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Symmetry
Special Issues
Quantum Information Applied in Neuroscience
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Quantum Information Applied in Neuroscience

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Life Sciences".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 25385

Special Issue Editor

Dr. Danko D. Georgiev

E-Mail Website
Guest Editor
Institute for Advanced Study, Varna, Bulgaria
Interests: quantum physics; quantum information; neuroscience; philosophy of mind; consciousness

Special Issue Information

Dear Colleagues,

Qubits are the smallest physical carriers of quantum information. The quantum information contained in the quantum state Ψ of a qubit has some truly remarkable properties. Qubits cannot be observed, read or deduced from experimental data as in the case of classical bits stored on a DVD. If we have a quantum version of DVD storing a string of qubits, in general, we also cannot copy, erase, or process with irreversible computational gates any of the stored qubits. Qubits can be transported from place to place similarly to classical bits, but each qubit cannot be cloned and delivered to multiple recipients. Because qubits cannot be wholly converted into classical bits, they cannot be broadcast. Multiple qubits, however, can be used to carry classical bits. Although n qubits can carry more than n classical bits of information, according to Holevo's theorem the greatest amount of classical information that can be retrieved by external observers is only n bits. Furthermore, the Bell and Kochen–Specker no-go theorems imply that quantum information is nonlocal and quantum correlations are enforced with superluminal speed. These fascinating properties of quantum information may not be reserved for manifestation only in modern quantum technologies, but may already have been employed for enhancement of the survival of evolving biological systems and boosting the power of their neural systems.

Continuous symmetries in the formulation of quantum mechanics are important for the identification of energy as a partial time derivative and momentum as a spatial gradient. Noether's theorem then establishes that every differentiable symmetry of the action of a physical system is associated with a corresponding conservation law, meaning that energy and momentum are conserved quantities. The Schrödinger equation, which is the core of quantum theory, can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated by the exponential of a self-adjoint operator, which is the quantum Hamiltonian. Unitarity of quantum evolution leads to conservation of quantum probabilities and constitutes an essential ingredient in the proofs of many of the quantum information-theoretic no-go theorems, including the celebrated quantum no-cloning theorem. But the appearance of symmetries in quantum foundations is not the only way that the concept of symmetry can enter neuroscience. The presence of biological order is essential for the operation of living systems and the spatial organization of repeated structural motifs has been shown to produce favorable boundary conditions for solving the Schrödinger equation that support extended life-time of quantum quasiparticles such as solitons in protein α-helices.

In this Special Issue, we invite contributions that apply quantum information theory as a tool for investigation of open questions in neuroscience and elucidation of brain function. Discussions on how symmetries in biological systems can support the harnessing of quantum effects by neural systems are most welcome.

Dr. Danko D. Georgiev
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Brain
  • Consciousness
  • Ion channels
  • Neural networks
  • Neural signaling
  • Proteins
  • Quantum chemistry
  • Quantum dynamics
  • Quantum entanglement
  • Quantum information
  • Quantum no-go theorems
  • Quantum tunneling

Published Papers (7 papers)

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Editorial

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3 pages, 192 KiB  
Editorial
Special Issue on Quantum Information Applied in Neuroscience
by Danko D. Georgiev
Symmetry 2022, 14(6), 1212; https://doi.org/10.3390/sym14061212 - 11 Jun 2022
Cited by 1 | Viewed by 1748
Abstract
The rapid progress achieved by quantum information science in recent decades was made possible by the realization that genuine quantum phenomena, for which their occurrences are forbidden by classical physics, are not a defect of quantum theory but are useful physical resources [...] [...] Read more.
The rapid progress achieved by quantum information science in recent decades was made possible by the realization that genuine quantum phenomena, for which their occurrences are forbidden by classical physics, are not a defect of quantum theory but are useful physical resources [...] Full article
(This article belongs to the Special Issue Quantum Information Applied in Neuroscience)

