Quantum Computing. Melanie Swan

materials

       Table 3.3.Qubit types by formation and control parameters

       Table 4.1.Quantum applications and number of qubits required

       Table 4.2.Church–Turing computability thesis

       Table 4.3.Quantum computing systems and error correction

       Table 4.4.Interpretations of Bell’s inequality

       Table 5.1.Computational trust model comparison and progression

       Table 5.2.Economic themes with instantiations in blockchain networks

       Table 6.1.Roadmap: Six steps to a quantum internet

       Table 7.1.Comparison of zero-knowledge proof systems

       Table 7.2.Transaction systems comparison: Confidentiality and anonymity

       Table 11.1.Key aspects of statistical neural field theory

       Table 11.2.Statistical neural field theory: System norm and criticality

       Table 11.3.Obtaining a master field equation for the neural system

       Table 11.4.Expanding the Markov random walk to a Markov random field

       Table 11.5.Linear and nonlinear models of the system action

       Table 11.6.Statistical neural field theory system criticality

       Table 11.7.Key aspects of the spin-glass model

       Table 11.8.Spin-glass model: System norm and criticality

       Table 12.1.SNFT: Minimal elements

       Table 12.2.SNFT: Particles and interactions

       Table 12.3.SNFT: System operating parameters

       Table 12.4.Operating parameters in smart network systems

       Table 12.5.System criticality parameters in smart network systems

       Table 12.6.Blockchain network services provided by peer-to-peer nodes

       Table 12.7.Deep learning services provided by perceptron nodes

       Table 13.1.Key historical moments in the AdS/CFT correspondence

       Table 13.2.Tools and methods used in AdS/CFT correspondence research

       Table 14.1.Examples of holographic quantum error-correcting codes

       Table 14.2.Quantum information science topics

       Table 15.1.SNQFT: Minimal elements

       Table 15.2.Natural security features built into quantum mechanical domains

       Table 15.3.Examples of bulk–boundary directional transformations

       Table 15.4.Examples of bulk–boundary correspondence relationships

       Table 15.5.Long-distance and short-distance descriptions in field theory systems

       Table 15.6.Eras in quantum computing, physical theory, and smart networks

       Chapter 1

       Introduction

       Quantum computing … has established an unprecedentedly deep link between the foundations of computer science and the foundations of physics

      — John Preskill (2000, p. 127)

      The implication is that reality can be computed. The startling premise of quantum computing is that the bizarre quantum mechanical realm that was thought incomprehensible can be computed. Quantum mechanics might remain incomprehensible, but at least it can be computed. The bigger notion is that the link between quantum computing and quantum physics suggests the possibility of delivering on the promise of understanding the true nature of physical reality.

      Merely the first step is simulating the quantum mechanical world with quantum computers in its image as Feynman envisioned. Beyond that milestone, the real endpoint is mobilizing the quantum mechanical domain to compute more difficult problems and create new possibilities.

      Engaging the quantum realm makes it clear that tools are needed to comprehend the two domains together, the microscale of the quantum and the macroscale of lived reality. The issue concerns not only understanding more about quantum mechanics, but also linking the quantum and non-quantum domains such that the quantum realm can be activated in a useful way at the macroscale. This book is a journey towards a model to do precisely this, incorporating the superposition, entanglement, and interference properties of quantum mechanics with the 3D time and space geometries of the macroscale world.

      Figure 1.1. Model of computational reality.

      With the assumption that physical reality can be computed with quantum information systems, the theme of computation is taken up through the lens of smart network technologies (self-operating computation networks) and their potential expansion into the quantum mechanical domain. A technophysics approach (the application of physics principles to the study of technology) is used to derive smart network field theory (conventional and quantum) as a physical theory of smart network technologies. The organizing principle of this work is encapsulated in a causal model (Figure 1.1).

      The model of computational reality posits that computation capability influences the ability to have knowledge about physical reality. Computation capability may be moderated by variables such as the properties of computational systems, the theories and algorithms that manage the computation process, and security features that protect and allow system criticality to be managed, essentially