Mathematics of Quantum Computation and Quantum Technology by Louis Kauffman, Samuel J. Lomonaco

By Louis Kauffman, Samuel J. Lomonaco

Книга arithmetic of Quantum Computation and Quantum know-how arithmetic of Quantum Computation and Quantum TechnologyКниги Физика Автор: Goong Chen, Louis Kauffman, Samuel J. Lomonaco Год издания: 2007 Формат: pdf Издат.:Chapman & Hall/CRC Страниц: 624 Размер: 3,6 ISBN: 1584888997 Язык: Английский0 (голосов: zero) Оценка:Research and improvement within the pioneering box of quantum computing contain with reference to each aspect of technology and engineering, together with the numerous components of arithmetic and physics. according to the enterprise knowing that arithmetic and physics are equivalent companions within the carrying on with research of quantum technological know-how, arithmetic of Quantum Computation and Quantum know-how explores the quick mathematical developments made during this box lately. Novel Viewpoints on quite a few facets of Quantum Computing and know-how Edited through a well-respected group of specialists, this quantity compiles contributions from experts throughout quite a few disciplines. It includes 4 major components, starting with subject matters in quantum computing that come with quantum algorithms and hidden subgroups, quantum seek, algorithmic complexity, and quantum simulation. the subsequent part covers quantum expertise, akin to mathematical instruments, quantum wave capabilities, superconducting quantum computing interference units (SQUIDs), and optical quantum computing. The part on quantum info offers with errors correction, cryptography, entanglement, and verbal exchange. the ultimate half explores topological quantum computation, knot thought, classification algebra, and common sense. The instruments you must take on the subsequent iteration of Quantum know-how This e-book allows either the development of a standard quantum language and the improvement of interdisciplinary quantum suggestions, for you to reduction efforts within the pursuit of the last word goal-a "real" scalable quantum computing device.

Show description

Read Online or Download Mathematics of Quantum Computation and Quantum Technology PDF

Similar mathematics books

Calculus II For Dummies (2nd Edition)

An easy-to-understand primer on complex calculus topics

Calculus II is a prerequisite for lots of well known collage majors, together with pre-med, engineering, and physics. Calculus II For Dummies bargains specialist guideline, suggestion, and how you can aid moment semester calculus scholars get a deal with at the topic and ace their exams.

It covers intermediate calculus issues in undeniable English, that includes in-depth insurance of integration, together with substitution, integration suggestions and whilst to exploit them, approximate integration, and wrong integrals. This hands-on consultant additionally covers sequences and sequence, with introductions to multivariable calculus, differential equations, and numerical research. better of all, it contains useful workouts designed to simplify and improve realizing of this advanced subject.

advent to integration
Indefinite integrals
Intermediate Integration themes
endless sequence
complex subject matters
perform exercises

Confounded by means of curves? confused by means of polynomials? This plain-English advisor to Calculus II will set you straight!

Didactics of Mathematics as a Scientific Discipline

This publication describes the state-of-the-art in a brand new department of technology. the elemental suggestion used to be to begin from a common point of view on didactics of arithmetic, to spot yes subdisciplines, and to indicate an total constitution or "topology" of the sphere of study of didactics of arithmetic. the quantity offers a pattern of 30 unique contributions from 10 various nations.

Extra info for Mathematics of Quantum Computation and Quantum Technology

Example text

For more details, we refer the reader to [31]. 13 Is Grover’s algorithm a QHS algorithm? In this section, our objective is to factor Grover’s algorithm into the QHS primitives developed in the previous sections of this paper. As a result, we will show that Grover’s algorithm is more closely related to Shor’s algorithm than one might at first expect. 13. IS GROVER’S ALGORITHM A QHS ALGORITHM? 37 will refer to as the Grover HSP. However, we will then show that the standard QHS algorithm for this HSP cannot possibly find a solution.

THE QUANTUM CIRCLE AND SHOR ALGORITHMS 27 Hence, ψ3 = ∑ |n dx e−2π inx |Φ (x) n∈Z 1/a = ∑ |n n∈Z = dx e−2π inx |Φ (x) δn=0 mod a 0 ⎛ 1/a ∑| a dx e−2π inx |Φ (x) ⎠ = ⎝ ∈Z ⎞ ∑| a 0 ∈Z |Ω ( a) . Step 4 Measurement of ψ3 = ∑ | a |Ω ( a) ∈HZ ⊗HC ∈Z with respect to the observable ∑ n |n n| n∈Z to produce a random eigenvalue a. 8 The above quantum circle algorithm can be extended to a quantum algorithm which finds the hidden period α of a function Φ : R/Z −→ C, when α is an arbitrary real number mod 1.

We assume that the hidden subgroup K is normal and of finite index in F. ) • Choose a finite group probe G with presentation (x1 , x2 , . . , xn : r1 , r2 , . . , rm )ν , where the subscript ν denotes the epimorphism ν : F −→ G induced by the map x j −→ x jCons r2 , . . , rm . 1. QHS ALGORITHMS 36 • Choose a minimal 2-sided Schreier transversal τ : G −→ F of the epimorphism ν : F −→ G. • Finally, construct the push ϕ = Push (ϕ ) = ϕ ◦ τ : G −→ S. Our generalized Shor algorithm for the free group F consists of the following steps: Shor’s Algorithm Generalized to Free Groups Step 1 Call QR AND(ϕ ) to produce a word s j in F close to a word s j lying in ϕ −1 ϕ (1).

Download PDF sample

Rated 4.50 of 5 – based on 8 votes