A model of quantum-von Neumann hybrid cellular automata: principles and simulation of quantum coherent superposition and dehoerence in cytoskeletal microtubules
Manuel Alfonseca, Alfonso Ortega, Marina de la Cruz, Stuart R. Hameroff, Rafael Lahoz-Beltrá
Although experimental evidence suggests the influence of quantum effects in living organisms, one of the most critical problems in quantum biology is the explanation of how those effects that take place in a microscopic level can manifest in the macroscopic world of living beings. At present, quantum decoherence associated with the wave function collapse is one of the most accepted mechanisms explaining how the classical world of living beings emerges from the quantum world. Whatever the cause of wave function collapse, there exist biological systems where a biological function arises as a result of this collapse (e.g. birds navigation, plants photosynthesis, sense of smell, etc.), as well as the opposite examples (e.g. release of energy from ATP molecules at actomyosin muscle) where a biological function takes place in a quantum coherent environment. In this paper we report the modelling and simulation of quantum coherent superposition in cytoskeletal microtubules including decoherence, thus the effect of the collapse of the microtubule coherent state wave function. Our model is based on a new class of hybrid cellular automata (QvN), capable of performing as either a quantum cellular automata (QCA) or as a classical von Neumann automata (CA). These automata are able to simulate the transition or reduction from a quantum microscopic level with superposition of several quantum states, to a macroscopic level with a single stable state. Our results illustrate the significance of quantum biology explaining the emergence of some biological functions. We believe that in the future quantum biology will have a deep effect on the design of new devices, e.g. quantum hardware, in electrical engineering.
Although experimental evidence suggests the influence of quantum effects in living organisms, one of the most critical problems in quantum biology is the explanation of how those effects that take place in a microscopic level can manifest in the macroscopic world of living beings. At present, quantum decoherence associated with the wave function collapse is one of the most accepted mechanisms explaining how the classical world of living beings emerges from the quantum world. Whatever the cause of wave function collapse, there exist biological systems where a biological function arises as a result of this collapse (e.g. birds navigation, plants photosynthesis, sense of smell, etc.), as well as the opposite examples (e.g. release of energy from ATP molecules at actomyosin muscle) where a biological function takes place in a quantum coherent environment. In this paper we report the modelling and simulation of quantum coherent superposition in cytoskeletal microtubules including decoherence, thus the effect of the collapse of the microtubule coherent state wave function. Our model is based on a new class of hybrid cellular automata (QvN), capable of performing as either a quantum cellular automata (QCA) or as a classical von Neumann automata (CA). These automata are able to simulate the transition or reduction from a quantum microscopic level with superposition of several quantum states, to a macroscopic level with a single stable state. Our results illustrate the significance of quantum biology explaining the emergence of some biological functions. We believe that in the future quantum biology will have a deep effect on the design of new devices, e.g. quantum hardware, in electrical engineering.
The background of this contribution is the ongoing extended debate over quantum effects in the biology since decades. Typical examples of the quantum biology are photosynthesis, enzymatic activities, bird navigation and especially the coherent movement of microtubules. The reason for all these effects is dominantly the quantum coherence of waves. The objective of this contribution is the quantum description of the instability dynamics of microtubules at their assembly and disassembly phases during the interphase. The corresponding theoretical investigations of this article confirm the existence of quantum coherence of microtubules. Experimental results assert such vibrations of microtubules by the observation of γ-waves in the human brain generated by bundles of microtubules. Tubulin subunits and the accessory proteins are of nano size; therefore, they are modeled as field quanta in the framework of non-relativistic quantum field theory. This approach describes the dynamics of these quantum particles and their interactions, by accentuation of their different performances as coherent or incoherent waves. The achieved results strongly depend from the preconditions: whether the fluctuating forces are turned on or turned off. With the inset of fluctuations, the quantum coherence is destroyed, and only incoherent particle solutions are obeyed. Without the impact of fluctuations wave solutions dominate. Another type of wave solution are coherent wave packets which are counter-running, where their superposition can extinct or enhance them. This kind of interfering coherent solutions is applied on the polymerization of protofilaments. The calculations of this contribution demonstrate that the quantum coherence can be only observed when fluctuations are excluded. The conclusion is that that dedicated biological processes must be able to suppress the destroying influences of the local environment. In contrary to technical-based experiments, where coherence is only obtained when the fluctuations are deliberately excluded (e.g. quantum computer). Therefore, the answer why the processes of quantum biology can generate quantum coherence at least in case of microtubules is actually not answered. Kinesins in combination with microtubules are fundamental for cellular functions and morphogenesis. Recent genetic experiments uncovered their role for tumor suppression and developmental patterning. However, these findings which open exciting new areas of kinesin research are not included in this contribution, because the description of the kinesin-microtubule system is to comprehensive for one article.
