggered an interest in understanding mind-brain relationships. Quantum Mechanics (QM) has been present in the debate from its beginnings through the well-known measurement paradox. The standard interpretation of QM considers two basic, fundamentally irreducible, processes: the deterministic evolution of the wave-function according to the Schrodinger equation, once the initial conditions have been settled; and the indeterministic wave-function collapse into one of the possible outcomes, after performing a specific measurement. So, QM would point to the limits of a purely deterministic view of nature and, in particular, of brains. Nevertheless, QM’s relevance for the brain’s physics is still to be proven. Detractors of the QM influence are confident of the role of decoherent processes at different physical scales in order to ensure a classical deterministic behavior of the brain. However, little attention is paid to the epistemic implications of invoking decoherence for the mind-brain problem. In this paper, (i) we present lasting QM models stating a specific view of human consciousness and make explicit their position regarding the relationship between the physical activity of neurons and/or networks of neurons and the phenomenal conscious experience; (ii) we review the main criticisms of the relevance of QM in the brain and, most importantly, we bring out the philosophical implications behind the usual recourse to decoherence in the transition from the quantum to the classical world, explaining why the mind-brain problem and the measurement paradox should not be disentangled.
Quantum mechanics exhibits a broad collection of theoretical results in complete agreement with experimental evidence. Besides showing unquestionable success in the description of isolated systems, it can be also successfully used to characterize non-isolated quantum system. In such a case, phenomena like dissipation, diffusion or decoherence. The theory of open quantum systems provides the framework where such features can be conveniently explained. \nThis thesis is about decoherence and collapse models. Albeit conceptually they are very far from each other, they both belong the framework of open quantum systems. Indeed, they consider systems interacting with an external entity: an environment for decoherence models, a noise for collapse models. Although the external influence has different origin, they can be described by similar dynamical equations and, to confirm or falsify them, the same experimental tests can be performed. \nThe quantum Brownian motion model can be considered the paradigm of decoherence models. We provide an exact and analytic equation for the time evolution of the operators and we show that the corresponding equation for the states is equivalent to well-known results in the literature. Our derivation allows to compute the time evolution of physically relevant quantities in a much easier way than previous formulations. Moreover, we are not bound to compute the time evolution of the state of the system, which in general is a complicated task. The explicit dependence on the initial state appears only in the initial expectation values and not in the dynamics. This makes possible the derivation of expectation values also for nontrivial states. \nAnother decoherence model we considered is a recently proposed model, based on the mass-energy equivalence. The model describes a decoherence source acting universally on every system whose superposition is extended on positions experiencing different gravitational potentials. We studied the conditions under which this mechanism becomes the dominant decoherence effect in typical interferometric experiments. We show that current experiments are off by several orders of magnitude. New ideas are needed to achieve the necessary requirements. \nThe second part of this thesis concerns collapse models, in particular the Continuous Spontaneous Localization (CSL) model. We focus on experimental tests that can probe it. In this respect, experiments can be grouped in two classes: interferometric tests and non-interferometric ones. The first class includes those experiments, which directly create and detect quantum superpositions of the center of mass of massive systems. The strongest bounds on the CSL parameters come from the second class of non-interferometric experiments, which are sensitive to small position displacements and detect CSL-induced diffusion in position. \nWe investigate how we can benefit from the non-interferometric perspective given by optomechanical setups, which have reached high sensitivities as force and position sensors. Three examples are considered.\nFirst, we compute the upper bounds on the CSL parameters, which can be inferred by the gravitational wave detectors LIGO, LISA Pathfinder and AURIGA.\nSecond, we report new results from an experiment based on a high-quality cantilever cooled to millikelvin temperature. High accuracy measurements of the cantilever thermal fluctuations reveal a nonthermal force noise of unknown origin. This excess noise is compatible with the CSL heating predicted by Adler. Several physical mechanisms able to explain the observed noise have been ruled out.\nThird, we propose an unattempted non-interferometric test aimed to investigate the still unexplored region of the CSL parameter space. Our proposal relies on torsional degrees of freedom rather than the usual vibrational ones. We believe that the test that has been put forward here, will eventually probe the unexplored CSL parameter space.