Quantum brain hypotheses // quantum simulations
If the human brain functions as a quantum device, let’s utilize quantum computers to simulate it.
The key points discussed in the interview with Dr. Stuart Hameroff are:
1. Hameroff co-created the Orch OR (Orchestrated Objective Reduction) theory of consciousness with Sir Roger Penrose. This theory proposes that consciousness arises from quantum computations in microtubules inside neurons.
2. Anesthetics selectively bind to and disrupt microtubules, suggesting microtubules are involved in consciousness. Experimental evidence supports the role of microtubules over other proposed mechanisms like membrane receptors.
3. Microtubules in neurons have unique properties like mixed polarity, stability over lifetimes, and the ability to encode memory that make them ideal candidates for consciousness.
4. Hameroff discusses the triple peak resonance frequencies found in microtubules that could underlie consciousness. Evidence from experiments measuring high-frequency electromagnetic activity from brains and plants supports this.
5. Hameroff is skeptical that classical computation-based AI will achieve consciousness but believes quantum computing could potentially reproduce consciousness if based on objective reduction.
6. He argues the Orch OR theory could allow for non-local consciousness persisting after death based on quantum entanglement effects, though he does not claim evidence for an afterlife.
7. As an anesthesiologist, Hameroff has been able to pursue potentially controversial ideas on consciousness relatively free from funding pressures that constrain other academics.
In recent years we have seen quantum physics advance in leaps and bounds. Living matter is becoming more comprehensible when we appeal to the fundamental states that define their existence, namely the quantum fields that comprise them. When we consider living matter (organisms), we are presented with the difficult complexity of understanding the human brain. The brain itself is not the human being neither does it comprise the totality of the human person, but is inherently embedded in the entire being of the human person. We are obviously aware of the fact that the major function of the brain pertains to consciousness, be it broad and specific, the former being that general/objective view of awareness recognized, such that is seen when one wakes up from sleep, and the specific that refers to the particular/subjective state of being aware of this or that (this comes after the broad though). Other functions include memory, thought-control, motorskills, vision, breathing, temperature, body-regulation etc. However, all these come after consciousness. Thus what Quantum Brain Dynamics (QBD) considers is not just these other functions of the brain, this is because they can be well analyzed with the workings of classical mechanics (even though they still play host to a quantum description). It rather considers two specific functions above all else consciousness and memory. QBD falls in line umbrella-covers aspects of the quantum brain analysis such as quantum-consciousness, quantum-mind and quantum-brain. The inspiration that lurks behind the Quantum Interpretation of the Brain (QIB), is traceable to the 1944 article written by E. Schrodinger, What is Life, in which he presents how a living organisms evades decay to equilibrium by the fact of negentropy, as such life which is in its ordered macroscopic state is created (in an environment of disorder), which moves against the second law of thermodynamics. The life that is created, that which is sustained, arises from an interaction that the organism engages in with the environment. This interaction is microscopic, albeit quantum, it is an interaction that underscores the reality of quantum entanglement (which also plays hosts to the superposition of quantum states). The quantum interpretation of the brain is a nascent, yet burgeoning as it might be that necessary tool required for a better articulation and comprehension of the brain
This paper discusses Quantum Brain Dynamics (QBD), which is a theoretical framework for describing the fundamental physical processes underlying brain dynamics from a quantum field theory perspective. The key points are:
1. QBD aims to provide a quantum interpretation of the brain, particularly for phenomena like consciousness and memory, which are difficult to explain using classical physics.
2. It describes the dynamics of two key molecular fields in the brain — the vibrational fields of biomolecules (B-field) and the dipolar fields of water molecules and dipolar solitons (W-field).
3. The mathematical formulation of QBD involves representing these fields using quantum field theory, with the B-field as a spinor field and the W-field as a vector field obeying certain commutation relations.
4. Processes like memory printing, recall, and learning are mapped to phase transitions, symmetry breaking/restoring, and quantum tunneling phenomena in the coupled B-W field system.
5. QBD may help resolve issues like the binding problem in consciousness by appealing to quantum electromagnetic phenomena rather than invoking quantum mechanical non-locality.
