Related papers: Quantum Turing Machines: Local Transition, Prepara…
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…
The effects of the measurement apparatus on quantum coherence are studied by considering a purely dephasing model of a qubit. The initial state is prepared from a thermal state of the whole system by performing a nonselective measurement on…
Expanding upon the widely recognized notion of mathematical universality in Turing machines, a concept of thermodynamic universality in Turing machines is introduced. Under the physical Church-Turing thesis, the existence of a…
It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement based quantum computation.…
Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite ($*$-finite) number of bits while keeping the finite…
A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
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…
We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which…
I provide an introduction to quantum computers, describing how they might be realized using language accessible to a solid state physicist. A listing of the minimal requirements for creating a quantum computer is given. I also discuss…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
Quantum tunneling allows electrons to be transferred between two regions separated by an energetically forbidden barrier. Performing a position measurement that finds a particle in the barrier forces the tunneling electrons to transition…
The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many…
We present a brief critical review of the proposals for quantum computation with trapped ions, with particular emphasis on the possibilities for quantum computation without the need for cooling to the quantum ground state of the ions'…
We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that…
We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
Invasiveness of quantum measurements is a genuinely quantum mechanical feature that is not necessarily detrimental: Here we show how quantum measurements can be used to fuel a cooling engine. We illustrate quantum measurement cooling (QMC)…
The inexorable miniaturisation of technologies, the relentless drive to improve efficiency and the enticing prospect of boosting performance through quantum effects are all compelling reasons to investigate microscopic machines. Thermal…
Quantum process tomography is an experimental technique to fully characterize an unknown quantum process. Standard quantum process tomography suffers from exponentially scaling of the number of measurements with the increasing system size.…
Quantum machine learning (QML) is a rapidly growing field that combines quantum computing principles with traditional machine learning. It seeks to revolutionize machine learning by harnessing the unique capabilities of quantum mechanics…