In this paper we investigate a categorical equivalence between square root qMV-algehras (a variety of algebras arising from quantum computation) and a category of preordered semigroups.

Predicting the binding mode of flexible polypeptides to proteins is an important task that falls outside the domain of applicability of most small molecule and protein-protein docking tools. Here, we test the small molecule flexible ligand docking program Glide on a set of 19 non-α-helical peptides and systematically improve pose prediction accuracy by enhancing Glide sampling for flexible polypeptides. In addition, scoring of the poses was improved by post-processing with physics-based implicit solvent MM- GBSA calculations. Using the best RMSD among (...) the top 10 scoring poses as a metric, the success rate (RMSD ≤ 2.0 \textbackslash AA for the interface backbone atoms) increased from 21 with default Glide SP settings to 58 with the enhanced peptide sampling and scoring protocol in the case of redocking to the native protein structure. This approaches the accuracy of the recently developed Rosetta FlexPepDock method (63 success for these 19 peptides) while being over 100 times faster. Cross-docking was performed for a subset of cases where an unbound receptor structure was available, and in that case, 40 of peptides were docked successfully. We analyze the results and find that the optimized polypeptide protocol is most accurate for extended peptides of limited size and number of formal charges, defining a domain of applicability for this approach. (shrink)

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. We study the basic algebraic properties of this system by introducing the notion of Shi-Aharonov quantum computational structure. We show that the quotient of this structure is isomorphic to a structure based on a particular set of complex numbers (the closed disc with center \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} (...) \begin{document}$(\frac{1}{2},\frac{1}{2})$\end{document} and radius \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{1}{2}$\end{document} ). (shrink)

A quantum algorithm succeeds not because the superposition principle allows ‘the computation of all values of a function at once’ via ‘quantum parallelism’, but rather because the structure of a quantum state space allows new sorts of correlations associated with entanglement, with new possibilities for information‐processing transformations between correlations, that are not possible in a classical state space. I illustrate this with an elementary example of a problem for which a quantum algorithm is more efficient than (...) any classical algorithm. I also introduce the notion of ‘pseudotelepathic’ games and show how the difference between classical and quantum correlations plays a similar role here for games that can be won by quantum players exploiting entanglement, but not by classical players whose only allowed common resource consists of shared strings of random numbers (common causes of the players’ correlated responses in a game). *Received October 2008. †To contact the author, please write to: Department of Philosophy, University of Maryland, College Park, MD 20742; e‐mail: [email protected]. (shrink)

EPR-type measurements on spatially separated entangled spin qubits allow one, in principle, to detect curvature. Also the entanglement of the vacuum state is affected by curvature. Here, we ask if the curvature of spacetime can be expressed entirely in terms of the spatial entanglement structure of the vacuum. This would open up the prospect that quantum gravity could be simulated on a quantum computer and that quantum information techniques could be fully employed in the study of (...) class='Hi'>quantum gravity. (shrink)

We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers.

An experimental realization of quantum computers is composed of two or more calcium ions trapped in a magnetic quadripole. Information is transferred to and read from the ions by means of structured lasers that interact with the ions’ vibration pattern, causing changes of energy distribution in their electronic structure. Departing from an initial state when the ions are cooled, the use of lasers modifies the internal state of one ion that is entangled with the others, then changing the collective (...) states. In such quantum computers, some of the physically possible electronic states are avoided or not taken into consideration, to force the system to work as a binary device. In this essay, we discuss the dynamics that the ions could spontaneously display and its possible implications for the principles of computational logics. (shrink)

An experimental realization of quantum computers is composed of two or more calcium ions trapped in a magnetic quadripole. Information is transferred to and read from the ions by means of structured lasers that interact with the ions’ vibration pattern, causing changes of energy distribution in their electronic structure. Departing from an initial state when the ions are cooled, the use of lasers modifies the internal state of one ion that is entangled with the others, then changing the collective (...) states. In such quantum computers, some of the physically possible electronic states are avoided or not taken into consideration, to force the system to work as a binary device. In this essay, we discuss the dynamics that the ions could spontaneously display and its possible implications for the principles of computational logics. (shrink)