6. Overall, QBD provides a quantum field theoretic framework to potentially decipher brain dynamics, though it is still a nascent field with scope for further development.
The evolution of the human mind through natural selection mandates that our conscious experiences are causally potent in order to leave a tangible impact upon the surrounding physical world. Any attempt to construct a functional theory of the conscious mind within the framework of classical physics, however, inevitably leads to causally impotent conscious experiences in direct contradiction to evolution theory. Here, we derive several rigorous theorems that identify the origin of the latter impasse in the mathematical properties of ordinary differential equations employed in combination with the alleged functional production of the mind by the brain. Then, we demonstrate that a mind–brain theory consistent with causally potent conscious experiences is provided by modern quantum physics, in which the unobservable conscious mind is reductively identified with the quantum state of the brain and the observable brain is constructed by the physical measurement of quantum brain observables. The resulting quantum stochastic dynamics obtained from sequential quantum measurements of the brain is governed by stochastic differential equations, which permit genuine free will exercised through sequential conscious choices of future courses of action. Thus, quantum reductionism provides a solid theoretical foundation for the causal potency of consciousness, free will and cultural transmission.
The paper discusses the implications of different approaches to understanding consciousness, particularly functionalism and reductionism within classical and quantum physics frameworks. The key points are:
1. Prehistoric cave art depicting animals suggests early humans had conscious experiences that causally influenced their physical actions, challenging functionalist views of consciousness as causally impotent.
2. The author analyzes the mind-brain relationship under four schemes: classical functionalism, classical reductionism, quantum functionalism, and quantum reductionism.
3. Only quantum reductionism, which attributes elementary experiences to quantum systems, supports both the causal potency of conscious mind and free will.
4. Quantum reductionism avoids the problem of reversed causation in models like Orch OR, where consciousness arises from unconscious brain dynamics.
5. The problems of mental causation and free will are hierarchically organized, with causally potent mind being required for free will.
6. Quantum reductionism explains how human consciousness could have evolved through natural selection by being causally potent in influencing behavior.
The author argues for quantum reductionism as the most viable approach, allowing for the causal efficacy and natural evolution of human consciousness.
The reality of our perceived universe has been questioned by deep thinkers of all times. And the discovery of the mysterious quantum mechanics has made it fundamental; and expectedly it is being addressed in quantum physics: the efforts are in the context of the genesis of the universe; from its quantum beginning to its possible quantum to-physical reduction; the end that we experience. The requirement for the reduction arises due to quantum particles multimodal indefinite existence; probabilistic varying sites and characteristics. Therefore, a real classical universe could only result from a universal autonomous reduction, which nonetheless may have happened despite lack of a falsifiable proof theory. The other possibility (avoiding the cataclysmic event) could be world classicality due to reduction in our minds, or brains. New findings about the latency of consciousness, point to autonomous brain as the site of such event. The scheme for such reductions is figured out in the interpretation theories of measurement of simple quantum systems of particles, which can also explicate having one definite universe from many indefinite alternatives of the quantum universe. The anthropocentric approaches are at best ad hoc and rely on choice, prompting of which remains unknown. My approach avoids these issues by isolating two entangled subsystems out of the pure quantum universe; the photons-phonons and beings nervous subsystems. Ignoring the remaining entangled mass particle subsystem, renders others in statistical correlation states (not quantum), where survival brain patterns make the selection. This state of the brain, forces also the selection of its entangled (mass) environment; and thus embracing the information of the mass particle universe, its classicality streamed to our consciousness; after all, our connection with everything external to us is through photons and phonons
This paper discusses the challenge of understanding the transition from the quantum reality of the universe to the classical world we perceive. It explores various interpretations and theories proposed by physicists to explain this “quantum-to-physical reduction” process, including the Copenhagen interpretation, the role of consciousness, decoherence theory, and the idea of a universal wave function.
The author proposes a hypothesis that leaves the quantum reality of the universe intact while accounting for our perception of classicality. The key idea is to consider three coherent quantum subsystems: the animate quantum medium (beings’ nervous systems), the external quantum system of the universe (mass particles), and the massless quantum medium (photons, phonons). By ignoring (tracing over) the information of the animate system, the other two subsystems become statistically correlated (mixed quantum) and are selected by the forces of survival, creating the illusion of a classical world.
