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III. An Organic, Genomic, Conducive UniVerse

2. Quantum Complex Systems

As our worldwide humankind proceeds to learn on her/his own, credibly filling in an episodic development from universe to us, new phases of integral clarity are being achieved. The realm of subatomic phenomena was dubbed “quantum,” from the Latin for “amount,” by way of Max Planck’s realization, circa 1900, that energy waves are composed of discrete units akin to matter. For over a century, as physicists have tried to study and comprehend, with a stellar cast of Einstein, Bohr, Schrodinger, Bohm, and more, quantum “mechanics” became daunted with arcane such as entanglement, decoherence, double-slit experiments, dead or alive cats, uncertainty, and so on.

Around 2000 however, theorists began to articulate an informational component, along with algorithmic communication, as reported in An Information Computation Turn. In recent years this project has flourished with a quest for quantum computers. As the work proceeded, since the 2010s a recognition of complex network systems similarly present in this deep domain arose. This new section circa Spring 2014 will try to document the historic revision, as if now due to humankind a century later. As the citations attest, a more familiar description accrues akin to every other scale of nature and society. For one example, an international Network Science conference (NetSci 2014 search) has a “Quantum Network” symposia.

A further significance is to remove the artificial classical – quantum divide and disconnect. No longer a remote, intractable realm, which by its fundamental locus seemed to dim hopes of understanding anything, it is now brought into the fold as another, albeit basic, scale. In addition, as a recent series of Emergent Quantum Mechanics conferences have explored (EmQM11 & 13), this is where the turtles bottom out. What lies beneath is not another material stage but a strongly implied mathematical, implicate, generative source. Within our collaborative vista, many diverse pieces are at last coming into place. An appropriate name to engage this might then be "Quantome."

Heinz von Foerster 100 Self-Organization and Emergence Congress. www.univie.ac.at/hvf11/congress/EmerQuM.html. Heinz von Foerster (1911-2002) was an Austrian American physicist, philosopher and a pioneer of cybernetics and systems theory. This centenary conference was held in November 2011 in Vienna with a dual focus on Self-Organization and Emergence in Nature and Society, and Emergent Quantum Mechanics. Keynoters for the first topic are Albert-Laszlo Barabasi, John Holland and Didier Sornette, and for the other Stephen Adler, Gerard ‘t Hooft, and Lee Smolin. Abstract are available for these talks, and some fifty others such as Emergence, Gravity, and Thermodynamics by Bei-Lok Hu, reviewed in A Thermodynamics of Life.

I review the proposal made in my 2004 book, that quantum theory is an emergent theory arising from a deeper level of dynamics. The dynamics at this deeper level is taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation-anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with phenomenological proposals for stochastic modifications to Schroedinger dynamics. (Adler)

Highly interconnected networks with amazingly complex structure de-scribe systems as diverse as the World Wide Web, our cells, social systems or the economy. In the past decade we learned that most of these networks are the result of self-organizing processes governed by simple but generic laws, resulting in architectural features that makes them much more similar to each other than one would have expected by chance. I will discuss the recurring patterns of our interconnected world and its implications to network robustness and spreading processes. (Barabasi)

Various classical systems are discussed that can be approached with standard statistical methods. It is shown how quantum mechanical procedures can be applied to such systems to study features such as large-distance behavior. As a result, one finds that the time evolution of its large distance correlations can be written in terms of rigorously quantum mechanical Schroedinger equations. One concludes that even though the dynamical laws are classical, the probability distributions are described by quantum states, showing quantum entanglement. These quantum states violate Bell's inequalities. The suspicion that our universe is also described by such a classical, deterministic underlying theory leads to a natural interpretation of quantum mechanics. (Gerard ‘t Hooft)

Quantum Complexity Science Initiative. Quamplexity.org. The site for Jacob Biamonte’s innovative group which seeks, as the quotes say, to join quantum systems with nonlinear networks, which each and all spring from an informative physical realm. See also Quantum Machine Learning by Biamonte, et al, above.

We are a vibrant and focused research group happily based in the Department of Physics at the University of Malta. We study the fundamental implications physics has on information and computation, typically viewed through the lens of quantum theory. Quantum theory has provided uninterrupted insights both in the fundamental laws governing our world and in the novel mathematics developed in its description.

By correctly studying information as an entity fundamentally governed by the laws of physics, development of an emerging common language is already binding certain ideas and mapping some techniques between the fields of quantum physics and complexity science. What’s more, the ubiquitous use of various network and graph theories inside of both disciplines, creates a stage for an abstracted comparison of networked systems, recovering both fields as special cases of more general mathematical entities. An ultimate goal of our effort is to form a new theory, uniting these disciplines.