The central motivating idea behind the development of this work is the concept of prespace, a hypothetical structure that is postulated by some physicists to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the rest of reality as we know it, and the implications of the existence of this structure for quantum theory. Understanding how this structure could relate to space and to the rest of reality requires, (...) I believe, that we consider how space itself relates to reality, and how other so-called "spaces" used in physics relate to reality. In chapter 2, I compare space and space-time to other spaces used in physics, such as configuration space, phase space and Hilbert space. I support what is known as the "property view" of space, opposing both the traditional views of space and space-time, substantivalism and relationism. I argue that all these spaces are property spaces. After examining the relationships of these spaces to causality, I argue that configuration space has, due to its role in quantum mechanics, a special status in the microscopic world similar to the status of position space in the macroscopic world. In chapter 3, prespace itself is considered. One way of approaching this structure is through the comparison of the prespace structure with a computational system, in particular to a cellular automaton, in which space or space-time and all other physical quantities are broken down into discrete units. I suggest that one way open for a prespace metaphysics can be found if physics is made fully discrete in this way. I suggest as a heuristic principle that the physical laws of our world are such that the computational cost of implementing those laws on an arbitrary computational system is minimized, adapting a heuristic principle of this type proposed by Feynman. In chapter 4, some of the ideas of the previous chapters are applied in an examination of the physics and metaphysics of quantum theory. I first discuss the "measurement problem" of quantum mechanics: this problem and its proposed solution are the primary subjects of chapter 4. It turns out that considering how quantum theory could be made fully discrete leads naturally to a suggestion of how standard linear quantum mechanics could be modified to give rise to a solution to the measurement problem. The computational heuristic principle reinforces the same solution. I call the modified quantum mechanics Critical Complexity Quantum Mechanics (CCQM). I compare CCQM with some of the other proposed solutions to the measurement problem, in particular the spontaneous localization model of Ghirardi, Rimini and Weber. Finally, in chapters 5 and 6, I argue that the measure of complexity of quantum mechanical states I introduce in CCQM also provides a new definition of entropy for quantum mechanics, and suggests a solution to the problem of providing an objective foundation for statistical mechanics, thermodynamics, and the arrow of time. (shrink)

. The deep structural properties of a quantum information theoretic approach to formal languages and universal computation, as well as those of the topology problem of defining the presentation of the Mapping Class Group of a smooth, compact manifold are shown to be grounded in the common categorical features of the two problems.

In a bipartite quantum system, quantum states are classified as classically correlated and quantum correlated states, the later are important resources of quantum information and computation protocols. Since correlations of quantum states may vary under a quantum channel, it is necessary to explore the influence of quantum channels on correlations of quantum states. In this paper, we discuss CC-preserving, QC-breaking and strongly CC-preserving local quantum channels of the form \ and obtain (...) the structures of these three types of local quantum channels. Moreover, we obtain a necessary and sufficient condition for a quantum state to be transformed into a CC state by a specific local channel \ in terms of the structure of the input quantum state. Lastly, as applications of the obtained results, we present a classification of local quantum channels \ and describe the quantum states which are transformed as CC ones by the corresponding local quantum channel. (shrink)

Recent developments in computer science, particularly ”data-driven procedures“ have opened a new level of design and engineering. This has also affected architecture. The publication collects contributions on Coding as Literacy by computer scientists, mathematicians, philosophers, cultural theorists, and architects. The main focus in the book is the observation of computer-based methods that go beyond strictly case-based or problem-solution-oriented paradigms. This invites readers to understand Computational Procedures as being embedded in an overarching ”media literacy“ that can be revealed through, and (...) acquired by, ”computational literacy“, and to consider the data processed in the above-mentioned methods as being beneficial in terms of quantum physics. ”Self-Organizing Maps“ (SOM), which were first introduced over 30 years ago, will serve as the concrete reference point for all further discussions. (shrink)

Samson Abramsky’s wide-ranging contributions to logical and structural aspects of Computer Science have had a major influence on the field. This book is a rich collection of papers, inspired by and extending Abramsky’s work. It contains both survey material and new results, organised around six major themes: domains and duality, game semantics, contextuality and quantum computation, comonads and descriptive complexity, categorical and logical semantics, and probabilistic computation. These relate to different stages and aspects of Abramsky’s work, reflecting its exceptionally (...) broad scope and his ability to illuminate and unify diverse topics. Chapters in the volume include a review of his entire body of work, spanning from philosophical aspects to logic, programming language theory, quantum theory, economics and psychology, and relating it to a theory of unification of sciences using dual adjunctions. The section on game semantics shows how Abramsky’s work has led to a powerful new paradigm for the semantics of computation. The work on contextuality and categorical quantum mechanics has been highly influential, and provides the foundation for increasingly widely used methods in quantum computing. The work on comonads and descriptive complexity is building bridges between currently disjoint research areas in computer science, relating Structure to Power. The volume also includes a scientific autobiography, and an overview of the contributions. The outstanding set of contributors to this volume, including both senior and early career academics, serve as testament to Samson Abramsky’s enduring influence. It will provide an invaluable and unique resource for both students and established researchers. (shrink)

Quantum physics, which offers an explanation of the world on the smallest scale, has fundamental implications that pose a serious challenge to ordinary logic. Particularly counterintuitive is the notion of entanglement, which has been explored for the past 30 years and posits an ubiquitous randomness capable of manifesting itself simultaneously in more than one place. This amazing 'non-locality' is more than just an abstract curiosity or paradox: it has entirely down-to-earth applications in cryptography, serving for example to protect financial (...) information; it also has enabled the demonstration of 'quantum teleportation', whose infinite possibilities even science-fiction writers can scarcely imagine. This delightful and concise exposition does not avoid the deep logical difficulties of quantum physics, but gives the reader the insights needed to appreciate them. From 'Bell's Theorem' to experiments in quantum entanglement, the reader will gain a solid understanding of one of the most fascinating areas of contemporary physics. (shrink)