Research

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13 pages, 780 KiB  
Article
Modeling Neuronal Systems as an Open Quantum System
by Yu-Juan Sun and Wei-Min Zhang
Symmetry 2021, 13(9), 1603; https://doi.org/10.3390/sym13091603 - 1 Sep 2021
Cited by 3 | Viewed by 2494
Abstract
We propose a physical model for neurons to describe how neurons interact with one another through the surrounding materials of neuronal cell bodies. We model the neuronal cell surroundings, include the dendrites, the axons and the synapses, as well as the surrounding glial [...] Read more.
We propose a physical model for neurons to describe how neurons interact with one another through the surrounding materials of neuronal cell bodies. We model the neuronal cell surroundings, include the dendrites, the axons and the synapses, as well as the surrounding glial cells, as a continuous distribution of oscillating modes inspired from the electric circuital picture of neuronal action potential. By analyzing the dynamics of this neuronal model by using the master equation approach of open quantum systems, we investigated the collective behavior of neurons. After applying stimulations to the neuronal system, the neuron collective state is activated and shows the action potential behavior. We find that this model can generate random neuron–neuron interactions and is appropriate for describing the process of information transmission in the neuronal system, which may pave a potential route toward understanding the dynamics of nervous system. Full article
(This article belongs to the Special Issue Quantum Information Applied in Neuroscience)
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19 pages, 335 KiB  
Article
Parts and Composites of Quantum Systems
by Stanley P. Gudder
Symmetry 2021, 13(6), 1031; https://doi.org/10.3390/sym13061031 - 8 Jun 2021
Cited by 7 | Viewed by 1675
Abstract
We consider three types of entities for quantum measurements. In order of generality, these types are observables, instruments and measurement models. If α and β are entities, we define what it means for α to be a part of β. This relationship [...] Read more.
We consider three types of entities for quantum measurements. In order of generality, these types are observables, instruments and measurement models. If α and β are entities, we define what it means for α to be a part of β. This relationship is essentially equivalent to α being a function of β and in this case β can be employed to measure α. We then use the concept to define the coexistence of entities and study its properties. A crucial role is played by a map α^ which takes an entity of a certain type to one of a lower type. For example, if I is an instrument, then I^ is the unique observable measured by I. Composite systems are discussed next. These are constructed by taking the tensor product of the Hilbert spaces of the systems being combined. Composites of the three types of measurements and their parts are studied. Reductions in types to their local components are discussed. We also consider sequential products of measurements. Specific examples of Lüders, Kraus and trivial instruments are used to illustrate various concepts. We only consider finite-dimensional systems in this article. Finally, we mention the role of symmetry representations for groups using quantum channels. Full article
(This article belongs to the Special Issue Quantum Information Applied in Neuroscience)
26 pages, 1290 KiB  
Article
The Brain and the New Foundations of Mathematics
by Alexey V. Melkikh
Symmetry 2021, 13(6), 1002; https://doi.org/10.3390/sym13061002 - 3 Jun 2021
Cited by 2 | Viewed by 3037
Abstract
Many concepts in mathematics are not fully defined, and their properties are implicit, which leads to paradoxes. New foundations of mathematics were formulated based on the concept of innate programs of behavior and thinking. The basic axiom of mathematics is proposed, according to [...] Read more.
Many concepts in mathematics are not fully defined, and their properties are implicit, which leads to paradoxes. New foundations of mathematics were formulated based on the concept of innate programs of behavior and thinking. The basic axiom of mathematics is proposed, according to which any mathematical object has a physical carrier. This carrier can store and process only a finite amount of information. As a result of the D-procedure (encoding of any mathematical objects and operations on them in the form of qubits), a mathematical object is digitized. As a consequence, the basis of mathematics is the interaction of brain qubits, which can only implement arithmetic operations on numbers. A proof in mathematics is an algorithm for finding the correct statement from a list of already-existing statements. Some mathematical paradoxes (e.g., Banach–Tarski and Russell) and Smale’s 18th problem are solved by means of the D-procedure. The axiom of choice is a consequence of the equivalence of physical states, the choice among which can be made randomly. The proposed mathematics is constructive in the sense that any mathematical object exists if it is physically realized. The consistency of mathematics is due to directed evolution, which results in effective structures. Computing with qubits is based on the nontrivial quantum effects of biologically important molecules in neurons and the brain. Full article
(This article belongs to the Special Issue Quantum Information Applied in Neuroscience)
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14 pages, 32281 KiB  
Article
Cytoskeletal Filaments Deep Inside a Neuron Are not Silent: They Regulate the Precise Timing of Nerve Spikes Using a Pair of Vortices
by Pushpendra Singh, Pathik Sahoo, Komal Saxena, Jhimli Sarkar Manna, Kanad Ray, Subrata Ghosh and Anirban Bandyopadhyay
Symmetry 2021, 13(5), 821; https://doi.org/10.3390/sym13050821 - 7 May 2021
Cited by 20 | Viewed by 6743
Abstract
Hodgkin and Huxley showed that even if the filaments are dissolved, a neuron’s membrane alone can generate and transmit the nerve spike. Regulating the time gap between spikes is the brain’s cognitive key. However, the time modula-tion mechanism is still a mystery. By [...] Read more.
Hodgkin and Huxley showed that even if the filaments are dissolved, a neuron’s membrane alone can generate and transmit the nerve spike. Regulating the time gap between spikes is the brain’s cognitive key. However, the time modula-tion mechanism is still a mystery. By inserting a coaxial probe deep inside a neuron, we have re-peatedly shown that the filaments transmit electromagnetic signals ~200 μs before an ionic nerve spike sets in. To understand its origin, here, we mapped the electromagnetic vortex produced by a filamentary bundle deep inside a neuron, regulating the nerve spike’s electrical-ionic vortex. We used monochromatic polarized light to measure the transmitted signals beating from the internal components of a cultured neuron. A nerve spike is a 3D ring of the electric field encompassing the perimeter of a neural branch. Several such vortices flow sequentially to keep precise timing for the brain’s cognition. The filaments hold millisecond order time gaps between membrane spikes with microsecond order signaling of electromagnetic vortices. Dielectric resonance images revealed that ordered filaments inside neural branches instruct the ordered grid-like network of actin–beta-spectrin just below the membrane. That layer builds a pair of electric field vortices, which coherently activates all ion-channels in a circular area of the membrane lipid bilayer when a nerve spike propagates. When biomaterials vibrate resonantly with microwave and radio-wave, simultaneous quantum optics capture ultra-fast events in a non-demolition mode, revealing multiple correlated time-domain operations beyond the Hodgkin–Huxley paradigm. Neuron holograms pave the way to understanding the filamentary circuits of a neural network in addition to membrane circuits. Full article
(This article belongs to the Special Issue Quantum Information Applied in Neuroscience)
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30 pages, 4908 KiB  
Article
Quantum Information in Neural Systems
by Danko D. Georgiev
Symmetry 2021, 13(5), 773; https://doi.org/10.3390/sym13050773 - 29 Apr 2021
Cited by 9 | Viewed by 5032
Abstract
Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be unaccommodating for a causally effective consciousness, the inherent indeterminism of [...] Read more.
Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be unaccommodating for a causally effective consciousness, the inherent indeterminism of quantum physics, together with its characteristic dichotomy between quantum states and quantum observables, provides a fertile ground for the physical modeling of consciousness. Here, we utilize the Schrödinger equation, together with the Planck–Einstein relation between energy and frequency, in order to determine the appropriate quantum dynamical timescale of conscious processes. Furthermore, with the help of a simple two-qubit toy model we illustrate the importance of non-zero interaction Hamiltonian for the generation of quantum entanglement and manifestation of observable correlations between different measurement outcomes. Employing a quantitative measure of entanglement based on Schmidt decomposition, we show that quantum evolution governed only by internal Hamiltonians for the individual quantum subsystems preserves quantum coherence of separable initial quantum states, but eliminates the possibility of any interaction and quantum entanglement. The presence of non-zero interaction Hamiltonian, however, allows for decoherence of the individual quantum subsystems along with their mutual interaction and quantum entanglement. The presented results show that quantum coherence of individual subsystems cannot be used for cognitive binding because it is a physical mechanism that leads to separability and non-interaction. In contrast, quantum interactions with their associated decoherence of individual subsystems are instrumental for dynamical changes in the quantum entanglement of the composite quantum state vector and manifested correlations of different observable outcomes. Thus, fast decoherence timescales could assist cognitive binding through quantum entanglement across extensive neural networks in the brain cortex. Full article
(This article belongs to the Special Issue Quantum Information Applied in Neuroscience)
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Review