This paper proposes a novel model utilizing Quantum Cellular Automata (QCA) to simulate complex system evolution. The core idea involves transforming classical Cellular Automata (CA) into QCA, incorporating quantum phenomena such as superposition and entanglement to model intricate dynamics. This approach offers a fresh perspective on complex system modeling by leveraging the principles of quantum mechanics. The model's design incorporates key QCA mechanisms, including the Bloch sphere representation of states and the application of unitary transformations to govern cell interactions. We present a foundational framework for QCA simulation and discuss potential applications in areas such as pattern formation, reaction-diffusion processes, and emergent behavior. The focus is on demonstrating the theoretical feasibility and outlining a methodology for future research, rather than presenting empirical experimental results. This work emphasizes the conceptual shift and potential computational advantages offered by QCA in understanding complex systems.
The existence of living organisms in the mesoscopic realm may be quite nontrivial and actuallymay emerge from the interplay between quantum mechanics and gravity. On one side, quantumbiology investigates how quantum mechanical phenomena, such as superposition, entanglement,and tunnelling, contribute to biological processes. These quantum effects, once thought to beirrelevant in the “warm, wet, and noisy” environment of living organisms due to decoherence, havebeen found to play significant roles in various biological systems, from photosynthesis to enzymecatalysis. On the other side, gravitational forces have been implicated in the organization ofmicrotubules, which are essential for maintaining cellular structure and function. Recent studieshave demonstrated that gravitational forces can induce three-dimensional chromosomal conformational changes, which are associated with rapid transcriptional responses in human T cells. Sometheories propose that gravity might play a role in decoherence, such as in the Penrose-Hameroffmodel, which proposes that quantum coherence in microtubules could be the basis for consciousawareness and quantum computing-like information processing, with gravity playing a role in thecollapse of the quantum wave function. The model predictions that microtubules can support longrange coherent phenomena have been confirmed by experimental observations of superradiancefrom mega-networks of tryptophan UV-excited transition dipoles, particularly in microtubulearchitectures. Another experimental research highlights that microtubule network exhibits ahierarchy of three-fold resonant frequency patterns across biological scales – from tubulin proteinsto microtubules and neurons. This suggests a quantum-to-classical transition governed by scalefree dynamics, potentially underlying information processing in the brain. A very intriguing fact isthat at the most fundamental level of the origin of life, the standard genetic code, we can observethe scale-free computing that arises from arithmetic regularities of the nucleon numbers related tothe code’s numerous symmetries. Given that some of these symmetries probably originate fromdifferent evolutionary epochs, such scale-free computing may be a latent background mechanismof the organization of the genetic code and therefore relevant to natural computing.
Abstract Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wave function “self-collapse” (objective reduction: OR - Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of microtubules suitable for quantum effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 ms) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent mass-energy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum → classical reduction occurs. Unlike the random, “subjective reduction” (SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. Possibilities and probabilities for post-reduction tubulin states are influenced by factors including attachments of microtubule-associated proteins (MAPs) acting as “nodes” which tune and “orchestrate” the quantum oscillations. We thus term the self-tuning OR process in microtubules “orchestrated objective reduction” (“Orch OR”), and calculate an estimate for the number of tubulins (and neurons) whose coherence for relevant time periods (e.g. 500 ms) will elicit Orch OR. In providing a connection among (1) pre-conscious to conscious transition, (2) fundamental space-time notions, (3) non-computability, and (4) binding of various (time scale and spatial) reductions into an instantaneous event (“conscious now”), we believe Orch OR in brain microtubules is the most specific and plausible model for consciousness yet proposed.
