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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.

This thesis is a contribution to the debate on the implications of quantum information theory for the foundations of quantum mechanics. In Part 1, the logical and conceptual status of various notions of information is assessed. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings `information' functions as an abstract noun, hence does not refer to a particular or substance (the worth of this point is illustrated in application to quantum teleportation). The claim that `Information is Physical' is assessed and argued to face a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. The reflections of Bruckner and Zeilinger (2001) and Deutsch and Hayden (2000) on the nature of information in quantum mechanics are critically assessed and some results presented on the characterization of entanglement in the Deutsch-Hayden formalism. Some philosophical aspects of quantum computation are discussed and general morals drawn concerning the nature of quantum information theory. In Part II, following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger's (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, Bub and Halvorson (2003) is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.

“Garbage in, garbage out” is a familiar phrase from the field of computer science. The concept surrounding the phrase is simple. Despite the most complex information processing systems, computers will unquestioningly process the most ridiculous of input data, “garbage in,” and produce ridiculous output, “garbage out.” Commonly used in other fields, including laboratory medicine, this phrase serves as an important reminder that in the context of healthcare, inaccurate data input—garbage in—leads to misleading results—garbage out. So before the laboratory can perform testing it is imperative that inherent, pre-analytical issues are understood and identified. This chapter focuses on specimen integrity in the pre-analytical phase of testing and discusses how the laboratory strives to link the quality of incoming specimens to quality results.

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.

Quantum mechanics is a revolutionary scientific field, which lies at the crossroad section of Physics, Mathematics, Computer and Computational Science. In essence, it is considered a cross-disciplinary STEM field, advancing the philosophy of Quantum Literacy (QL), which addresses the transdisciplinary nature of real world complex problems. QL addresses the challenges of learning and skills acquisition, through specific computing activities, within a highly bounded discipline and of access to the kind of powerful knowledge that should be more accessible to a wide group of learners. It is therefore important that quantum computing and quantum technologies knowledge is accessible to students and teachers who work with real problems, in a more inclusive and interactive way. In this paper, we argue for the necessity of exposing students to new and powerful quantum tools, as provided by cutting edge quantum computing technologies. We do that by proposing contemporary and STEM related activities and gamification scenarios, in which they acquire stronger mathematical and computational - problem decomposition and modelling skills, working as real researchers. By engaging students in games and activities related to quantum computing and quantum information processing, they acquire all necessary knowledge related to: superposition, teleportation, entanglement, quantum gates and quantum information. The serious games proposed in this paper relates to quantum strategic games, necessary for STEM activities to train students within the computational thinking 2.0 framework. All scenarios were implemented using the didactic model of inquiry-based learning using Python libraries.

This clear and pedagogical text delivers a concise overview of classical and quantum statistical physics. Essential Statistical Physics shows students how to relate the macroscopic properties of physical systems to their microscopic degrees of freedom, preparing them for graduate courses in areas such as biophysics, condensed matter physics, atomic physics and statistical mechanics. Topics covered include the microcanonical, canonical, and grand canonical ensembles, Liouville's Theorem, Kinetic Theory, non-interacting Fermi and Bose systems and phase transitions, and the Ising model. Detailed steps are given in mathematical derivations, allowing students to quickly develop a deep understanding of statistical techniques. End-of-chapter problems reinforce key concepts and introduce more advanced applications, and appendices provide a detailed review of thermodynamics and related mathematical results. This succinct book offers a fresh and intuitive approach to one of the most challenging topics in the core physics curriculum and provides students with a solid foundation for tackling advanced topics in statistical mechanics.

This clear and pedagogical text delivers a concise overview of classical and quantum statistical physics. Essential Statistical Physics shows students how to relate the macroscopic properties of physical systems to their microscopic degrees of freedom, preparing them for graduate courses in areas such as biophysics, condensed matter physics, atomic physics and statistical mechanics. Topics covered include the microcanonical, canonical, and grand canonical ensembles, Liouville's Theorem, Kinetic Theory, non-interacting Fermi and Bose systems and phase transitions, and the Ising model. Detailed steps are given in mathematical derivations, allowing students to quickly develop a deep understanding of statistical techniques. End-of-chapter problems reinforce key concepts and introduce more advanced applications, and appendices provide a detailed review of thermodynamics and related mathematical results. This succinct book offers a fresh and intuitive approach to one of the most challenging topics in the core physics curriculum and provides students with a solid foundation for tackling advanced topics in statistical mechanics.

