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Research and Development Corrective Automorphism of Repeated Code for Quantum Error Correction
Abstract
One of the main problems to be overcome in the near future for the practical creation of quantum computer to make quantum computing resistant to interaction with the external environment and to eliminate inaccuracy of operations. In this paper we study quantum codes correcting errors, proposed as a way to protect against the occurrence errors due to the influence of the external environment. Results of work are considered software implemented model of the simplest quantum code. This work is a study of the influence of the environment on a quantum system of qubits. The article is supposed to describe the foundations of quantum information theory, as well as the place in it of the concept of quantum entanglement. A technique for correcting two main types of quantum errors has been developed, based on the implementation and execution of certain quantum circuits. The main difficulties of ensuring the protection of a quantum channel from various types of errors are analyzed and considered. Demonstrated are the dependences of data distortion on the noise level and the measure of decoherence on the noise level in one qubit.
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The paper outlines the historical development of spin in physics from about
1920 to the present day. It aims to provide the student with an accurate
chronology of important developments, both scientific and technical.
The paper outlines the historical development of spin in physics from about 1920 to the present day. It aims to provide the student with an accurate chronology of important developments, both scientific and technical.
By the year 2020, the basic memory components of a computer will be the size of individual atoms. At such scales, the current theory of computation will become invalid. A new field called "quantum computing" is emerging that is reinventing the foundations of computer science and information theory in a way that is consistent with quantum physics - the most accurate model of reality that is currently known. Remarkably, this new theory predicts that quantum computers can perform certain tasks breathtakingly faster than classical computers, and, better yet, can accomplish mind-boggling feats such as teleporting information, breaking supposedly "unbreakable" codes, generating true random numbers, and communicating with messages that betray the presence of eavesdropping. "Explorations in Quantum Computing" explains these burgeoning developments in simple terms, and describes the key technological hurdles that must be overcome in order to make quantum computers a reality. This book draws upon the very latest research and uses executable software simulations to help explain the material and allow the reader to experiment with the ideas behind quantum computers. This is the ideal text for anyone wishing to learn more about the next, perhaps "ultimate," computer revolution.
This paper considers the principles of architecture models of quantum calculators. It describes the existing problems of construction and implementation of their work, as well as ways to overcome these problems. The distinction model of the relevant modules in its composition is achieved. Withdrawal functionality number of three parts modules, their graphics (interface) components, which are produced as a result of differentiation of the model into separate modules included in its composition. We describe the interface of the model and place it in the auxiliary modules and libraries.
We construct the first Message Authentication Codes (MACs) that are existentially unforgeable against a quantum chosen message attack. These chosen message attacks model a quantum adversary’s ability to obtain the MAC on a superposition of messages of its choice. We begin by showing that a quantum secure PRF is sufficient for constructing a quantum secure MAC, a fact that is considerably harder to prove than its classical analogue. Next, we show that a variant of Carter-Wegman MACs can be proven to be quantum secure. Unlike the classical settings, we present an attack showing that a pair-wise independent hash family is insufficient to construct a quantum secure one-time MAC, but we prove that a four-wise independent family is sufficient for one-time security. Keywords: Quantum computing, MAC,chosen message attacks, post-quantum security 1
In this chapter we introduced the idea of a quantum gate, and contrasted it with logically irreversible and logically reversible
classical gates. Quantum gates are, like classical reversible gates, logically reversible, but they differ markedly on their
universality properties. Whereas the smallest universal classical reversible gates have to use three bits, the smallest universal
quantum gates need only use two bits. As the classical reversible gates are also unitary, it is conceivable that one of the
first practical applications of quantum gates is in non-standard (e.g., “spintronic”) implementations of classical reversible
computers.
We give an algorithm for approximating the quantum Fourier
transform over an arbitrary Z<sub>p</sub> which requires only O(n log n)
steps where n=log p to achieve an approximation to within an arbitrary
inverse polynomial in n. This improves the method of A.Y. Kitaev (1995)
which requires time quadratic in n. This algorithm also leads to a
general and efficient Fourier sampling technique which improves upon the
quantum Fourier sampling lemma of L. Hales and S. Hallgren (1997). As an
application of this technique, we give a quantum algorithm which finds
the period of an arbitrary periodic function, i.e. a function which may
be many-to-one within each period. We show that this algorithm is
efficient (polylogarithmic in the period of the function) for a large
class of periodic functions. Moreover, using standard quantum
lower-bound techniques, we show that this characterization is right.
That is, this is the maximal class of periodic functions with an
efficient quantum period-finding algorithm
The Comparative Method
- D Collier