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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet Lifescape

1. Quantum Organics in the 21st Century

Kreula, Juha, et al. Few-Qubit Quantum-Classical Simulation of Strongly Correlated Lattice Fermions. EPJ Quantum Technology. Online August, 2016. Oxford University and University of the Basque Country physicists press the frontiers of human inquires into nature’s basic realms to deeply understand, so as to take up and over a new matter-energy, space-time, information knowledge, genesis creation. See also Non-linear Quantum-Classical Scheme to Simulate Non-equilibrium Strongly Correlated Fermionic Many-body Dynamics by this group in Nature Scientific Reports (6/32940). We cite both Abstracts, and introduce this new European Physics Journal online edition.

We study a proof-of-principle example of the recently proposed hybrid quantum-classical simulation of strongly correlated fermion models in the thermodynamic limit. In a ‘two-site’ dynamical mean-field theory (DMFT) approach we reduce the Hubbard model to an effective impurity model subject to self-consistency conditions. The resulting minimal two-site representation of the non-linear hybrid setup involves four qubits implementing the impurity problem, plus an ancilla qubit on which all measurements are performed. We outline a possible implementation with superconducting circuits feasible with near-future technology. (EPJ Abstract)

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. (NSR Abstract)

EPJ QT Aims and Scope Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics. Topics can include: Quantum measurement, complex systems, networks, cellular automata, electro & opto-mechanical systems, nanorobotics, information, communication, computation, thermodynamics, metamaterials, biology, sensing, and hybrid systems.

Laughlin, Robert. Self-Organization of Matter. http://large.stanford.edu/rbl/lectures/index.htm. A slide presentation of the Nobel laureate physicist’s conception of a different, emergent universe which is not referable to or mediated by a bottom “theory of everything.” By shifting one’s perspective toward what and whom nature can create, a dynamic materiality able to organize itself into an increasing animate complexity is revealed. Rather than a quantum arbiter down “there,” the same universal pattern and process is found “everywhere.” Also noted in Current Vistas.

The true origin of these rules is the tendency of natural systems to organize themselves according to collective principles. Many phenomena in nature are like pointillist paintings. Observing the fine details yields nothing but meaningless fact. To correctly understand the painting one must step back and view it as a whole. In this situation a huge number of imperfect details can add up to larger entities of great perfection. We call this effect in the physical world emergence. (Slide 3)

Li, Bo, et al. Quantum Clique Gossiping. Nature Scientific Reports. 8/2747, 2018. We cite from the Chinese Academy of Sciences as a current example of how quantum phenomena, long held to be remote and inexplicable, is now treated as any other classical domain. Today the same complex, dynamical networks are commonly perceived, in this case for social media information discourse. If the quantum realm remains a fundamental arbiter, what kind of cosmic reality could such cerebral, often genomic, communicative features so imply. See also Open Quantum Generalization of Hopfield Neural Networks at arXiv:1701.01727.

This paper establishes a framework of quantum clique gossiping by introducing local clique operations to networks of interconnected qubits. Cliques are local structures in complex networks being complete subgraphs, which can be used to accelerate classical gossip algorithms. Based on cyclic permutations, clique gossiping leads to collective multi-party qubit interactions. Remarkably, the use of larger quantum cliques does not necessarily increase the speed of the network density aggregation, suggesting quantum network dynamics is not entirely decided by its classical topology. (Abstract excerpt)

Li, Qiang, et al. Evolution of Quantum and Classical Strategies on Networks by Group Interactions. New Journal of Physics. 14/103034, 2012. We note this paper by Chongquig University, China, and University of Adelaide, researchers including Derek Abbott as a good example of how readily complex system phenomena are now being found in this deepest realm. See also the 2014 and 2015 volumes of the Annual Review of Condensed Matter Physics for an increasing number of similar treatments.

In this paper, quantum strategies are introduced within evolutionary games in order to investigate the evolution of quantum and classical strategies on networks in the public goods game. Comparing the results of evolution on a scale-free network and a square lattice, we find that a quantum strategy outperforms the classical strategies, regardless of the network. Moreover, a quantum strategy dominates the population earlier in group interactions than it does in pairwise interactions. In particular, if the hub node in a scale-free network is occupied by a cooperator initially, the strategy of cooperation will prevail in the population. However, in other situations, a quantum strategy can defeat the classical ones and finally becomes the dominant strategy in the population. (Abstract)

Lombardi, Olimpia, et al, eds. Quantum Chaos and Complexity. Entropy. Online July, 2018. This is a Special Issue proposal by Argentine and Brazilian physicists which is open for manuscripts until December 31, 2018. We also note as a late 2010s instance of how much quantum phenomena, which retains its deep fundamental import, is yet being treated in similar nonlinear system methods to all other classical stages.

