The problem of emergence in physical theories makes necessary to build a general theory of the relationships between the observed system and the observing system. It can be shown that there exists a correspondence between classical systems and computational dynamics according to the Shannon-Turing model. A classical system is an informational closed system with respect to the observer; this characterizes the emergent processes in classical physics as phenomenological emergence. In quantum systems, the analysis based on the computation theory fails. It is here shown that a quantum system is an informational open system with respect to the observer and able to exhibit processes of observational, radical emergence. Finally, we take into consideration the role of computation in describing the physical world.
The problem of emergence in physical theories makes necessary to build a general theory of the relationships between the observed system and the observing system. It can be shown that there exists a correspondence between classical systems and computational dynamics according to the Shannon-Turing model. A classical system is an informational closed system with respect to the observer; this characterizes the emergent processes in classical physics as phenomenological emergence. In quantum systems, the analysis based on the computation theory fails. It is here shown that a quantum system is an informational open system with respect to the observer and able to exhibit processes of observational, radical emergence. Finally, we take into consideration the role of computation in describing the physical world.
The problem of emergence in physical theories makes necessary to build a general theory of the relationships between the observed system and the observing system. It can be shown that there exists a correspondence between classical systems and computational dynamics according to the Shannon-Turing model. A classical system is an informational closed system with respect to the observer; this characterizes the emergent processes in classical physics as phenomenological emergence. In quantum systems, the analysis based on the computation theory fails. It is here shown that a quantum system is an informational open system with respect to the observer and able to exhibit processes of observational, radical emergence. Finally, we take into consideration the role of computation in describing the physical world.
This paper examines whether unitary evolution alone is sufficient to explain emergence of the classical world from the perspective of computability theory. Specifically, it looks at the problem of how the choice related to the measurement is made by the observer viewed as a quantum system. In interpretations where the system together with the observers is completely described by unitary transformations, the observer cannot make any choices and so measurement is impossible. From the perspective of computability theory, a quantum machine cannot halt and so it cannot observe the computed state, indicating that unitarity alone does not explain all matter processes. Further it is argued that the consideration of information and observation requires an overarching system of knowledge and expectations about outcomes.
Abstract. What mathematical or physicalmechanism that exactly empowers quantumcomputing over classical computers is still an openquestion. By reexamining physics-based methodsand computational primitives, we study quantumspeedups and limitations related to problems’structure, physical resources and no-go laws. Weaim at some fundamental issues by seeking nonclassicalresolutions on the puzzle via rigorousproofs or evidences: 1) Is quantum entanglement themagic? General physical theories show that theconcept is generic for all non-classical systems, yettoo rare as the computation resource for exponentialquantum speedups in various entanglementquantifications. We reinforce that entanglementalone is insufficient as the characteristic measure. 2)Then, what is the physical dynamic behind? howmuch underlying structure is necessary forexponential quantum speedups? We prove that anyquantum search with cumulative memory such asin Darvin’s evolution, instead of ergodic process, ismathematically sufficient to overcome theexponential NP hardness gap. 3) Can quantummechanics compute beyond Turing machines?Quantum adiabatic process and Brownian diffusionmodel are constructed explicitly to demonstrate thatlaws of physics and emergences offer extendedcomputability in principle. We argue that the openquestion on super Turing computing is independentof physical infinities.Based on quantitative analyses and fundamentalconstraints, we arrive at a few theoretical claimstoward generalized computing: a) Exponentialquantum speedups, ranging from minimal to groupstructures, broadly allow utilizations andgeneralizations of quantum methods to any processwith specific dynamic. Namely, there exist degreesof computational jump. b) Inductive and emergentcomputing are necessary to complement logical,deductive computing; where natural laws arereversely captured by compression or emergencevia observation, interaction. Fundamental rules areapplied forward by nature or observer as generativecomputing. c) Generalized physical computing forpartially describable processes is needed to study,understand and control generative realities, generalAI, mental process and emerging social phenomena;that seem beyond conventional logic or physics, yetare computationally unifiable.The article reviews basic concepts, key logic onselect topics in quantum computing, and integratesseminal results, proof sketches and open questionsto offer ranges of handles, bounds and outlooks indevising a unified framework. Basic elements areoutlined toward a powerful computing theory ofnovel applications for generic systems andprocesses, with convergent capacities of universalTuring machine, general physical theories andendless evolution. It lays out a foundation for followup initiatives on specific problems in computation,physics and intelligence by applying with existingphysical methods and computing models.
One of the fundamental insights of quantummechanics is that complete knowledge of the state of a quantum system is not possible. Such incomplete knowledge of a physical system is the norm rather than the exception. This is becoming increas-ingly apparent as we apply scientific methods to increasingly complex situations. Empirically intensive disciplines in the biological, human, and geosciences all operate in situations where valid conclusions must be drawn, but deductive com-pleteness is impossible. This paper argues that such situations are emerging exam-ples of Open World Science. In this paradigm, scientific models are known to be acting with incomplete information. Open World models acknowledge their incompleteness, and respond positively when new information becomes available. Many methods for creating Open World models have been explored analytically in quantitative disciplines such as statis-tics, and the increasingly mature area of machine learning. This paper examines the role of quantum theory and quan-tum logic in the underpinnings of Open World models, ex-amining the importance of structural features of such as non-commutativity, degrees of similarity, induction, and the im-pact of observation. Quantum mechanics is not a problem around the edges of classical theory, but is rather a secure bridgehead in the world of science to come.
Quantum computing raises novel meditation upon the nature of information, notably a number of theorists set out the critical elements of Shannon’s work, which currently emerges as the most popular reference in the quantum territory. The present paper follows this vein and highlights how the prerequisites of the information theory, which should detail the precise hypotheses of this theory, appear rather obscure and the problem of the existence of information is still open. This work puts forward a theoretical scheme that calculates the existence of elementary items. These results clarify basic assumptions in information engineering. Later we bring evidence how information is not an absolute quantity and close with a discussion upon the information relativity.
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarize not just quantum computing, but the whole subject of quantum information theory. Information can be identified as the most general thing which must propagate from a cause to an effect. It therefore has a fundamentally important role in the science of physics. However, the mathematical treatment of information, especially information processing, is quite recent, dating from the mid-20th century. This has meant that the full significance of information as a basic concept in physics is only now being discovered. This is especially true in quantum mechanics. The theory of quantum information and computing puts this significance on a firm footing, and has led to some profound and exciting new insights into the natural world. Among these are the use of quantum states to permit the secure transmission of classical information (quantum cryptography), the use of quantum entanglement to permit reliable transmission of quantum states (teleportation), the possibility of preserving quantum coherence in the presence of irreversible noise processes (quantum error correction), and the use of controlled quantum evolution for efficient computation (quantum computation). The common theme of all these insights is the use of quantum entanglement as a computational resource. It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, this review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the Einstein, Podolsky and Rosen (EPR) experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory and, arguably, quantum from classical physics. Basic quantum information ideas are next outlined, including qubits and data compression, quantum gates, the `no cloning' property and teleportation. Quantum cryptography is briefly sketched. The universal quantum computer (QC) is described, based on the Church-Turing principle and a network model of computation. Algorithms for such a computer are discussed, especially those for finding the period of a function, and searching a random list. Such algorithms prove that a QC of sufficiently precise construction is not only fundamentally different from any computer which can only manipulate classical information, but can compute a small class of functions with greater efficiency. This implies that some important computational tasks are impossible for any device apart from a QC. To build a universal QC is well beyond the abilities of current technology. However, the principles of quantum information physics can be tested on smaller devices. The current experimental situation is reviewed, with emphasis on the linear ion trap, high- Q optical cavities, and nuclear magnetic resonance methods. These allow coherent control in a Hilbert space of eight dimensions (three qubits) and should be extendable up to a thousand or more dimensions (10 qubits). Among other things, these systems will allow the feasibility of quantum computing to be assessed. In fact such experiments are so difficult that it seemed likely until recently that a practically useful QC (requiring, say, 1000 qubits) was actually ruled out by considerations of experimental imprecision and the unavoidable coupling between any system and its environment. However, a further fundamental part of quantum information physics provides a solution to this impasse. This is quantum error correction (QEC). An introduction to QEC is provided. The evolution of the QC is restricted to a carefully chosen subspace of its Hilbert space. Errors are almost certain to cause a departure from this subspace. QEC provides a means to detect and undo such departures without upsetting the quantum computation. This achieves the apparently impossible, since the computation preserves quantum coherence even though during its course all the qubits in the computer will have relaxed spontaneously many times. The review concludes with an outline of the main features of quantum information physics and avenues for future research.