Background: how mind functions is subject to continuing scientific discussion. A simplistic approach says that, since no convincing way has been found to model subjective experience, mind cannot exist. A second holds that, since mind cannot be described by classical physics, it must be described by quantum physics. Another perspective concerns mind's hypothesized ability to interact with the world of quanta: it should be responsible for reduction of quantum wave packets; physics producing 'Objective Reduction' is postulated to form (...) the basis for mind-matter interactions. This presentation describes results derived from a new approach to these problems. It is based on well-established biology involving physics not previously applied to the fields of mind, or consciousness studies, that of critical feedback instability. -/- Methods: 'self-organized criticality' in complexity biology places system loci of control at critical instabilities, physical properties of which, including information properties, are presented. Their elucidation shows that they can model hitherto unexplained properties of experience. -/- Results: All results depend on physical properties of critical instabilities. First, at least one feed-back or feed-forward loop must have feedback gain, g = 1: information flows round the loop impress perfect images of system states back on themselves: they represent processes of perfect self-observation. This annihilates system quanta: system excitations are instability fluctuations, which cannot be quantized. Major results follow: -/- 1. Information vectors representing criticality states must include at least one attached information loop denoting self-observation. -/- 2. Such loop structures are attributed a function, 'registering the state's own existence', explaining -/- a. Subjective 'awareness of one's own presence' -/- b. How content-free states of awareness can be remembered (Jon Shear) -/- c. Subjective experience of time duration (Immanuel Kant) -/- d. The 'witness' property of experience – often mentioned by athletes 'in the zone' -/- e. The natural association between consciousness and intelligence -/- This novel, physically and biologically sound approach seems to satisfactorily model subjectivity. -/- Further significant results follow: -/- 1. Registration of external information in excited states of systems at criticality reduces external wave-packets: the new model exhibits 'Objective Reduction' of wave packets. -/- 2. High internal coherence (postulated by Domash & Penrose) leading to a. Non-separable information vector bundles. b. Non-reductive states (Chalmers's criterion for experience). -/- 3. Information that is: a. encoded in coherence negentropy; b. non-digitizable, and therefore c. computationally without digital equivalent (posited by Penrose). -/- Discussion and Conclusions: instability physics implies anharmonic motion, preventing excitation quantization, and totally different from the quantum physics of simple harmonic motion at stability. Instability excitations are different from anything hitherto conceived in information science. They can model aspects of mind never previously treated, including genuine subjectivity, objective reduction of wave-packets, and inter alia all properties given above. (shrink)

Quantum probability (QP) theory can be seen as a type of vector symbolic architecture (VSA): mental states are vectors storing structured information and manipulated using algebraic operations. Furthermore, the operations needed by QP match those in other VSAs. This allows existing biologically realistic neural models to be adapted to provide a mechanistic explanation of the cognitive phenomena described in the target article by Pothos & Busemeyer (P&B).

Although a few new results are presented, this is mainly a review article on the relationship between finite-dimensional quantum mechanics and finite groups. The main motivation for this discussion is the hidden subgroup problem of quantum computation theory. A unifying role is played by a mathematical structure that we call a Hilbert *-algebra. After reviewing material on unitary representations of finite groups we discuss a generalized quantum Fourier transform. We close with a presentation concerning position-momentum measurements in (...) this framework. (shrink)

Recently the interest in Bohm realist interpretation of quantum mechanics has grown. The important advantage of this approach lies in the possibility to introduce non-locality ab initio, and not as an "unexpected host". In this book the authors give a detailed analysis of quantum potential, the non-locality term and its role in quantum cosmology and information. The different approaches to the quantum potential are analysed, starting from the original attempt to introduce a realism of particles trajectories (...) (influenced by de Broglie's pilot wave) to the recent dynamic interpretation provided by Goldstein, Durr, Tumulka and Zanghì, and the geometrodynamic picture, with suggestion about quantum gravity. Finally we focus on the algebraic reading of Hiley and Birkbeck school, that analyse the meaning of the non-local structure of the world, bringing important consequences for the space, time and information concepts. (shrink)

Quantum mechanical and molecular dynamics methods were used to analyze the structure and stability of neutral and zwitterionic configurations of the extracted active site sequence from a Burkholderia cepacia lipase, histidyl-seryl-glutamin (His86-Ser87-Gln88) and its mutated form, histidyl-cysteyl-glutamin (His86-Cys87-Gln88) in vacuum and different solvents. The effects of solvent dielectric constant, explicit and implicit water molecules and side chain mutation on the structure and stability of this sequence in both neutral and zwitterionic forms are represented. The quantum mechanics computations represent (...) that the relative stability of zwitterionic and neutral configurations depends on the solvent structure and its dielectric constant. Therefore, in vacuum and the considered non-polar solvents, the neutral form of the interested sequences is more stable than the zwitterionic form, while their zwitterionic form is more stable than the neutral form in the aqueous solution and the investigated polar solvents in most cases. However, on the potential energy surfaces calculated, there is a barrier to proton transfer from the positively charged ammonium group to the negatively charged carboxylat group or from the ammonium group to the adjacent carbonyl oxygen and or from side chain oxygen and sulfur to negatively charged carboxylat group. Molecular dynamics simulations (MD) were also performed by using periodic boundary conditions for the zwitterionic configuration of the hydrated molecules in a box of water molecules. The obtained results demonstrated that the presence of explicit water molecules provides the more compact structures of the studied molecules. These simulations also indicated that side chain mutation and replacement of sulfur with oxygen leads to reduction of molecular flexibility and packing. (shrink)