This paper explores the potential of Quantum Cellular Automata (QCA) for simulating complex systems with enhanced efficiency compared to their classical counterparts. Classical Cellular Automata (CCA) face limitations when modeling systems exhibiting quantum phenomena or requiring computational power for intricate simulations. QCA, leveraging the principles of quantum mechanics, offers a fundamentally different approach. This work details the design of a QCA where cells are represented by qubits, and the governing rules are defined by quantum gates. The core argument presented is that QCA's inherent parallelism and superposition capabilities can lead to significant speedups in simulating complex systems. This research proposes a novel methodology for applying QCA to various complex systems, highlighting its potential advantages and exploring the theoretical foundations underpinning this approach. The investigation focuses on the theoretical aspects of QCA design and simulation, without the need for experimental validation.
Every process of our universe is based on the fundamental elements of nature: information and computation.The basic motivation behind the study of quantum cellular automata (QCA) is the wish to analyze the processes of nature.QCA provide a natural framework within which to describe many classically undescribable and uncomputable physical phenomena, such as the properties of quantum physical systems and the complex background of quantum dynamics.Quantum cellular automata models are based on the working mechanism of classical cellular automata models and use the power of reversible quantum computation.Cellular automata can be used in many fields of science, such as parallel computation, artificial intelligence, image processing, biological systems, simulation of physics systems, hardware design, algorithm theory, and many more.In the first part of this chapter, we give a brief overview of the basic properties of quantum information processing and analyze the quantum versions of classical cellular automata models.We present all materials in a clear, perspicuous, and comprehensible manner, without using a complex mathematical background.After reviewing physical QCA implementations, we sketch future directions, and then conclude the first part.In the second part of the chapter, we examine one possible application of QCA, which uses quantum computing to realize real-life based, truly random network organization.This abstract machine is called a Quantum Cellular Machine (QCM), and we design it for controlling a truly random biologically-inspired network, and to integrate quantum learning algorithms and quantum searching into a controlled, self-organizing system.The selforganizing processes in classical systems cannot be truly random.Using our quantum probabilistic QCM unit, we can add truly random behavior to the self-organizing processes of biological networks.A quantum mechanical-based quantum cellular machine (QCM) controls the self-organizing processes of the network and uses a closed, non-classical quantum mechanical-based language inside the QCM.The proposed QCM solution has deep relevance in the evolution of truly random quantum probabilistic self-organizing network structures.The QCM controls the evolution of the system, changes its environment and creates plans without any human interaction, using truly random quantum probabilistic decisions.In a classical system, the classical circuits can only exhibit deterministic behavior.In a quantum probabilistic control system, the quantum circuits can follow both deterministic and quantum probabilistic quantum cellular machine control behaviors.The QCM has classical and quantum communication layers, it uses the classical layer to detect www.intechopen.comCellular Automata -Innovative Modelling for Science and Engineering 114 the network environment.The lower layer of the quantum cellular machine contains the non-deterministic quantum probabilistic decisions and interacts with the classical level.The quantum cellular machine model with the power of quantum computing can be used for the development of a real-life based network organism.We show, that a real, biologically inspired, non-deterministic, truly random network model can be achieved by the discussed QCM model.In the third part of this chapter, we show that a very efficient quantum searching algorithm can be integrated into the QCM, to find the best solution to a given network input command.We present a quantum searching based method specially designed for quantum probabilistic self-organizing networks, to reduce the complexity of the classical traditional search in the network.The proposed QCM can process both quantum and classical information, and accomplish both deterministic and quantum probabilistic tasks.The information unit is a quantum bit, which can lie in a coherent superposition state of logical states zero and one, and can thus simultaneously store zero and one.Using quantum bits, we can speed up the solutions of classical problems, and even solve some hard problems that classical computers can't solve.The key aspect behind the optimal decisions of a QCM is to design a high-efficiency searching algorithm.A QCM updates the probability amplitudes of its quantum register, according to a given reward value, derived from the network environment.The QCM repeatedly applies a unitary transformation to the quantum states, thus it can enhance, for example, the probability amplitude of the optimal path in the self-organizing network environment, while suppressing the amplitude of all other solutions.The QCM's quantum searching algorithm can help resolve many hard tasks, for example it could be applied to find an optimal logical path, using the effects of quantum mechanics.In the numerical analysis we will show that the quantum communication layer could improve the performance of classical systems.