相关论文: Quantum Principles and Mathematical Computability
We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic processes is considered…
We explore in the framework of Quantum Computation the notion of {\em Computability}, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to…
Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into either a problem involving a set of infinitely coupled differential equations or a problem involving a Shr\"odinger propagator…
We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbert's tenth problem which is equivalent to the Turing halting problem in Computer Science. The Quantum Adiabatic Theorem…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
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…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not…
A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
The Halting problem of a quantum computer is considered. It is shown that if halting of a quantum computer takes place the associated dynamics is described by an irreversible operator.
Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into problems involving either a set of infinitely-coupled non-linear differential equations or a class of linear Schr\"odinger…
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
Is there any hope for quantum computing to challenge the Turing barrier, i.e. to solve an undecidable problem, to compute an uncomputable function? According to Feynman's '82 argument, the answer is {\it negative}. This paper re-opens the…
This paper reviews connections between physics and computation, and explores their implications. The main topics are computational "hardness" of physical systems, computational status of fundamental theories, quantum computation, and the…
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…
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…
We give an update on a quantum adiabatic algorithm for the Turing noncomputable Hilbert's tenth problem, and briefly go over some relevant issues and misleading objections to the algorithm.