A Computable Universe is a collection of papers discussing computation in nature and the nature of computation, a compilation of the views of the pioneers in the contemporary area of intellectual inquiry focused on computational and informational theories of the world. This volume is the definitive source of informational/computational views of the world, and of cutting-edge models of the universe, both digital and quantum, discussed from a philosophical perspective as well as in the greatest technical detail. The (...) book discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? How does nature compute? The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and their philosophical implications. The volume provides a state-of-the-art collection of technical papers and non-technical essays representing a field that takes information and computation to be key to understanding and explaining the basic structure underpinning physical reality. It also includes a new edition of Konrad Zuse's "Calculating Space", and a panel discussion transcription on the topic, featuring worldwide experts (including a Nobel prize) in quantum mechanics, physics, cognition, computation and algorithmic complexity.A Computable Universe is a collection of papers discussing computation in nature and the nature of computation, a compilation of the views of the pioneers in the contemporary area of intellectual inquiry focused on computational and informational theories of the world. This volume is the definitive source of informational/computational views of the world, and of cutting-edge models of the universe, both digital and quantum, discussed from a philosophical perspective as well as in the greatest technical detail. The book discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? How does nature compute? The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and their philosophical implications. The volume provides a state-of-the-art collection of technical papers and non-technical essays representing a field that takes information and computation to be key to understanding and explaining the basic structure underpinning physical reality. It also includes a new edition of Konrad Zuse's "Calculating Space", and a panel discussion transcription on the topic, featuring worldwide experts (including a Nobel prize) in quantum mechanics, physics, cognition, computation and algorithmic complexity. (shrink)

In my 2013 article, “A New Theory of Free Will”, I argued that several serious hypotheses in philosophy and modern physics jointly entail that our reality is structurally identical to a peer-to-peer (P2P) networked computer simulation. The present paper outlines how quantum phenomena emerge naturally from the computational structure of a P2P simulation. §1 explains the P2P Hypothesis. §2 then sketches how the structure of any P2P simulation realizes quantum superposition and wave-function collapse (§2.1.), quantum indeterminacy (...) (§2.2.), wave-particle duality (§2.3.), and quantum entanglement (§2.4.). Finally, §3 argues that although this is by no means a philosophical proof that our reality is a P2P simulation, it provides ample reasons to investigate the hypothesis further using the methods of computer science, physics, philosophy, and mathematics. (shrink)

An original quantum foundations concept of a deep learning computational Universe is introduced. The fundamental information of the Universe (or Triuniverse)is postulated to evolve about itself in a Red, Green and Blue (RGB) tricoloured stable self-mutuality in three information processing loops. The colour is a non-optical information label. The information processing loops form a feedback-reinforced deep learning macrocycle with trefoil knot topology. Fundamental information processing is driven by ψ-Epistemic Drive, the Natural appetite for information selected for advantageous knowledge. (...) From its substrate of Mathematics, the knotted information processing loops determine emergent Physics and thence the evolution of super-emergent Life (biological and artificial intelligence). RGB-tricoloured information is processed in sequence in an Elemental feedback loop (R), then an Operational feedback loop (G), then a Structural feedback loop (B) and back to an Elemental feedback loop (R), and so on around the trefoil in deep learning macrocycles. It is postulated that hierarchical information correspondence from Mathematics through Physics to Life is mapped and conserved within each colour. The substrate of Mathematics has RGB-tricoloured feedback loops which are respectively Algebra (R), Algorithms (G) and Geometry (B). In Mathematics, the trefoil macrocycle is Algebraic Algorithmic Geometry and its correlation system is a Tensor Neural Knot Network enabling Qutrit Entanglement. Emergent Physics has corresponding RGB-tricoloured feedback loops of Quantum Mechanics (R), Quantum Deep Learning (G) and Quantum Geometrodynamics(B). In Physics, the trefoil macrocycle is Quantum Intelligent Geometrodynamics and its correlation system is Quantum Darwinism. Super-emergent Life has corresponding RGB-tricoloured loops of Variation (R), Selection (G) and Heredity (B). In the evolution of Life, the trefoil macrocycle is Variational Selective Heredity and its correlation ecosystem is Darwin’s ecologically “Entangled Bank”. (shrink)