Quantum Interaction. www.quantuminteraction.org/conferences/qi2016. As the quote describes, an eclectic meeting to imagine a humantum (just coined) merger of these separate micro sub-atomic, macro classical, and regnant sapiens phases. Typical papers are Quantum Cognition beyond Hilbert Space, and Categorical Compositional Cognition (arXiv:1608.03785). Proceedings are now published with this title as Springer Lecture Notes in Computer Science 10106.

The 10th international conference on Quantum Interaction (QI 2016) was held at the Downtown Campus of San Francisco State University (SFSU), 835 Market Street, San Francisco, California, from July 20—22, 2016. Over the years, the Quantum Interaction conferences have provided a debating ground for applications of formal concepts of quantum theory to a variety of areas outside of the natural remit of physics. Quantum Interaction has developed into an emerging interdisciplinary area of science combining research topics in mathematics, physics, psychology, economics, cognitive and computer science. These include: decision making in a variety of social science fields, studies of non-separable concept combinations in natural language, information retrieval and semantic networks in computer science, proposals to test temporal nonlocality in perception and cognition, and the study of non-commutative structures in learning behavior.

Quantum Many-Body Systems Far from Equilibrium. www.physics.sun.ac.za/~kastner/qmb18/index. This is a March 2018 conference at the National Institute for Theoretical Physics in Stellenbosch, South Africa about quench dynamics, thermalization and many-body localization. We also note as an example of how quantum phenomena are now being perceived and treated in similar ways to classical condensed matter.

Recent progress in manipulating cold atoms and ions has brought the study of non-equilibrium behavior of isolated quantum systems into the focus of research. This has given rise to the development of novel theoretical concepts and numerical tools, but also led to a renewed interest in foundational questions. Important recent developments, like quench protocols, thermalisation in isolated quantum systems, as well as absence of thermalisation due to many-body localisation, will be in the focus of this workshop. We aim to bring together researchers from a variety of fields related to this topic, including quantum information, statistical physics, mathematical physics, cold atoms and condensed matter physics.

Aerts, Diederik and Sandro Sozzo. What is Quantum? Unifying Its Micro-Physical and Structural Appearance. arXiv:1405.7572. We cite this posting by Vrije Universiteit Brussel, Center Leo Apostel for Interdisciplinary Studies, theorists as an example of the 2010s worldwide expansion of this primal realm. Two aspects may be noted – a reinterpretation of micro quantum phenomena away from arcane terms and strangeness to admit complex systems, and their effect in macro, classical scales from proteins and cells to psychology and economies. Consider also these arXiv papers: Quantum Structure in Economics (1301.0751) and Quantum Structure in Cognition (1104.1322) by the authors, Quantum Structure in Competing Lizard Communities by Aerts, et al (search, 1212.0109), and On the Foundations of the Theory of Evolution (search Aerts, 1212.0107). Continue on with Liane Gabora, Jerome Busemeyer, others as you find them. In our 2014 midst, the daunting quantum divide is being breached to achieve a true natural wholeness of universe and human.

We can recognize two modes in which 'quantum appears' in macro domains: (i) a 'micro-physical appearance', where quantum laws are assumed to be universal and they are transferred from the micro to the macro level if suitable 'quantum coherence' conditions (e.g., very low temperatures) are realized, (ii) a 'structural appearance', where no hypothesis is made on the validity of quantum laws at a micro level, while genuine quantum aspects are detected at a structural-modeling level. In this paper, we inquire into the connections between the two appearances. We put forward the explanatory hypothesis that, 'the appearance of quantum in both cases' is due to 'the existence of a specific form of organisation, which has the capacity to cope with random perturbations that would destroy this organisation when not coped with'. We analyse how 'organisation of matter', 'organisation of life', and 'organisation of culture', play this role each in their specific domain of application, point out the importance of evolution in this respect, and put forward how our analysis sheds new light on 'what quantum is'. (Abstract)

Asano, Masanari, et al. Quantum Adaptivity in Biology: From Genetics to Cognition. Springer, 2015. At the frontiers of this vital unification of life and cosmos, an international team from Japan and Sweden including Andrei Khrennikov shows how current revisions of nature’s basic substance in terms of information processing can neatly meld with an organic systems science. A companion paper, Quantum Information Biology: From Information Interpretation of Quantum Mechanics to Applications in Molecular Biology and Cognitive Psychology, by this group is posted at arXiv:1503.02515.

