Nature computes: Information processing in quantum dynamical systems

It is known that the development and deep understanding of modern interaction theory and classical mechanics are made through geometry and symmetry. Yet, quantum mechanics which was regarded to be the microscopic theory of classical mechanics and achieved the crowning success in interpreting the entire microscopic world was developed purely from algebraic methods. In this thesis, we will study the geometry and dynamical symmetry in quantum systems, from which the question of integrability and chaos are explicitly addressed. First of all, the quantum dynamical degrees of freedom and quantum integrability are precisely defined and the inherent geometrical structure of quantum systems is explored from the fundamental structure of quantum theory. Such a geometrical structure can provide a framework to simultaneously build quantum and classical mechanics. The quantum-classical correspondence is then explicitly deduced. The dynamics of quantum system before it reaches the classical limit is formulated. Thus, the classical chaos is proven to be a special limiting phenomena of quantum systems and the dynamics before the system reaches its classical chaos is explored. The latter is the first step to seek the quantum manifestation of chaos. The relationship between integrability and dynamical symmetry are studied and some universal properties are discovered: a dynamical system (both quantum and classical) is integrable if it possesses a dynamical symmetry. Chaos will occur if the system undergoes a dynamical symmetry breaking and is accompanied by a structural phase transition. Thus, the concept of dynamical symmetry can be used to predict the general behaviors of a system. The theoretical underpinnings developed in this thesis are verified by many basic quantum mechanical examples. In the second part, we have applied the theory to construct the geometrical description for fermionic systems and then use this general formulation to study the geometrical properties, integrability and chaos in nuclear collective motions. The study of geometry for the fermion systems clearly show how the pure quantum properties (e.g. Pauli principle) are exhibited in geometry and how these geometrical manifestations can interpret experimental facts in nuclear collective motion (e.g. the satiation of nuclear deformation and narrow oblate window). The dynamical symmetry and dynamical symmetry breaking in nuclear collective motion are extensively studied.

We discuss some open problems in the theory of dynamical systems, classical and quantum mechanics.

A Busy March Meeting Is Brewing in Seattle

Recently, the dynamics of quantum systems that involve both unitary evolution and quantum measurements have attracted attention due to the exotic phenomenon of measurement-induced phase transitions. The latter refers to a sudden change in a property of a state of n qubits, such as its entanglement entropy, depending on the rate at which individual qubits are measured. At the same time, quantum complexity emerged as a key quantity for the identification of complex behaviour in quantum many-body dynamics. In this work, we investigate the dynamics of the quantum state complexity in monitored random circuits, where n qubits evolve according to a random unitary circuit and are individually measured with a fixed probability at each time step. We find that the evolution of the exact quantum state complexity undergoes a phase transition when changing the measurement rate. Below a critical measurement rate, the complexity grows at least linearly in time until {saturating to a value eΩ(n).} Above, the complexity does not exceed poly⁡(n). In our proof, we make use of percolation theory to find paths along which an exponentially long quantum computation can be run below the critical rate, and to identify events where the state complexity is reset to zero above the critical rate. We lower bound the exact state complexity in the former regime using recently developed techniques from algebraic geometry. Our results combine quantum complexity growth, phase transitions, and computation with measurements to help understand the behavior of monitored random circuits and to make progress towards determining the computational power of measurements in many-body systems.

This chapter defines dynamic systems, its relevance to sports performance analysis, and explains the inter-personal coordination and perturbations during sport competition. It is concerned with outlining a dominant motor control theory that can aid the explanation and interpretation of performance analysis data dynamic systems theory. The chapter has three central principles of dynamic systems theory: synergies, self-organisation and constraints. It is built upon the existing research using dynamic systems theory to study attacker-defender interactions in rugby union, it could be argued that the practical implications were limited. Future research using dynamic systems theory will be a theoretical framework for analysing inter-personal coordination, ensuring the analysis can be more effectively linked to the attacking/defending principles of play, and be useful and informative for sports coach and performance analysts. There are clear links between the theory and the principles of play of the sport, i.e. the attacking principles of soccer: width, mobility, support, facilitating the exploration of the available playing space.

Quantum computing is a multidisciplinary field at the intersectionof quantum physics, computer science, and mathematics, aiming to har-ness quantum mechanical phenomena for computational advantage. Thisarticle provides a comprehensive review of both the foundational princi-ples and advanced theoretical models of quantum computing. We beginwith the basic framework of quantum computation, introducing the con-cept of qubits as two-level quantum systems, the linear algebra of Hilbertspaces, Dirac’s bra–ket notation, and the postulates of quantum mechan-ics (state superposition, unitary evolution, and projective measurement).We then discuss quantum logic gates and circuits, highlighting how clas-sical reversible computation principles extend to universal quantum gatesets. Next, we survey key quantum algorithms (from Shor’s factoring toGrover’s searching and beyond) and the complexity-theoretic implicationsof quantum computers, contrasting the class BQP with classical complex-ity classes. We cover the theoretical foundations of quantum error cor-rection and fault tolerance, explaining how quantum information can beprotected from decoherence using redundancy and how fault-tolerant pro-tocols can, in principle, allow scalable quantum computation despite noisyhardware. We then explore advanced models and paradigms of quantumcomputation, including measurement-based quantum computing (one-wayquantum computing), topological quantum computation with anyons, adi-abatic quantum computing and quantum annealing, continuous-variablequantum computing, and related approaches. We also provide an overviewof quantum information theory as it relates to computation, discussingentanglement, quantum entropy, and information-theoretic limits like theHolevo bound. Finally, we review the leading physical implementations(quantum hardware models) of quantum computers—trapped ions, super-conducting circuits, photonic systems, solid-state spin qubits, and oth-ers—outlining the challenges and achievements of each approach.