Density matrices for mixed state qubits, parametrized by the Bloch vector in the open unit ball of the Euclidean 3-space, are well known in quantum computation theory. We bring the seemingly structureless set of all these density matrices under the umbrella of gyrovector spaces, where the Bloch vector is treated as a hyperbolic vector, called a gyrovector. As such, this article catalizes and supports interdisciplinary research spreading from mathematical physics to algebra and geometry. Gyrovector spaces are mathematical objects that (...) form the setting for the hyperbolic geometry of Bolyai and Lobachevski just as vector spaces form the setting for Euclidean geometry. It is thus interesting, in geometric quantum computation, to realize that the set of all qubit density matrices has rich structure with strong link to hyperbolic geometry. Concrete examples for the use of the gyro-structure to derive old and new, interesting identities for qubit density matrices are presented. (shrink)

The topics approached in the 52 papers included in this book are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single (...) valued trapezoidal neutrosophic number; inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; Maclaurin symmetric mean; pseudo-BCI algebra; hesitant fuzzy set; photovoltaic plan; decision-making trial and evaluation laboratory (DEMATEL); Choquet integral; fuzzy measure; clustering algorithm; and many more. (shrink)

We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a substitution and arrive at operation algebras that are not lattices what proves the claim. We devise algorithms and programs which write down any two-variable expression in an orthomodular lattice by means of classical and quantum operations in an identical form. Our (...) results show that lattice structure and classical operations uniquely determine quantum logic underlying Hilbert space. As a consequence of our result, recent proposals for a deduction theorem with quantum operations in an orthomodular lattice as well as a, substitution of quantum operations for the usual standard Hilbert space ones in quantum logic prove to be misleading. Quantum computer quantum logic is also discussed. (shrink)

This book provides an interdisciplinary approach to one of the most fascinating and important open questions in science: What is quantum mechanics really talking about? In the last decades quantum mechanics has given rise to a new quantum technological era, a revolution taking place today especially within the field of quantum information processing; which goes from quantum teleportation and cryptography to quantum computation. Quantum theory is probably our best confirmed physical theory. However, in (...) spite of its great empirical effectiveness it stands today still without a universally accepted physical representation that allows us to understand its relation to the world and reality. The novelty of the book comes from the multiple perspectives put forward by top researchers in quantum mechanics, from Europe as well as North and South America, discussing the meaning and structure of the theory of quanta. The book comprises in a balanced manner physical, philosophical, logical and mathematical approaches to quantum mechanics and quantum information. Going from quantum superpositions and entanglement to dynamics and the problem of identity; from quantum logic, computation and quasi-set theory to the category approach and teleportation; from realism and empiricism to operationalism and instrumentalism; the book considers from different angles some of the most intriguing questions in the field. From Buenos Aires to Brussels and Cagliari, from Florence to Florianópolis, the interaction between different groups is reflected in the many different articles. This book is interesting not only to the specialists but also to the general public attempting to get a grasp on some of the most fundamental questions of present quantum physics. (shrink)

Quantum cognition is a new theoretical framework for constructing cognitive models based on the mathematical principles of quantum theory. Due to its increasing empirical success, one wonders what it tells us about the underlying process of cognition. Does it imply that we have quantum minds and there is some sort of quantum structure in the brain? In this paper, I address this important issue by using a new result in the research of quantum foundations. Based (...) on the PBR theorem about the reality of the wave function, I show, given certain assumptions, that the wave function assigned to a cognitive system such as our brain, which is used to calculate probabilities of thoughts/judgment outcomes in quantum cognition, is a real representation of the cognitive state of the system, not a mere representation of incomplete knowledge about the state of the system. This result supports a realist interpretation of quantum cognition, according to which the cognitive state of our brain and its dynamics are not classical but quantum in quantum cognition. In short, quantum cognition implies quantum minds. However, this result does not mean that we have quantum minds and our brain is a quantum computer, since quantum cognition by its standard formulation has not been fully confirmed by experiments. The hope is that more crucial experiments can be done in the near future to determine whether or not quantum cognition is real. (shrink)

The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here (...) something that has until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRW world, for example the number of collapses in a system during a chosen time interval. (shrink)

The essential biological processes that sustain life are catalyzed by protein nano-engines, which maintain living systems in far-from-equilibrium ordered states. To investigate energetic processes in proteins, we have analyzed the system of generalized Davydov equations that govern the quantum dynamics of multiple amide I exciton quanta propagating along the hydrogen-bonded peptide groups in α-helices. Computational simulations have confirmed the generation of moving Davydov solitons by applied pulses of amide I energy for protein α-helices of varying length. The stability (...) and mobility of these solitons depended on the uniformity of dipole-dipole coupling between amide I oscillators, and the isotropy of the exciton-phonon interaction. Davydov solitons were also able to quantum tunnel through massive barriers, or to quantum interfere at collision sites. The results presented here support a nontrivial role of quantum effects in biological systems that lies beyond the mechanistic support of covalent bonds as binding agents of macromolecular structures. Quantum tunneling and interference of Davydov solitons provide catalytically active macromolecular protein complexes with a physical mechanism allowing highly efficient transport, delivery, and utilization of free energy, besides the evolutionary mandate of biological order that supports the existence of such genuine quantum phenomena, and may indeed demarcate the quantum boundaries of life. (shrink)

The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here (...) something that has until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRWm or GRWf world. (shrink)

