Related papers: On Measurement and Computation
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…
Endeavoring to formulate an exhaustive solution to the measurement problem in view of the theory of decoherence leads to a better understanding of the status of the collapse and of the emergence of classicality, thanks to a precise…
This review gives a survey of numerical algorithms and software to simulate quantum computers.It covers the basic concepts of quantum computation and quantum algorithms and includes a few examples that illustrate the use of simulation…
The purpose of this thesis is to make an analysis of the concept of Hypercomputation and of some hypermachines. This thesis is separated in three main parts. We start in the first chapter with an analysis of the concept of Classical…
Some contemporary views of the universe assume information and computation to be key in understanding and explaining the basic structure underpinning physical reality. We introduce the Computable Universe exploring some of the basic…
When can a model of a physical system be regarded as computable? We provide the definition of a computable physical model to answer this question. The connection between our definition and Kreisel's notion of a mechanistic theory is…
We study the complexity of computational problems from quantum physics. Typically, they are studied using the complexity class QMA (quantum counterpart of NP) but some natural computational problems appear to be slightly harder than QMA. We…
This paper proposed a framework based on quantum computing for reliability assessment of complex systems. The 'Quantum Twin' concept was also proposed. The framework can be used to accelerate the reliability assessment of large-scale…
Quantum computing has been a fascinating research field in quantum physics. Recent progresses motivate us to study in depth the universal quantum computing models (UQCM), which lie at the foundation of quantum computing and have tight…
The conceptual relation between the measurability of quantum mechanical observables and the computability of numerical functions is re-examined. A new formulation is given for the notion of measurability with finite precision in order to…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
After a brief introduction to the principles and promise of quantum information processing, the requirements for the physical implementation of quantum computation are discussed. These five requirements, plus two relating to the…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
We study effects of the physical realization of quantum computers on their logical operation. Through simulation of physical models of quantum computer hardware, we analyse the difficulties that are encountered in programming physical…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…
Future quantum computers are anticipated to be able to perform simulations of quantum many-body systems and quantum field theories that lie beyond the capabilities of classical computation. This will lead to new insights and predictions for…
It is possible in principle to construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolution, would contradict the Church-Turing thesis, which lies at the…