The aim of this book is to introduce a theoretical/conceptual principle (based on quantum information theory and non-Kolmogorov probability theory) to understand information processing phenomena in biology as a whole—the information biology — a new research field, which is based on the application of open quantum systems (and, more generally, adaptive dynamics) outside of physics as a powerful tool. Thus this book is about information processing performed by biosystems. Since quantum information theory generalizes classical information theory and presents the most general mathematical formalism for the representation of information flows, we use this formalism. In short, this book is about quantum bioinformation. (Synopsis) However, it is not about quantum physical processes in bio-systems. We apply the mathematical formalism of quantum information as an operational formalism to bio-systems at all scales: from genomes, cells, and proteins to cognitive and even social systems. (xi)

Baez, John and Jacob Biamonte. A Course on Quantum Techniques for Stochastic Mechanics. arXiv:1209.3632. UC Riverside, National University of Singapore, and Institute for Scientific Interchange ISI, Torino, mathematicians post a 235 page draft for a volume about nascent realizations that subatomic phenomena, long seen remote to macro states like us, actually has many innate affinities. This novel bridging can be facilitated by clearing up and aligning terms and definitions. Check the websites for each author, and a “Quantum Network” from California to Italy, Singapore, for more. As the second quote notes, again a prime aspect is to illume networks across nature and society, from which can be distilled, as much implied, an independent, universal source.

Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, there is a widely used and successful theory of "chemical reaction networks," which describes the interactions of molecules in a stochastic rather than quantum way. Computer science and population biology use the same ideas under a different name: "stochastic Petri nets". But if we look at these theories from the perspective of quantum theory, they turn out to involve creation and annihilation operators, coherent states and other well-known ideas - but in a context where probabilities replace amplitudes. We explain this connection as part of a detailed analogy between quantum mechanics and stochastic mechanics. We also study the overlap of quantum mechanics and stochastic mechanics, which involves Hamiltonians that can generate either unitary or stochastic time evolution. (Abstract)

Mathematical Network Theory Network theory is a diverse subject which developed independently in several disciplines to rely on graphs with additional structure to model complex systems. We study the mathematical theory underlying the relations between these seemingly different systems. This unified mathematical language of networks has provided interoperability between—for example—ecological and chemical reaction networks, field theories, analog electrical circuits, tensor networks and quantum systems. This research has formed the basis for the recent push towards studying increasingly larger quantum mechanical systems, where the analysis is undergoing a shift towards embracing the concepts of complex networks. An ultimate goal is a mathematical theory and fully categorical description which pinpoints the similarities and differences between the use of networks throughout the sciences. This would give rise to a theory of networks augmenting the current statistical mechanics approach to complex network structure, evolution, and process with a theory based on quantum mechanics. (Quantum Network site)

Bawden, David, et al. “Potentialities or Possibilities:” Towards Quantum Information Science.. Journal of the Association for Information Science and Technology (JASIST). Online June, 2014. The City University London, Centre for Information Science, scholar continues his project to broaden appreciations of our distinguishing capacity for knowledge and conversation by finding occasions and roots for it in such substantial physics domains.

The use of quantum concepts and formalisms in the information sciences is assessed through an analysis of published literature. Five categories are identified: use of loose analogies and metaphors between concepts in quantum physics and library/information science; use of quantum concepts and formalisms in information retrieval; use of quantum concepts and formalisms in studying meaning and concepts; quantum social science, in areas adjacent to information science; and the qualitative application of quantum concepts in the information disciplines. Quantum issues have led to demonstrable progress in information retrieval and semantic modelling, with less clear-cut progress elsewhere. Whether there may be a future “quantum turn” in the information sciences is debated, the implications of such a turn are considered, and a research agenda outlined. (Abstract)

Biamonte, Jacob, et al. Quantum Machine Learning. arXiv:1611.09347. A six member team with postings in Malta, Canada, Spain, Sweden, Germany, and the USA, including Seth Lloyd, advance a novel synthesis of recurrent neural net machine processes with quantum phenomena seen to possess algorithmic, complex dynamic system, information processing affinities. An expansive scope, speed and capability can thus be availed. Once again, from quantum depths to human heights, cosmic evolutionary optimization seems most about an educative experience. See also a citation herein for Biamonte’s Quantum Complexity Science Initiative.

Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking and control of experimental quantum computing systems, including adaptive quantum phase estimation and designing quantum computing gates. On the other hand, quantum mechanics offers tantalizing prospects to enhance machine learning, ranging from reduced computational complexity to improved generalization performance. The most notable examples include quantum enhanced algorithms for principal component analysis, quantum support vector machines, and quantum Boltzmann machines. Progress has been rapid, fostered by demonstrations of midsized quantum optimizers which are predicted to soon outperform their classical counterparts. Further, we are witnessing the emergence of a physical theory pinpointing the fundamental and natural limitations of learning. (Abstract)

Bianconi, Ginestra. Interdisciplinary and Physics Challenges of Network Theory. arXiv:1509.00345. As a grand synthesis across nature and nurture proceeds apace, a Queen Mary University of London mathematical physicist sketches out how a newly found “universally of complex networks” can be extended even to quantum domains. Such a perception then reveals their generic, scale-free presence from every cosmic to cerebral realm. See also her paper Network Geometry from Complexity to Quantum Geometry (1511.04539), Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free with Christoph Rahmede (search, 1506.02648).and Emergent Complex Network Geometry (1412.3405).

Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and dynamics. After almost twenty years of the field, new challenges lie ahead. These challenges concern the multilayer structure of most of the networks, the formulation of a network geometry and topology, and the development of a quantum theory of networks. Making progress on these aspects of network theory can open new venues to address interdisciplinary and physics challenges including progress on brain dynamics, new insights into quantum technologies, and quantum gravity. (Abstract)

A quantum theory of networks, combining quantum mechanics and complex networks properties, could play a pivotal role in the future development of quantum communication technologies. When fully implemented on the large scale, it is likely that they will share some of the complexity properties of the current communication systems. Therefore the cross-disciplinary field between complex network and quantum information is gaining increasing attention. On one side, quantum dynamical processes are increasingly explored on network structures. On the other side, quantum information proposals, are pushing the frontier of our understanding of how quantum networks could be realized. (2)

Bianconi, Ginestra and Christoph Rahmede. Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free. arXiv:1506.02648. In accord with her Interdisciplinary and Physics Challenges of Network Theory (search, 1509.00345) the Queen Mary University of London theorist is joined by a Karlsruhe Institute of Technology, Germany, physicist to add more credence to a spontaneously self-organizing quantum cosmology. A graphic display therein of a scale-free complex quantum network could just as well be a rich-hub neural network, or any other domain such as social media. In these 2010s, largely unnoticed, a radical new perception of this fundamental phase has accrued which makes it no longer separate by an unrealistic divide from classical macro phenomena. A lengthy bibliography braces this fertile advance.

Several theoretical approaches have been proposed in quantum gravity for the description and characterization of quantum discrete spaces including loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, energetic spin networks, and diffusion processes on such quantum geometries. In most of these approaches, the discrete spaces are network manifolds with homogeneous degree distribution and do not have common features with complex networks describing complex systems such as the brain or the biological networks in the cell. Nevertheless it has been discussed that a consistent theory of quantum cosmology could also be a theory of self-organization, sharing some of its dynamical properties with complex systems and biological evolution. In the last decades, the field of network theory has made significant advances in the understanding of the underlying network topology of complex systems as diverse as the biological networks in the cell, the brain networks, or the Internet. Therefore an increasing interest is addressed to the study of quantum gravity from the information theory and complex network perspective. (2)

Briegel, Hans. On Creative Machines and the Physical Origins of Freedom. Nature Scientific Reports. 2/522, 2012. The University of Innsbruck physicist affirms from the latest integration of statistical mechanics with nonlinear dynamics (article keywords) that “higher biological entities” like us do indeed possess a valid free will. This does not quite accord with his “creative machines” term, so natural philosophy clarifications are still in order. We also refer to Briegel’s companion Projective Simulation for Artificial Intelligence in this journal (2/400, 2012) which is the basis for the Giuseppe Paparo, et al, paper on Quantum Learning Systems (search).

We discuss the possibility of free behavior in embodied systems that are, with no exception and at all scales of their body, subject to physical law. We relate the discussion to a model of an artificial agent that exhibits a primitive notion of creativity and freedom in dealing with its environment, which is part of a recently introduced scheme of information processing called projective simulation. This provides an explicit proposal on how we can reconcile our understanding of universal physical law with the idea that higher biological entities can acquire a notion of freedom that allows them to increasingly detach themselves from a strict dependence on the surrounding world. (2/522 Abstract)

We can show, on the basis of physical laws as we understand them today, that entities with a certain degree of physical or biological organization, capable of evolving a specific type of memory, can indeed develop an original notion of creativity and freedom in their dealing with the environment. Our argument will be based on the concept of projective simulation which is a physical model of information processing for artificial agents. (1) This demonstrates, first, that a notion of freedom can indeed exist for entities that operate, without exception and at all scales, under the laws of physics. It also shows that free behavior can be understood as an emergent property of biological systems of sufficient complexity that has evolved a specific form of memory. (2)

We propose a model of a learning agent whose interaction with the environment is governed by a simulation-based projection, which allows the agent to project itself into future situations before it takes real action. Projective simulation is based on a random walk through a network of clips, which are elementary patches of episodic memory. The network of clips changes dynamically, both due to new perceptual input and due to certain compositional principles of the simulation process. During simulation, the clips are screened for specific features which trigger factual action of the agent. The scheme is different from other, computational, notions of simulation, and it provides a new element in an embodied cognitive science approach to intelligent action and learning. Our model provides a natural route for generalization to quantum-mechanical operation and connects the fields of reinforcement learning and quantum computation. (2/400 Abstract)

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