1 edition of **Geometry of quantum computations** found in the catalog.

Geometry of quantum computations

Gia Giorgadze

- 316 Want to read
- 24 Currently reading

Published
**2012**
.

Written in English

- Geometry,
- Quantum theory,
- Quantum computers,
- Data processing,
- Mathematics

**Edition Notes**

Includes bibliographical references and index.

Statement | Gia Giorgadze (Department of Mathematics, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University 2, Tbilisi, Georgia) |

Classifications | |
---|---|

LC Classifications | QA448.D38 G56 2012 |

The Physical Object | |

Pagination | pages cm |

ID Numbers | |

Open Library | OL25384402M |

ISBN 10 | 9781622573257 |

LC Control Number | 2012022859 |

Quantum computation is the eld that investigates the computational power and other prop-erties of computers based on quantum-mechanical principles. An important objective is to nd quantum algorithms that are signi cantly faster than any classical algorithm solving the same Size: 1MB. OR is taken to be a quantum-gravity process related to the fundamentals of spacetime geometry, so Orch OR suggests a connection between brain biomolecular processes and fine-scale structure of the universe. Here we review and update Orch OR in light of criticisms and developments in quantum biology, neuroscience, physics and cosmology.

QUANTUM COMPUTATION USING GEOMETRIC ALGEBRA Publication No. _____ Douglas J. Matzke, Ph. D. The University of Texas at Dallas, Supervising Professor: Cyrus Cantrell This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal. Download PDF Statistical Mechanics Algorithms And Computations book full free. Statistical Mechanics Algorithms And Computations available for download and read online in such as quantum computing and cryptography, complex systems, and quantum fluids. This book sets these issues into a larger and more coherent theoretical context than is.

Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved Cited by: Rather, quantum geometry serves as a ‘bridge’ to another large classical space-time. This summary will focus on structural issues from a mathematical physics per-spective. Complementary perspectives and further details can be found in articles on loop quantum gravity, canonical formalism, quantum cosmology, black hole thermo-Cited by: 2.

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ISBN: OCLC Number: Description: ix, pages ; 26 cm. Contents: Preface; Basic of Quantum Computation; Quantum Computers Based on Exactly Solvable Models & Geometric Phases; Quantum Processor Based on the Three-Level Quantum System; Methods of Geometric Control Theory for Quantum Computations; Analytic Methods in Quantum Computation.

ISBN: X OCLC Number: Description: 1 online resource (ix, pages). Contents: GEOMETRY OF QUANTUM COMPUTATION ; GEOMETRY OF. Determining the quantum circuit complexity of a unitary operation is closely related to the problem of finding minimal length paths in a particular curved geometry [Nielsen et al, Science()].

This paper investigates many of the basic geometric objects associated to this space, including the Levi-Civita connection, the geodesic equation, the curvature, and the Jacobi Cited by: If for the description of the computing dynamical system, a configuration space with nontrivial-geometry or topology is chosen, one can talk about the geometric character of the computation.

The book examines the known holonomic and topological models of quantum computation and the new monodromic model of quantum computation is discussed in detail. Geometric Quantum Computation.

as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the.

Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry.

By recasting the problem of finding quantum circuits as a geometric problem, we open up Cited by: Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the.

Avi Wigderson Mathematics and Computation Draft: Ma Acknowledgments In this book I tried to present some of the knowledge and understanding I acquired in my four decades in the eld.

The main source of this knowledge was the Theory of Computation commu-nity, which has been my academic and social home throughout this period. Each theory of quantum gravity uses the term "quantum geometry" in a slightly different fashion.

String theory, a leading candidate for a quantum theory of gravity, uses the term quantum geometry to describe exotic phenomena such as T-duality and other geometric dualities, mirror symmetry, topology-changing transitions [clarification needed], minimal possible distance scale, and other effects.

Book: The geometry of physics, an introduction, first edition Cambridge University Press, ISBN pages = A4 pages. No quantization, but does contain lots of gauge theory and Yang-Mills, all based on connection forms.

Books shelved as quantum-computing: Quantum Computing Since Democritus by Scott Aaronson, Quantum Computation and Quantum Information by Michael A.

Niels. This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of the spectral approach, a concise primer on spectral triples is given. Chapter 2 is designed to serve as a toolkit for computations.

The book is concerned with the geometric theory of computation. We have in mind the trivial geometry or topology is chosen, one can talk about the geometric character of the computation.

The book examines the known holonomic and topological models of quan- In the monodromic quantum computations, the ﬁbre of the vector bundle induced by. It was about four years ago that Springer-Verlag suggested that a revised edition in a single volume of my two-volume work may be worthwhile.

I agreed enthusiastically but the project was delayed for many reasons, one of the most important of which was that I did not have at that time any clear idea as to how the revision was to be carried out. The present Theorem have explained the circuits complexity of in quantum computation with n-qudit systems in terms of the Riemannian r to the qubit c13 and qutrit case 14 the optimal quantum circuit is reduced to the shortest path problem based on special curved geometry of SU(d n).The qudit systems present different algebraic derivations from qubits and by: The present Theorem have explained the circuits complexity of in quantum computation with n-qudit systems in terms of the Riemannian r to the qubit c13 and Cited by: In recent work pertaining to digital quantum computations—the quantum parallel to classical computations—algebraic concepts are being introduced as a resource.

(finite groups such as Paulis and Cliffords, free groups with relations, group covariance in generalized quantum measurements, etc.), of geometry (e.g., finite geometries for. A Novel Algebraic Geometry Compiling Framework for Adiabatic Quantum Computations.

10/02/ ∙ by Raouf Dridi, et al. ∙ 0 ∙ share Adiabatic Quantum Computing (AQC) is an attractive paradigm for solving hard integer polynomial optimization problems.

This book was set in Syntax and Times Roman by Westchester Book Group. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Rieffel, Eleanor, – Quantum computing: a gentle introduction / Eleanor Rieffel and Wolfgang Polak.

cm.—(Scientiﬁc and engineering computation)File Size: 6MB. The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students.

The book provides an entree into a field that promises to remain exciting and important for years to come.5/5(1).

Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis.

For many researchers working in this field in ma- thematics and physics, computer algebra software systems have become indispensable tools in theory. The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory.

The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can .The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory.

The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann.