Quantum computing for computer scientists pdf download

Quantum computing for computer scientists pdf download

PDF Download< Quantum Computing for Computer Scientists,PDF Download Quantum Computing for Computer Scientists, by Noson S. Yanofsky, Mirco A. Mannucci

26/01/ · Read PDF Here => Quantum Computing for Computer Scientists > The multidisciplinary field of quantum computing strives to exploit some of the uncanny aspects 01/07/ · Abstract Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement. A quantum computer is a device that 23/09/ · Quantum Computing for Computer Scientists takes readers on a tour of this fascinating area of cutting-edge research. Written in an accessible yet rigorous fashion, this Quantum Computer Science An Introduction In the s it was realized that quantum physics has some spectacular applications in computer science. This book is a concise introduction 30/05/ · It will also be of interest to physicists who want to learn the theory of quantum computation, and to physicists and philosophers of science interested in quantum ... read more

Jan 27, , AM Jan Reply to author. Report message as abuse. Show original message. DMCA Privacy Policy Contact. Read All Book ReadAllBook. Org with rich sourcebook, you can download thousands of books in many genres and formats such as PDF, EPUB, MOBI, MP3, ……. Home Books-Genres FAQ Request Ebooks Contact. Search Ebook here:. Book Preface In the s it was realized that quantum physics has some spectacular applications in computer science. To help you become more at home with this notation, you are urged to prove from 1. The construction 1. If you substitute expressions of the form 1. Note that, if we were to interchange X and Z in the second line of 1. So interchanging the X and Z operators has the effect of switching which Cbit is the control and which is the target, changing Ci j into C j i. Quantum physicists invariably use H to denote the Hamiltonian function in classical mechanics or Hamiltonian operator in quantum mechanics. Fortunately Hamiltonian operators, although of crucial importance in the design of quantum computers, play a very limited role in the general theory of quantum computation, being completely overshadowed by the unitary transformations that they generate.

So physicists can go along with the computer-science notation without getting into serious trouble. We shall see that this simple relation can be put to some quite remarkable uses in a quantum computer. Of course, the action of H on the state of a Cbit that follows from 1. Nevertheless, when combined with other operations, as on the right side of 1. In a quantum computer the action of H on 1-Qbit states turns out to be not only meaningful but also easily implemented, and the possibility of interchanging control and target Qbits using only 1-Qbit operators in the manner shown in 1. The use of Hadamards to interchange the control and target Qbits of a cNOT operation is sufficiently important in quantum computation to merit a second derivation of 1. In strict analogy to the definition of cNOT see 1. As a final exercise in treating operations on Cbits as linear operations on vectors, we construct an alternative form for the swap operator. If we use 1.

All three are Hermitian. A fuller statement in a broader context can be found in Appendix A. All the relations in 1. They can also be complex numbers, but in most useful applications they are real. Then one easily confirms that all the relations in 1. Together with the unit matrix 1, the matrices σ x , σ y , and σ z form a basis for the four-dimensional algebra of two-dimensional matrices of complex numbers: any such matrix is a unique linear combination of these four with complex coefficients. The matrices σ x , σ y , and σ z were introduced in the early days of quantum mechanics by Wolfgang Pauli, to describe the angular momentum associated with the spin of an electron. They have many other useful purposes, being simply related to the quaternions invented by Hamilton to deal efficiently with the composition of three-dimensional rotations. The beautiful and useful connection between Pauli matrices and three-dimensional rotations discovered by Hamilton is developed in Appendix B.

Some of their properties, developed further in Appendix B, prove to be quite useful in treating Qbits, to which we now turn. Happily, nature has provided us with physical systems, Qbits, described by states that do not suffer from this limitation. If one of α0 and α1 is 0 and the other is 1 — i. We shall often sacrifice correctness for ease of expression. Some reasons for this apparently pedantic terminological hair splitting will emerge below. Just as the general state of a single Qbit is any normalized superposition 1. Therefore c 0 is the greatest common divisor of f and c. But f1 and c 1 are given by explicit integral linear combinations of the pair at the preceding stage, f2 and c 2 , which in turn are explicit integral linear combinations of f3 and c 3 , etc.

