Related papers: A Foundation of Programming a Multi-Tape Quantum T…
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…
As quantum computers become real, it is high time we come up with effective techniques that help programmers write correct quantum programs. In classical computing, formal verification and sound static type systems prevent several classes…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
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…
Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we…
Recently, among experiments for realization of quantum computers, NMR quantum computers have achieved the most impressive succession. There is a model of the NMR quantum computation,namely Atsumi and Nishino's bulk quantum Turing Machine.…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
We demonstrate how quantum field theory problems can be embedded on quantum annealers. The general method we use is a discretisation of the field theory problem into a general Ising model, with the continuous field values being encoded into…
Superconducting quantum circuit is a promising system for building quantum computer. With this system we demonstrate the universal quantum computations, including the preparing of initial states, the single-qubit operations, the two-qubit…
In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. In…
We consider how changes in transfinite machine architecture can sometimes alter substantially their capabilities. We approach the subject by answering three open problems touching on: firstly differing halting time considerations for…
A quantum processor is a device with a data register and a program register. The input to the program register determines the operation, which is a completely positive linear map, that will be performed on the state in the data register. We…
The development of quantum computing technologies builds on the unique features of quantum physics while borrowing familiar principles from the design of conventional devices. We introduce the fundamental concepts required for designing and…
Quantum computers are becoming real, and they have the inherent potential to significantly impact many application domains. We sketch the basics about programming quantum computers, showing that quantum programs are typically hybrid…
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…
Clift and Murfet (2019) introduced a naive Bayesian smooth relaxation of Turing machines motivated by work in differential linear logic; this was subsequently used to endow spaces of program codes of bounded length with a smooth manifold…
Quantum systems have an exponentially large degree of freedom in the number of particles and hence provide a rich dynamics that could not be simulated on conventional computers. Quantum reservoir computing is an approach to use such a…
The Universal Turing Machine (TM) is a model for VonNeumann computers --- general-purpose computers. A human brain can inside-skull-automatically learn a universal TM so that he acts as a general-purpose computer and writes a computer…
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental…
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…