Allen Newell and Herbert A. Simon. The logic theory machine. A complex information processing system. Institute of Radio Engineers, Transactions on information theory, vol. IT-2 no. 3 (1956), pp. 61–79. - Volume 22 Issue 3

In this paper we describe a complex information processing system, which we call the logic theory machine, that is capable of discovering proofs for theorems in symbolic logic. This system, in contrast to the systematic algorithms that are ordinarily employed in computation, relies heavily on heuristic methods similar to those that have been observed in . human problem solving activity. The specification is written in a formal language, of the nature of a pseudo-code, that is suitable for coding for digital computers. However, the present paper is concerned exclusively with specification of the system, and not with its realization in a computer. The logic theory machine is part of a program of research to understand complex information processing systems by specifying and synthesizing a substantial variety of such systems for empirical study.

Quantum-Information Conservation. The Problem About ‘Hidden Variables’, or the ‘Conservation of Energy Conservation’ in Quantum Mechanics: A Historical Lesson for Future Discoveries

This Research to Practice Full Paper discusses an approach to motivating graduate computer science and electrical engineering students in the study of quantum computing. The U.S. Congress and other governmental and industrial organizations have recognized that teaching Quantum Computing in university-level Computer Science and Electrical Engineering programs is strategically important for workforce development along with technology development. Success in this endeavor requires generating genuine interest in the topic and motivating potential students. Quantum Computing requires an understanding of relatively difficult related subjects including physics, math and computer science. Many computer science and electrical engineering students shy away from quantum computing because of its complexity. This paper discusses our success with generating interest in quantum computing among graduate students and motivating them through exploring, in related courses, some aspects of quantum computing that have the potential to generate discontinuities. The approach is also examined in terms of the Scientific Learning Cycle as discussed by Wankat & Oreovicz. Opportunities and challenges of adding Quantum Computing to Computer Science and Electrical Engineering programs were studied through a student small group project in a cybersecurity course. The work built on extensive research into the effectiveness of small group projects and the role of “play” in learning. Our small group project on quantum computing was introduced three years ago into a cybersecurity course which is required for all students in our university's Masters in Computer Science and Masters in Electrical Engineering programs. The basic goals of the project are to teach students some basics of quantum computing by allowing them to “play with it” and to alert students to the fact that quantum computing is a rapidly developing new field that they need to follow during at least the next decade. The small group project helped students to explore the potential of quantum computing to substantially undermine current Public Key Cryptography and, at the same time provide a new approach to encryption that is even more secure than Public Key Cryptography. A qualitative analysis of discussions and assigned tasks suggests that this strategy succeeded in generating significant interest in quantum computing among students. They became motivated and immersed in a difficult subject despite the requirement for investment of significant time and effort to understand a complex combination of physics, math and computer science.

In this chapter, I explain how the journal Epistemological Letters helped the foundations of quantum mechanics consolidate as an important and respectable scientific field during a time when the discipline itself was not very well respected by the broader physics community. In particular, I show that the following five features of the journal played a significant role in helping the foundations of quantum mechanics flourish during the 1970s: (1) the subject matter, as this was the only journal completely dedicated to the foundations of quantum mechanics; (2) the interdisciplinary methodology encouraged by the journal and the institution behind it; (3) their efforts to reach out to anybody interested in the foundations of quantum mechanics, regardless of their department, position, or “academic status”; (4) the informal style of the journal, which facilitated an environment for open, frequent, and productive debates; (5) its high quality contributions.

Information entropy has played a key role in a wide range of disciplines, for instance, classical and quantum information processing, quantum computing, quantum dynamics and quantum metrology. Here, we develop an information theoretic formalism using Shannon entropy, to investigate the quantum dynamics of Hamiltonian systems with position-dependent mass. Such systems are of fundamental interest in many areas, for instance, condensed matter, mathematical physics and foundations of quantum mechanics. We explore the phenomenon of fractional revivals for the temporal evolution of wave-packet solutions of Schrödinger equation with position-dependent mass by studying, analytically and numerically, the time-development of Shannon information entropy in position and momentum spaces. It is shown by our numerical results that the effect of spatially varying mass on the fractional revivals can not be fully harnessed using conventional measures, for instance, autocorrelation function. However, based on our numerical analysis it is concluded that information entropy is not only more sensitive to identify the fractional revivals but it also better elucidates the effect of position-dependent mass on the structure of fractional revivals in the form of symmetry breaking.