Quantum stochastic models are developed within the framework of a measure entity. An entity is a structure that describes the tests and states of a physical system. A measure entity endows each test with a measure and equips certain sets of states as measurable spaces. A stochastic model consists of measurable realvalued function on the set of states, called a generalized action, together with measures on the measurable state spaces. This structure is then employed to compute quantum probabilities (...) of test outcomes. We characterize those measure entities that are isomorphic to a quantum probability space. We also show that stochastic models provide a phase space description of quantum mechanics and a realistic model of spin. (shrink)

Part I Introduction -/- Passion at a Distance (Don Howard) -/- Part II Philosophy, Methodology and History -/- Balancing Necessity and Fallibilism: Charles Sanders Peirce on the Status of Mathematics and its Intersection with the Inquiry into Nature (Ronald Anderson) -/- Newton’s Methodology (William Harper) -/- Whitehead’s Philosophy and Quantum Mechanics (QM): A Tribute to Abner Shimony (Shimon Malin) -/- Bohr and the Photon (John Stachel) -/- Part III Bell’s Theorem and Nonlocality A. Theory -/- Extending the Concept of (...) an “Element of Reality” to Work with Inefficient Detectors (Daniel M. Greenberger) -/- A General Proof of Nonlocality without Inequalities for Bipartite States (GianCarlo Ghirardi and Luca Marinatto) -/- On the Separability of Physical Systems (Jon P. Jarrett) -/- Bell Inequalities: Many Questions, a Few Answers (Nicolas Gisin) -/- B. Experiment -/- Do Experimental Violations of Bell Inequalities Require a Nonlocal Interpretation of Quantum Mechanics? II: Analysis a la Bell (Edward S. Fry, Xinmei Qu, and Marlan O. Scully) -/- The Physics of 2 = 1 + 1 (Yanhua Shih) -/- Part IV Probability, Uncertainty, and Stochastic Modifications of Quantum Mechanics -/- Interpretations of Probability in Quantum Mechanics: A Case of “Experimental Metaphysics” (Geoffrey Hellman) -/- “No Information Without Disturbance”: Quantum Limitations of Measurement (Paul Busch) -/- How Stands Collapse II (Philip Pearle) -/- Is There a Relation Between the Breakdown of the Superposition Principle and an Indeterminacy in the Structure of the Einsteinian Space-Time? (Andor Frenkel) -/- Indistinguishability or Stochastic Dependence? (D. Costantini and U. Garibaldi) -/- Part V Relativity -/- Plane Geometry in Spacetime (N. David Mermin) -/- The Transient nows (Steven F. Savitt) -/- Quantum in Gravity? (Michael Horne) -/- A Proposed Test of the Local Causality of Spacetime (Adrian Kent) -/- Quantum Gravity Computers: On the Theory of Computation with Indefinite Causal Structure (Lucien Hardy) -/- “Definability,” “Conventionality,” and Simultaneity in Einstein–Minkowski Space-Time (Howard Stein) -/- Part VI Concluding Words -/- Bistro Banter: A Dialogue with Abner Shimony and Lee Smolin -/- Unfinished Work: A Bequest (Abner Shimony) -/- Bibliography of Abner Shimony. (shrink)

Dynamical activities within living eukaryotic cells are organized by microtubules, main structural components of the cytoskeleton and cylindrical polymers of the protein tubulin. Evidence and theoretical models suggest that states of tubulin may play the role of “bits” in classical microtubule computational automata. The advent of quantum information devices, key roles played by quantum processes in protein dynamics, and coherent ordering in the cell cytoplasm further suggest that microtubules may function as quantum computational devices, and (...) that mesoscopic and macroscopic quantum states are characteristic of living systems. In this paper new results from molecular dynamics simulation based on recently obtained atomic structure of tubulin are presented which provide support for classical and quantum modes of microtubule information processing. (shrink)

This paper proposes an extension of Chaitin's halting probability Ω to a measurement operator in an infinite dimensional quantum system. Chaitin's Ω is defined as the probability that the universal self-delimiting Turing machine U halts, and plays a central role in the development of algorithmic information theory. In the theory, there are two equivalent ways to define the program-size complexity H of a given finite binary string s. In the standard way, H is defined as the length of the (...) shortest input string for U to output s. In the other way, the so-called universal probability m is introduced first, and then H is defined as –log2m without reference to the concept of program-size.Mathematically, the statistics of outcomes in a quantum measurement are described by a positive operator-valued measure in the most general setting. Based on the theory of computability structures on a Banach space developed by Pour-El and Richards, we extend the universal probability to an analogue of POVM in an infinite dimensional quantum system, called a universal semi-POVM. We also give another characterization of Chaitin's Ω numbers by universal probabilities. Then, based on this characterization, we propose to define an extension of Ω as a sum of the POVM elements of a universal semi-POVM. The validity of this definition is discussed.In what follows, we introduce an operator version equation image of H in a Hilbert space of infinite dimension using a universal semi-POVM, and study its properties. (shrink)

First-ever comprehensive introduction to the major new subject of quantum computing and quantum information.