Introduction: Children with cerebral palsy may receive various rehabilitative intervention programs aimed at facilitating their development and improving their functional independence in such areas as movement, self-care, playing, leisure and school activities. Occupational therapists working with children with Cerebral Palsy (CP) employ a variety of therapeutic approaches among which neurodevelopmental treatment approach has been traditionally the most common. Considering the expansion of family-centered therapy approaches, the importance of obligation to the International Classification of Functioning, Disabilities and Health principles (ICF, WHO, 2001), limitations of current therapy approaches and recent advances from dynamic systems theory, there is an urgent need to develop a new approach in occupational therapy at the present time. The aims of this study were to present a brief description of CP with an emphasis on the role of occupational therapy in it and to explore the benefits of family-centered approach, dynamic systems theory and family-centered functional therapy in the rehabilitation process of children with cerebral palsy. Materials and Methods: In this study, a comprehensive review of the literature published from 1966 to 2011 was conducted via PubMed, Scopus, ProQuest and Google Scholar data bases. The keywords used in search were “cerebral palsy”, “functional”, “therapy”, “family-centered”. All articles were initially evaluated according to predefined inclusion and exclusion criteria and then selected article were reviewed. Results : Of 128 articles found, 22 articles met the inclusion and exclusion criteria and were considered as appropriate for this study. Conclusion: Family-centered functional therapy, which combines theoretical principles of occupational therapy, family centered approach and dynamic systems theory of motor development, is an optimal response to developmental needs of children with cerebral palsy. However, the efficacy of this approach has not been proven empirically. Keywords: Cerebral palsy, Family centered functional therapy, Dynamic systems theory

In the present work, we suggest an approach for describing dynamics of finite-dimensional quantum systems in terms of pseudostochastic maps acting on probability distributions, which are obtained via minimal informationally complete quantum measurements. The suggested method for probability representation of quantum dynamics preserves the tensor product structure, which makes it favourable for the analysis of multi-qubit systems. A key advantage of the suggested approach is that minimal informationally complete positive operator-valued measures (MIC-POVMs) are easier to construct in comparison with their symmetric versions (SIC-POVMs). We establish a correspondence between the standard quantum-mechanical formalism and the MIC-POVM-based probability formalism. Within the latter approach, we derive equations for the unitary von-Neumann evolution and the Markovian dissipative evolution, which is governed by the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) generator. We apply the MIC-POVM-based probability representation to the digital quantum computing model. In particular, for the case of spin-1/2 evolution, we demonstrate identifying a transition of a dissipative quantum dynamics to a completely classical-like stochastic dynamics. One of the most important findings is that the MIC-POVM-based probability representation gives more strict requirements for revealing the non-classical character of dissipative quantum dynamics in comparison with the SIC-POVM-based approach. Our results give a physical interpretation of quantum computations and pave a way for exploring the resources of noisy intermediate-scale quantum devices.

An analysis of a quantum counterpart of a parametrically kicked nonlinear oscillator is given. The method, using as a basic criterion the recently introduced quantum characteristic exponents, is analogous to the technique developed in classical dynamical system theory. However, our approach to the characterization of the stability of an observable's evolution is done in pure quantum terms.

Mesoscale ocean turbulence is the best-known expression of Chaotic Intrinsic Variability (CIV), which spontaneously emerges from the unstable ocean circulation regardless of the atmospheric variability. Substantial amounts of CIV are also found up to the scale of basins and decades, potentially produced by large-scale baroclinic instability or resulting from spatiotemporal inverse cascade processes.A 56-year atmospherically-forced 50-member 1/4° large ensemble simulation of the global eddying ocean/sea-ice system has been performed to explore these phenomena using the NEMO model. We first show that the low-frequency large-scale (LFLS) CIV has climate-relevant imprints over most of the globe, is largest in western boundary currents and south of about 30°S, and competes with (and in certain zones exceeds) the atmospherically-forced ocean variability (AFV) in terms of amplitude.However, the separability of AFV and CIV is questionable in certain cases. Concepts from dynamical system and information theories are leveraged to avoid this separation, and to probabilistically describe the ocean variability as an atmospherically-modulated oceanic "chaos". The partly random character of multi-scale ocean fluctuations in the eddying regime questions the attribution of observed signals to sole atmospheric drivers, the turbulent ocean predictability and its potential influence in high-resolution coupled simulations.

This article introduces post-quantum models–advanced theories that aim to bridge the gap between quantum mechanics and general relativity, two of physics' most groundbreaking yet unaligned frameworks. It explores key theories like string theory, which suggests that the universe's fundamental building blocks are vibrating strings, and loop quantum gravity, proposing that spacetime itself is made up of tiny, discrete loops. Additionally, non-linear quantum mechanics and the holographic principle are discussed, providing insights into the nature of black holes, dark matter, and the structure of spacetime at the quantum level. These theories not only offer potential solutions to the mysteries of the cosmos but also hold practical applications in fields like quantum computing and information theory. This article is an attempt to provide an accessible yet intellectually stimulating journey through some of the most cutting–edge ideas in modern physics, challenging readers to expand their understanding of the universe's fundamental nature.

Abstract. Numerical climate simulations produce vast amounts of high-resolution data. This poses new challenges to the palaeoclimate community – and indeed to the broader climate community – in how to efficiently process and interpret model output. The palaeoclimate community also faces the additional challenge of having to characterise and compare a much broader range of climates than encountered in other subfields of climate science. Here we propose an analysis framework, grounded in dynamical systems theory, which may contribute to overcoming these challenges. The framework enables the characterisation of the dynamics of a given climate through a small number of metrics. These may be applied to individual climate variables or to several variables at once, and they can diagnose properties such as persistence, active number of degrees of freedom and coupling. Crucially, the metrics provide information on instantaneous states of the chosen variable(s). To illustrate the framework's applicability, we analyse three numerical simulations of mid-Holocene climates over North Africa under different boundary conditions. We find that the three simulations produce climate systems with different dynamical properties, such as persistence of the spatial precipitation patterns and coupling between precipitation and large-scale sea level pressure patterns, which are reflected in the dynamical systems metrics. We conclude that the dynamical systems framework holds significant potential for analysing palaeoclimate simulations. At the same time, an appraisal of the framework's limitations suggests that it should be viewed as a complement to more conventional analyses, rather than as a wholesale substitute.

During quantum era, new rules governing physical phenomena and reality contribute to the development of quantum technology, which will change people’s lives, in the near future. A great range of quantum technologies, based on quantum information theory and quantum computing, lead to new applications. Revolutionary quantum computing algorithms benefit from basic quantum mechanics properties, such as entanglement and superposition effects, to advance calculations in polynomial time. In essence, Quantum Mechanics (QM) is considered a cross – disciplinary STEM Physics field, aiming to advance the philosophy of Quantum Literacy (QL), which addresses the transdisciplinary nature of real world complex problems. QL addresses the challenges of quantum technologies learning and skills acquisition, through gamification and computing problem – solving environments. Simulations, virtual labs and interactive tools through serious games, create an attractive learning environment and promote at the same time an interdisciplinary field of physics, technology and information sciences. Technological interventions, often combined with contemporary teaching methods, provide guidelines for better and long-lasting learning outcomes. To this end, literature often emphasizes students’ engagement with serious games, especially if the content is interdisciplinary and lies in the crossroad section of Physics, Mathematics, Computer and Computational Sciences. Our work focuses on mapping the State of the Art among contemporary teaching methods and gamification techniques and tools, as applied for quantum mechanics concepts and quantum computing problems, to best advance QL. We also discuss the trends among contemporary teaching methods, effective gamification tools and quantum learning topics, fostering quantum physics knowledge from K-12 educational level.

The relationship between efficient verification and quantum computing is one of the most important and least well-understood questions in the theory of computation. In particular, is there a problem that can be solved efficiently on a quantum computer that cannot be verified? In this thesis we give evidence that BQP ⊄ PH, relating the classes of languages decidable with a quantum computer to a generalization of NP. In so doing we connect a question in pseudorandomness, first studied [BSW03] to the problem of finding an oracle relative to which BQP ⊄ PH. The primary technical challenge is to construct a unitary matrix, realized by an efficient quantum circuit and whose rows are supported on nearly disjoint subsets. Using this matrix and assuming the validity of the aforementioned question in pseudorandomness, we show an instantiation of the Nisan-Wigderson pseudorandom generator that can be broken with quantum computers, but not with the relevant mode of classical computation.

Any technology that functions at the quantum level must face the issues of measurement and control. We have good reasons to believe that quantum physics enables communication and computation tasks that are either impossible or intractable in a classical world [NC00]. The security of widely used classical cryptographic systems relies upon the difficulty of certain computational tasks, such as breaking large semi-prime numbers into their two prime factors in the case of RSA encryption. By contrast, quantum cryptography can be absolutely secure, and is already a commercial reality. At the same time, the prospect of a quantum computer vastly faster than any classical computer at certain tasks is driving an international research programme to implement quantum information processing. Shor's factoring algorithm would enable a quantum computer to find factors exponentially faster than any known algorithm for classical computers, making classical encryption insecure. In this chapter, we investigate how issues of measurement and control arise in this most challenging quantum technology of all, quantum computation.