The quantum chaos field is usually defined as the study of the connection between quantum mechanics and classical chaotic behavior, in order to understand how a well-defined characterization of the stationary and dynamical aspects of classical chaos emerges, both in the energy and in the time domains. However, research on quantum chaos has certainly extended its scope during recent decades, due to the increasing discovery of connections with other disciplines in physics. It is nowadays an active field that has become of fundamental importance in the study of the properties, dynamics and control of complex quantum systems, and has found applications in a vast range of phenomena: nonlinear quantum dynamics, quantum complex networks, chaotic scattering in open systems, phase transitions in mixed quantum dynamics, Anderson localization, atoms in strong fields, and more.

Lorenzo, Salvatore, et al. Quantum Critical Scaling under Periodic Driving. Nature Scientific Reports. 7/5672, 2017. University of Palermo, Milan, Calabria, and Cologne physicists identify another occasion of physical phase transition criticality, in this case for quantum phenomena. If one might join many similar reports from evolutionary (Gilpin), animal behaviors (Popkin) and more within a worldwide vista, an infinitely recurrent in kind uniVerse to human epitome is indeed being filled in.

Universality is key to the theory of phase transitions, stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model’s microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time proportional to the size of the system. Our results suggest that relevant features of the universality do hold also when the system is brought out-of-equilibrium by a periodic driving. (Abstract)

A paradigm of phase transitions is the concept of universality, i.e., the insensitivity to microscopic details at the critical point of many particle systems at equilibrium. Universality allows to classify phase transitions according to critical exponents, which govern the scaling of several quantities close to the critical point. A quantum many body system at zero temperature can encounter a phase transition driven by quantum fluctuations when some of its control parameters are tuned to a critical value, which in the simplest case separates an ordered from a disordered phase. (1)

Martyn, John, et al. Grand Unification of Quantum Algorithms. PRX QUANTUM. 2/040203,, 2021. We cite this 40 page entry in a new Physical Review journal by four MIT physicists as an example of the extent that this deepest phenomenal domain has become as amenable to our Earthuman collaborations and cocreative take over, so it seems, as the long prior classical stage.

Quantum algorithms offer significant speed-ups over classical counterparts as evident by their advantage for quantum search, quantum phase estimation, and Hamiltonian simulation by way of composite algorithm subroutines. Here, we provide a tutorial through these developments, illustrating how quantum signal processing may be generalized to the Quantum Singular Value Transformation method. This overview illustrates how QSVT can operate as an overall framework so as to suggest a grand unification of quantum algorithms. (Abstract)

Melko, Roger, et al. Restricted Boltzmann Machines in Quantum Physics. Nature Physics. 15/9, 2019. While a 20th century mindset that this field of study is so strange as to be beyond comprehension persists, we cite this entry by Perimeter Institute, Flatiron Institute (Giuseppe Carleo), MPI Quantum Physics, and Vector Institute for AI, Toronto, researchers as another example of its worldwide 21st century reconception. While still foundational, it is being widely treated by the same complex network phenomena akin to every other macro-phase. See Philip Ball’s and Lee Smolin’s 2019 books for a full length treatment. See also Quantum Natural Gradient by GC, et al at arXiv:1909.02108 for similar excursions.

A type of stochastic neural network called a restricted Boltzmann machine has been widely used in artificial intelligence applications for decades. They are now finding new life in the simulation of complex wavefunctions in quantum many-body physics.

To solve all these issues, we need to wipe the data clean, go back to the first principles of quantum theory and general relativity, decide which are necessary and which are open to question, and see what new principles we might need. Do that, and an alternative description of physics becomes possible, one that explains things not in terms of objects situated in a pre-existing space as we do now, but in terms of events and the relationships between them. (Lee Smolin, New Scientist, August 24, 2019, 36)

Norrman, Andreas and Lukasz Rudnicki. Quantum Correlations and Complementarity of Vectorial Light Fields. arXiv:1904.07533. MPI Science of Light researchers advance the 2019 frontier of quantum comprehensions by way of adding, as the quotes say, a third, integral aspect to the standard particle-wave pairing. This unifying quality is dubbed a “triality,” a novel word which well serves. Our interest is to see natural light and vision gain a correspondent wholeness and affinity, for example, with the perennial yang-yin Tao image.