If j and r happen to have no factors in common, r is given by the denominator of the partial sum with the largest denominator less than N. Otherwise the continued-fraction expansion of x gives r 0 : r divided by whatever factor it has in common with the random integer j. If several small multiples of r 0 fail to be a period of f , one repeats the whole procedure, getting a different submultiple r 1 of r. There is a good chance that r will be the least common multiple of r 0 and r 1 , or a not terribly large multiple of it. If not, one repeats the whole procedure a few more times until one succeeds in finding a period of f. We illustrate this with two examples. Example 1. Successful the first time. What is r? Example 2. Two attempts required. The partial sum with the largest denominator less than is the one we are looking for.

Once we have found the answer we can easily check that it is correct. Hardy and E. Wright, An Introduction to the Theory of Numbers, 4th edition, Oxford University Press Then it follows from K. By the partial sums of the continued fraction K. Analysis of example 1. Analysis of example 2. The number r is thus a multiple of 13 less than , of which there are nine. One easily applies these to the sequence a 0 , a 1 , a 2 ,. So r is also a multiple of 6 less than Appendix L Better estimates of success in period finding In Section 3. Now when N is the product of two odd primes p and q , as it is in the case of RSA encryption, then the required period r is not only less than N, but also less than 12 N. Gerjuoy has estimated that this increases the probability of a successful run to about 0. Bourdon and H. Appendix M Factoring and period finding We establish here the only hard part of the connection between factoring and period finding: that the probability is at least 12 that if a is a random member of G pq for prime p and q , then the order r of a in G pq satisfies both r even M.

Note first that the order r of a in G pq is the least common multiple of the orders r p and r q of a in G p and in G q. Consequently condition M. Condition M. But this is inconsistent with a failure of condition M. Our effort to factor N can fail only if we have picked a random a for which r p and r q are both odd multiples of the same power of 2. So to show that the probability of failure is at most 12 , we must show that the probability is at most 12 that the orders r p and r q of such a randomly and independently selected pair are both odd multiples of the same power of 2. We do this by showing that for any prime p, no more than half of the numbers in G p can have orders r p that are odd multiples of any given power of 2.

Given this theorem — which is proved at the end of this appendix — we complete the argument by showing that the orders of the odd powers of any such primitive b are odd multiples of 2k , but the orders of the even powers are not. So r 0 is an odd multiple of 2k. This concludes the proof that the probability is at least 12 that a random choice of a in G pq will satisfy both of the conditions M. The relevant property of the multiplicative group of integers {1, 2, 3,. This provides all the structure necessary to ensure that a polynomial of degree d has at most d roots. This follows from the fact that if two numbers in G p have orders that are coprime, then the order of their product is 1 This is easily proved by induction on the degree of the equation, using the fact that every nonzero integer modulo p has a multiplicative inverse modulo p.

It is obviously true for degree 1. So the order v of d divides wu, and since v and u have no common factors, v divides w. In the same way one concludes that u divides w. Therefore, since v and u are coprime, w must be a multiple of uv. These can be viewed as an extension of the simple 3-Qbit codewords we examined in Section 5. An encoding circuit for the 9-Qbit code — with an obvious resemblance to Figure 5. The form 5. One easily confirms from N. Each one of the 22 corrupted terms in N. Note the relation to the simpler 3-Qbit encoding circuit in Figure 5. The nine Qbits are the nine lower wires. The circuit is of the type illustrated in Figure 5.