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15 pages, 2220 KiB  
Review
Quantum Calculations on Ion Channels: Why Are They More Useful Than Classical Calculations, and for Which Processes Are They Essential?
by Alisher M. Kariev and Michael E. Green
Symmetry 2021, 13(4), 655; https://doi.org/10.3390/sym13040655 - 12 Apr 2021
Cited by 10 | Viewed by 2433
Abstract
There are reasons to consider quantum calculations to be necessary for ion channels, for two types of reasons. The calculations must account for charge transfer, and the possible switching of hydrogen bonds, which are very difficult with classical force fields. Without understanding charge [...] Read more.
There are reasons to consider quantum calculations to be necessary for ion channels, for two types of reasons. The calculations must account for charge transfer, and the possible switching of hydrogen bonds, which are very difficult with classical force fields. Without understanding charge transfer and hydrogen bonding in detail, the channel cannot be understood. Thus, although classical approximations to the correct force fields are possible, they are unable to reproduce at least some details of the behavior of a system that has atomic scale. However, there is a second class of effects that is essentially quantum mechanical. There are two types of such phenomena: exchange and correlation energies, which have no classical analogues, and tunneling. Tunneling, an intrinsically quantum phenomenon, may well play a critical role in initiating a proton cascade critical to gating. As there is no classical analogue of tunneling, this cannot be approximated classically. Finally, there are energy terms, exchange and correlation energy, whose values can be approximated classically, but these approximations must be subsumed within classical terms, and as a result, will not have the correct dependence on interatomic distances. Charge transfer, and tunneling, require quantum calculations for ion channels. Some results of quantum calculations are shown. Full article
(This article belongs to the Special Issue Quantum Information Applied in Neuroscience)
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