We explore quantum correlations of general vector-light fields in multi-slit interference and show that the nth-order field-coherence matrix is directly linked with the reduced n-photon density matrix. The connection is utilized to examine photon wave-particle duality in the double-slit configuration, revealing that there is a hidden information-theoretic contribution that complements the standard inequality associated with such duality by transforming it into a strict equality, a triality identity. We also establish a general quantum complementarity relation among the field correlations and the particle correlations which holds for any number of slits, correlation orders, and vector-light states. (Abstract)

The quantum theory of optical coherence, dealing with field correlations of light, is ubiquitous in the physical sciences; it is widely exploited in quantum optics, atomic physics, optomechanics, quantum simulation, quantum electronics, and cosmology, among other research areas. Recently quantum coherence of genuine vector-light fields was examined in double-slit interference, revealing a new fundamental aspect of photon wave-particle duality. The rapid progress in quantum information science has at the same time led to an ever-growing interest towards nonclassical correlations that may prevail in multipartite quantum compositions of diverse physical nature. (1)

In this Letter, we investigate the relationship between field correlations and particle correlations of true vectorial light of any quantum state in multi-slit interference. We show that the nth-order field correlations are directly connected to the particle correlations among n photons. This relationship is especially employed to explore quantum complementarity in the celebrated double-slit setup, resulting in the discovery of a tight equality which may be interpreted as describing photon wave-particle triality (1)

Orus, Roman. Tensor Networks for Complex Quantum Systems. Nature Reviews Physics. 1/9, 2019. We cite this extensive, well referenced paper by the Spanish physicist with postings such as Barcelona Supercomputing Center and CSO Multiverse Computing (see RO’s site) for how it treats this quantum domain in several nonlinear ways. The author goes on to develop affinities with Chomsky linguistics, machine learning, chemistry, neural net topologies and more. In regard, the entry exemplifies progress toward our current micro quantum and macro classical integral unification.

Tensor network states and methods have advanced in recent years. Originally developed in condensed matter physics and based on renormalization group ideas, tensor networks are being revived thanks to quantum information theory and understandings of entanglement in quantum many-body systems. Tensor network states play a key role in other disciplines such as quantum gravity and artificial intelligence. In this context, we provide an overview of basic concepts and key developments such as structures and algorithms, global and gauge symmetries, fermions, topological order, classification of phases, entanglement Hamiltonians, AdS/CFT, conformal field theory, quantum chemistry, disordered systems, and many-body localization. (Abstract excerpt)

Overbye, Dennis. Quantum Trickery. New York Times. December 27, 2005. From Einstein and Bohr to today’s theorists, the quantum realm seems to resist comprehension. The article touches many bases to convey an uneasy sense of something being missed, that fundamental conjectures still need revision. Are we finding irreducible randomness, or is reality in some way informational in essence.

Paparo, Giuseppe, et al. Quantum Google in a Complex Network. arXiv:1303.3891. Mathematicians Paparo, with Mark Muller and Miguel Martin-Delgado, Universidad Complutense, Madrid, and Francesc Comellas, Universitat Politecnica de Catalunya, Barcelona, make a quantum leap from this deep domain to the algorithmic worldwide web to propose that the same dynamic computational systems can be found in effect in both cases. In any event, the latest inklings of a grand unitary scale of nature and society, universe to human, as long intimated and sought, as must be there and true.

We investigate the behavior of the recently proposed quantum Google algorithm, or quantum PageRank, in large complex networks. Applying the quantum algorithm to a part of the real World Wide Web, we find that the algorithm is able to univocally reveal the underlying scale-free topology of the network and to clearly identify and order the most relevant nodes (hubs) of the graph according to their importance in the network structure. Moreover, our results show that the quantum PageRank algorithm generically leads to changes in the hierarchy of nodes. In addition, as compared to its classical counterpart, the quantum algorithm is capable to clearly highlight the structure of secondary hubs of the network, and to partially resolve the degeneracy in importance of the low lying part of the list of rankings, which represents a typical shortcoming of the classical PageRank algorithm. (Abstract)

It is of great interest to explore and classify the large amount of information that is stored in huge complex networks like the World Wide Web (WWW). A central problem of bringing order to classical information stored in networks such as the WWW amounts to rank nodes containing such information according to their relevance. A highly successful and nowadays widespread tool for this purpose has been the PageRank algorithm, which lies at the core of Google's ranking engine. In the foreseeable future where large-scale quantum networks have become a reality, classifying the quantum information stored therein will become a priority. It is in this sense that the recently introduced quantum PageRank algorithm is an important achievement as it constitutes a quantization of the classical PageRank protocol. This new quantum algorithm has shown, applied to small networks, a striking behavior with respect to its classical counterpart, such as producing a different hierarchy of nodes together, paired with a better performance. In this paper we investigate the properties of the quantum algorithm for networks which model large real-world complex systems. (1)

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