In previous work we gave a mathematical foundation, referred to as DisCoCat, for how words interact in a sentence in order to produce the meaning of that sentence. To do so, we exploited the perfect structural match of grammar and categories of meaning spaces. Here, we give a mathematical foundation, referred to as DisCoCirc, for how sentences interact in texts in order to produce the meaning of that text. First we revisit DisCoCat. While in DisCoCat all meanings are fixed as (...) states, in DisCoCirc word meanings correspond to a type, or system, and the states of this system can evolve. Sentences are gates within a circuit which update the variable meanings of those words. Like in DisCoCat, word meanings can live in a variety of spaces e.g. propositional, vectorial, or cognitive. The compositional structure are string diagrams representing information flows, and an entire text yields a single string diagram in which word meanings lift to the meaning of the entire text. While the developments in this paper are independent of a physical embodiment, both the compositional formalism and suggested meaning model are highly quantum-inspired, and implementation on a quantum computer would come with a range of benefits. We also praise Jim Lambek for his role in mathematical linguistics in general, and the development of the DisCo program more specifically. (shrink)

We offer to extend structural realism into the field of mind and brain studies. The naturalised metaphysics of structural realism has been defined in terms of unification of sciences. The unification program has been carried out nicely in fields of Quantum Mechanics and General Relativity. But for the structural realist metaphysics to receive a recommendation, the unification program needs to be extended to the fields of especial sciences. Our aim in the paper is twofold. On the one hand, we (...) present a structural realist theory of the brain that is well-supported by the best theories of computational neurosciences. On the other hand, and at the same time, we provide further reason for being optimistic about the structural realism metaphysical claim which is based on the idea of unification in sciences. (shrink)

The variety of residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., \-groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated \-groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated \-groupoids, their ideals, and develop a theory of left nuclei. (...) Finally, we extend some parts of the theory of join-completions of residuated \-groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices. (shrink)

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 milliseconds) 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. (shrink)

The topics approached in this collection of papers are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single valued trapezoidal neutrosophic (...) number; inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; fuzzy measure; clustering algorithm; and many more. (shrink)

The book presents investigations into the world of info-computational nature, in which information constitutes the structure, while computational process amounts to its change. Information and computation are inextricably bound: There is no computation without informational structure, and there is no information without computational process. Those two complementary ideas are used to build a conceptual net, which according to Novalis is a theoretical way of capturing reality. We apprehend the reality within a framework known as natural computationalism, the (...) view that the whole universe can be understood as a computational system at many different levels - from quantum mechanical world, to biological organisms including intelligent minds and their societies. Questions about nature of information and computation and their unified view are addressed along with application of info- computational approach to knowledge generation. (shrink)

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559–572, 2009), where we have introduced the notion of Shi-Aharonov quantum computational structure. In this paper we propose an algebraic abstraction from the Hilbert-space quantum computational structures, by introducing the notion of (...) Toffoli-Hadamard algebra. From an intuitive point of view, such abstract algebras represent a natural quantum generalization of both classical and fuzzy-like structures. (shrink)

At present, the Chinese government is trying to resolve various social contradictions, such as people’s ever-growing need for a better life and unbalanced and inadequate development. To do so, urban governance practices including holistic governance, decentralized and interconnected governance, multiple participatory governance, and smart governance have been developed in China. Urban smart governance supported by mobile Internet, the Internet of Things, quantum computing, big data, artificial intelligence, and other information technologies has also entered the field of vision of academics (...) and administrators. However, the research and practice on the integration of organizational structure and smart governance technology for urban governance in China are still insufficient. Hence, this paper proposes the design of the organizational structure of an urban smart governance platform and presents the “1 + N” integrated smart information platform and the “power-sharing linkage, one-center and dual-track” platform construction command system. In this system, the functional module of the information platform for smart urban governance is elaborated. This paper contributes to promoting the modernization of China’s urban governance capacity, which can enhance social equity and social order, promote social democracy and rule of law, and enhance the efficiency of urban governance. (shrink)

From the philosopher’s perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: Physics, in particular Quantum Mechanics, and Computer Science, each long a subject of philosophical speculation and analysis in its own right. Quantum computing combines both of these more traditional areas of inquiry into one wholly new, if not quite independent, science. Over the course of this chapter we will be discussing some of the most (...) important philosophical questions that arise from this merger and philosophical lessons to be learned. (shrink)

The original development of the formalism of quantum mechanics involved the study of isolated quantum systems in pure states. Such systems fail to capture important aspects of the warm, wet, and noisy physical world which can better be modelled by quantum statistical mechanics and local quantum field theory using mixed states of continuous systems. In this context, we need to be able to compute quantum probabilities given only partial information. Specifically, suppose that B is a (...) set of operators. This set need not be a von Neumann algebra. Simple axioms are proposed which allow us to identify a function which can be interpreted as the probability, per unit trial of the information specified by B, of observing the (mixed) state of the world restricted to B to be σ when we are given ρ – the restriction to B of a prior state. This probability generalizes the idea of a mixed state (ρ) as being a sum of terms (σ) weighted by probabilities. The unique function satisfying the axioms can be defined in terms of the relative entropy. The analogous inference problem in classical probability would be a situation where we have some information about the prior distribution, but not enough to determine it uniquely. In such a situation in quantum theory, because only what we observe should be taken to be specified, it is not appropriate to assume the existence of a fixed, definite, unknown prior state, beyond the set B about which we have information. The theory was developed for the purposes of a fairly radical attack on the interpretation of quantum theory, involving many-worlds ideas and the abstract characterization of observers as finite information-processing structures, but deals with quantum inference problems of broad generality. (shrink)