The proposed approach removes the need for an autonomous mind or consciousness to play a role in the reduction process. Instead, it suggests that our perception of classicality arises from the entanglement between our nervous systems and the photons and phonons, which carry information about the mass particle quantum universe. This entanglement stimulates our brains to render the classical world we experience, driven by survival patterns and neural computations.
Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily modular hierarchical structures, with a number of key features. Firstly, they cannot be described by a single wave function: only local wave functions can exist, rather than a single wave function for a living cell, a cat, or a brain. Secondly, the quantum to classical transition is characterised by contextual wave-function collapse shaped by macroscopic elements that can be described classically. Thirdly, downward causation occurs in the physical hierarchy in two key ways: by the downward influence of time dependent constraints, and by creation, modification, or deletion of lower level elements. Fourthly, there are also logical modular hierarchical structures supported by the physical ones, such as algorithms and computer programs, They are able to support arbitrary logical operations, which can influence physical outcomes as in computer aided design and 3-d printing. Finally, complex systems are necessarily open systems, with heat baths playing a key role in their dynamics and providing local arrows of time that agree with the cosmological direction of time that is established by the evolution of the universe.
Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. Establishing this capability, especially for impactful and meaningful problems, remains a central challenge. One such problem is the simulation of nonequilibrium dynamics of a magnetic spin system quenched through a quantum phase transition. State-of-the-art classical simulations demand resources that grow exponentially with system size. Here we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schr¨odinger equation. We demonstrate area-law scaling of entanglement in the model quench in two-, three- and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for classical approaches. We assess approximate methods based on tensor networks and neural networks and conclude that no known approach can achieve the same accuracy as the quantum annealer within a reasonable timeframe. Thus quantum annealers can answer questions of practical importance that classical computers cannot.
The paper presents evidence of computational supremacy of quantum annealing processors (QPUs) in simulating the quantum dynamics of transverse-field Ising spin glass models quenched through a quantum phase transition. The key findings are:
1. QPU results are in close agreement with ground truth solutions from classical tensor network simulations for small system sizes of up to 64 spins, verifying the accuracy of the QPUs.
2. For larger system sizes beyond classical simulation capabilities, QPU observables exhibit universal quantum critical scaling behavior, with extracted critical exponents matching theoretical predictions.
3. State-of-the-art classical tensor network (MPS, PEPS) and neural network simulation methods fail to match QPU accuracy beyond modest system sizes of around 100 spins, even with considerable computational effort.
4. Extrapolating the computational requirements of the tensor network method that comes closest (MPS), matching QPU accuracy for a few hundred spins would require millions of years on leading supercomputers like Frontier, with infeasible memory and energy demands.
The authors conclude that QPUs can simulate the quantum critical dynamics of these spin models essentially without approximations up to system sizes where no known classical method is computationally feasible, demonstrating supremacy for a problem of practical relevance in physics and optimization.
Quantum dynamics, typically expressed in the form of a time-dependent Schr¨odinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, when simulating quantum dynamics that involves the emission of electrons, it is necessary to use artificial boundary conditions (ABC) to confine the computation within a fixed domain. The introduction of ABCs alters the Hamiltonian structure of the dynamics, and existing quantum algorithms can not be directly applied since the evolution is no longer unitary. The current paper utilizes a recently introduced Schr¨odingerisation method [JLY22a, JLY22b] that converts non-Hermitian dynamics to a Schr¨odinger form, for the artificial boundary problems. We implement this method for three types of ABCs, including the complex absorbing potential technique, perfectly matched layer methods, and Dirichlet-to-Neumann approach. We analyze the query complexity of these algorithms, and perform numerical experiments to demonstrate the validity of this approach. This helps to bridge the gap between available quantum algorithms and computational models for quantum dynamics in unbounded domains.
The paper introduces a method called Schrödingeriazation to enable quantum simulation of quantum dynamics with artificial boundary conditions (ABCs). ABCs are used to confine the computation within a fixed domain when simulating quantum dynamics in unbounded domains, but they alter the Hamiltonian structure and make existing quantum algorithms inapplicable.
The key idea is to convert the non-Hermitian dynamics introduced by ABCs into a Schrödinger form, which can then be handled by Hamiltonian simulation algorithms. Three popular ABCs are considered: complex absorbing potential, perfectly matched layers, and Dirichlet-to-Neumann maps.
The paper provides the implementation details and complexity analysis for quantumly simulating these ABCs using the Schrödingeriazation approach. Numerical experiments demonstrate that the Schrödingeriazation form accurately captures the dynamics with ABCs.
In summary, this work bridges the gap between quantum algorithms and computational models for quantum dynamics in unbounded domains by converting the ABC dynamics into a Hamiltonian form amenable to quantum simulation. The simplicity and generality of the Schrödingeriazation approach makes it a promising technique for simulating PDEs with boundary/interface conditions on quantum computers.
Quantum Simulation of Boson-Related Hamiltonians: Techniques, Effective Hamiltonian Construction, and Error Analysis
Elementary quantum mechanics proposes that a closed physical system consistently evolves in a reversible manner. However, control and readout necessitate the coupling of the quantum system to the external environment, subjecting it to relaxation and decoherence. Consequently, system-environment interactions are indispensable for simulating physically significant theories. A broad spectrum of physical systems in condensed-matter and highenergy physics, vibrational spectroscopy, and circuit and cavity QED necessitates the incorporation of bosonic degrees of freedom, such as phonons, photons, and gluons, into optimized fermion algorithms for near-future quantum simulations. In particular, when a quantum system is surrounded by an external environment, its basic physics can usually be simplified to a spin or fermionic system interacting with bosonic modes. Nevertheless, troublesome factors such as the magnitude of the bosonic degrees of freedom typically complicate the direct quantum simulation of these interacting models, necessitating the consideration of a comprehensive plan. This strategy should specifically include a suitable fermion/boson-to-qubit mapping scheme to encode sufficiently large yet manageable bosonic modes, and a method for truncating and/or downfolding the Hamiltonian to the defined subspace for performing an approximate but highly accurate simulation, guided by rigorous error analysis. In this paper, we aim to provide such an exhaustive strategy, focusing on encoding and simulating certain bosonicrelated model Hamiltonians, inclusive of their static properties and time evolutions. Specifically, we emphasize two aspects: (1) the discussion of recently developed quantum algorithms for these interacting models and the construction of effective Hamiltonians, and (2) a detailed analysis regarding a tightened error bound for truncating the bosonic modes for a class of fermion-boson interacting Hamiltonians.
Simulation of a Variational Quantum Perceptron using Grover’s Algorithm
The quantum perceptron, the variational circuit, and the Grover algorithm have been proposed as promising components for quantum machine learning. This paper presents a new quantum perceptron that combines the quantum variational circuit and the Grover algorithm. However, this does not guarantee that this quantum variational perceptron with Grover’s algorithm (QVPG) will have any advantage over its quantum variational (QVP) and classical counterparts. Here, we examine the performance of QVP and QVP-G by computing their loss function and analyzing their accuracy on the classification task, then comparing these two quantum models to the classical perceptron (CP). The results show that our two quantum models are more efficient than CP, and our novel suggested model QVP-G outperforms the QVP, demonstrating that the Grover can be applied to the classification task and even makes the model more accurate, besides the unstructured search problems.
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links. Continuous-time quantum walk algorithms assume that we can simulate the dynamics of quantum systems where the Hamiltonian is given by the adjacency matrix of the graph. It is known that such can be simulated efficiently if the underlying graph is row-sparse and efficiently row-computable. While this is sufficient for many applications, it limits the applicability for this class of algorithms to study real world complex networks, which, among other properties, are characterized by the existence of a few densely connected nodes, called hubs. In other words, complex networks are typically not row-sparse, even though the average connectivity over all nodes can be very small. In this work, we extend the state-of-the-art results on quantum simulation to graphs that contain a small number of hubs, but that are otherwise sparse. Hopefully, our results may lead to new applications of quantum computing to network science.
