Related papers: The Computational Status of Physics: A Computable …
Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily…
Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can physics be simulated by a quantum computer? Do we believe that a quantum field is ultimately made of a numerable set of quantum systems that are unitarily interacting? A…
As quantum computers become real, it is high time we come up with effective techniques that help programmers write correct quantum programs. Inspired by Hoare Type Theory in classical computing, we propose Quantum Hoare Type Theory (QHTT),…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here we…
Powered by advanced information technology, more and more complex systems are exhibiting characteristics of the Cyber-Physical-Social Systems (CPSS). Understanding the mechanism of CPSS is essential to our ability to control their actions,…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve…
Turing's (1936) paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure…
Quantum computing promises to help humanity solve problems that would otherwise be intractable on classical computers. Unlike today's machines, quantum computers use a novel computing process that leverages the foundational quantum…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Suspicions that the world might be some sort of a machine or algorithm existing ``in the mind'' of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached…
The commonly used circuit model of quantum computing leaves out the problems of imprecision in the initial state preparation, particle statistics (indistinguishability of particles belonging to the same quantum state), and error correction…
We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical…
Computer simulations that demonstrate the valueof novel approaches are crucial to developing more flexibleand robust power systems operations with high penetrations ofrenewable energy at multiple geographic and temporal scales.However,…
In this paper we present a new unified theoretical framework that describes the full dynamics of quantum computation. Our formulation allows any questions pertaining to the physical behavior of a quantum computer to be framed, and in…
Simulating chemical systems is highly sought after and computationally challenging, as the number of degrees of freedom increases exponentially with the size of the system. Quantum computers have been proposed as a computational means to…
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…