Part I presents a model of interactive computation and a metric for expressiveness, Part II relates interactive models of computation to physics, and Part III considers empirical models from a philosophical perspective. Interaction machines, which extend Turing Machines to interaction, are shown in Part I to be more expressive than Turing Machines by a direct proof, by adapting Gödel's incompleteness result, and by observability metrics. Observation equivalence provides a tool for measuring expressiveness according to which interactive systems are more expressive (...) than algorithms. Refinement of function equivalence by observation of outer interactive behavior and inner computation steps is examined. The change of focus from algorithms specified by computable functions to interaction specified by observation equivalence captures the essence of empirical computer science. Part II relates interaction in models of computation to observation in the natural sciences. Explanatory power in physics is specified by the same observability metric as expressiveness in interactive systems. Realist models of inner structure are characterized by induction, abduction, and Occam's Razor. Interactive realism extends the hidden-variable model of Einstein to hidden interfaces that provide extra degrees of freedom to formulate hypotheses with testable predictions conforming with quantum theory. Greater expressiveness of collaborative computational observers (writers) than single observers implies that hidden-interface models are more expressive than hidden-variable models. By providing a common foundation for empirical computational and physical models we can use precise results about computational models to establish properties of physical models. Part III shows that the evolution in computing from algorithms to interaction parallels that in physics from rationalism to empiricism. Plato's cave metaphor is interactively extended from Platonic rationalism to empiricism. The Turing test is extended to TMs with hidden interfaces that express interactive thinking richer than the traditional Turing test. Interactive (nonmonotonic) extensions of logic such as the closed-world assumption suggest that interactiveness is incompatible with monotonic logical inference. Procedure call, atomicity of transactions, and taking a fixed point are techniques for closing open systems similar to "preparation" followed by "observation" of a physical system. Pragmatics is introduced as a framework for extending logical models with a fixed syntax and semantics to multiple-interface models that support collaboration among clients sharing common resources. (shrink)

Combining physics, mathematics and computer science, quantum computing and its sister discipline of quantum information have developed in the past few decades from visionary ideas to two of the most fascinating areas of quantum theory. General interest and excitement in quantum computing was initially triggered by Peter Shor (1994) who showed how a quantum algorithm could exponentially “speed-up” classical computation and factor large numbers into primes far more efficiently than any (known) classical algorithm. Shor’s algorithm (...) was soon followed by several other algorithms that aimed to solve combinatorial and algebraic problems, and in the years since theoretical study of quantum systems serving as computational devices has achieved tremendous progress. Common belief has it that the implementation of Shor’s algorithm on a large scale quantum computer would have devastating consequences for current cryptography protocols which rely on the premise that all known classical worst-case algorithms for factoring take time exponential in the length of their input (see, e.g., Preskill 2005). Consequently, experimentalists around the world are engaged in attempts to tackle the technological difficulties that prevent the realisation of a large scale quantum computer. But regardless whether these technological problems can be overcome (Unruh 1995; Ekert and Jozsa 1996; Haroche and Raimond 1996), it is noteworthy that no proof exists yet for the general superiority of quantum computers over their classical counterparts. -/- The philosophical interest in quantum computing is manifold. From a social-historical perspective, quantum computing is a domain where experimentalists find themselves ahead of their fellow theorists. Indeed, quantum mysteries such as entanglement and nonlocality were historically considered a philosophical quibble, until physicists discovered that these mysteries might be harnessed to devise new efficient algorithms. But while the technology for harnessing the power of 50–100 qubits (the basic unit of information in the quantum computer) is now within reach (Preskill 2018), only a handful of quantum algorithms exist, and the question of whether these can truly outperform any conceivable classical alternative is still open. From a more philosophical perspective, advances in quantum computing may yield foundational benefits. For example, it may turn out that the technological capabilities that allow us to isolate quantum systems by shielding them from the effects of decoherence for a period of time long enough to manipulate them will also allow us to make progress in some fundamental problems in the foundations of quantum theory itself. Indeed, the development and the implementation of efficient quantum algorithms may help us understand better the border between classical and quantum physics (Cuffaro 2017, 2018a; cf. Pitowsky 1994, 100), and perhaps even illuminate fundamental concepts such as measurement and causality. Finally, the idea that abstract mathematical concepts such as computability and complexity may not only be translated into physics, but also re-written by physics bears directly on the autonomous character of computer science and the status of its theoretical entities—the so-called “computational kinds”. As such it is also relevant to the long-standing philosophical debate on the relationship between mathematics and the physical world. (shrink)