Measurement of the eight ancillas projects the state of the nine lower Qbits into the appropriate simultaneous eigenstate of those eight operators. And each of the 22 terms in N. APPENDIX N a The three errors Z0 , Z3 , and Z6 are distinguished from the Xi and Yi by the fact that they commute with every one of the six Z-operators in N. These three Zi can be distinguished from each other because Z0 anticommutes with one of the two X-operators, Z6 anticommutes with the other, and Z3 anticommutes with both. b All nine errors Xi are distinguished both from the Zi and from the Yi by the fact that they commute with both X-operators. They can be distinguished from each other because X0 , X2 , X3 , X5 , X6 , and X8 each anticommutes with a single one of the six Z-operators in N.

c Finally, the nine errors Yi have the same pattern of commutations with the Z-operators in N. They can be distinguished from the Xi operators by their failure to commute with at least one of the two X-operators in N. So, as with the other codes we have examined, the simultaneous measurement of the eight commuting operators in N. One then applies the appropriate inverse unitary transformation to restore the uncorrupted state. A circuit that diagnoses the 9-Qbit error syndrome is shown in Figure N. Figure O. This figure demonstrates that when M0 is brought to the left through all the gates in the circuit it acts directly as Z0 on the input state on the left, which is invariant under Z0. The caption explains why essentially the same argument applies to the other Mi : when brought all the way to the left, M1 reduces to Z1 acting on the input state, and M2 reduces to Z2.

We exploit the fact that bringing an X, acting on the control Qbit of a cNOT, from one side of the cNOT to the other introduces an additional X acting on the target Qbit and the fact that an X acting on the target Qbit commutes with the cNOT. Bringing the X acting on Qbit 0 to the left of the three cNOT gates, represented by the controlled triple-NOT on the right, introduces X operators on all three target Qbits, which combine with the three X already acting on those Qbits to produce unit operators. So all four X gates on the right reduce to X0 , as indicated in inset a.

That X0 can be moved further to the left through H0 , if it is changed into Z0 , as shown in inset b. So M0 acting on the extreme right is equivalent to Z0 acting on the extreme left. We exploit the fact that bringing a Z, acting on the target Qbit of a cNOT, from one side of the cNOT to the other introduces an additional Z acting on the control Qbit and the fact that a Z acting on the control Qbit commutes with the cNOT. So bringing Z4 , Z5 , and Z6 to the left of all three cNOT gates represented by the controlled triple-NOT on the right introduces three Z operators on the control Qbit 0, which combine with the Z0 already acting to produce the unit operator, reducing the collection of four Z gates on the left to the three Z acting on Qbits 4, 5, and 6, as indicated in a.

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There are chapters on computer architecture, algorithms, programming languages, theoretical computer science, cryptography, information theory, and hardware. The text has step-by-step examples, more than two hundred exercises with solutions, and programming drills that bring the ideas of quantum computing alive for today's computer science students and researchers. Review "The book has the potential to fill a void that needs to be filled: to bring the excitement of quantum computing to undergraduate computing majors, especially those with modest math backgrounds.

While there are a few outstanding graduate textbooks on the topic, this one has the unique feature of being accessible to typical CS undergraduates The authors have written this with great pedagogical skill. Readers will feel that they are having a conversation with the authors which makes it a great book for self-study. This one differs from all those I have seen in that it is explicitly written for undergraduates with a very limited knowledge of physics or math, but some minimal training in classical computing. As such the book is extremely user friendly and has many exercises to explain the material, some in the form of programs the student can write to explore many sides of a given problem, almost like playing computer games.

More complicated topics are illustrated by examples, rather than complicated formal proofs. There is a good list of references for further reading on individual topics, and suggested topics for projects. The book is clearly geared to the student of limited background who wants to learn about quantum computing without waiting to become an expert in classical computing. For this audience the book has no peers and is highly recommended. This book stresses the computer science aspect of quantum computing. a very good addition to the list. This work has many attractive features. Definitely, a very fine book. Bharath, Northern Michigan University for Choice Magazine "In a word, this is a well-structured text which deserves careful from consideration from instructors not only engaged with computer science teaching but also those in physics and electronic engineering.

Alan Shore, Contemporary Physics "this is a book that I can recommend to anyone with a basic knowledge of linear algebra. Not only will it make a very nice textbook for undergraduate computer scientists and mathematicians; it is also the kind of book one can give to a bright student to read on her own. Coutinho, SIGACT News "Happily, I found that I could fight my way through much more of the maths than I'd expected, largely because of the clarity of the style and the exemplary use of language. Presentation: Clear, elegant and comprehensive - with every effort made to make it comprehensible too. Would you recommend it? About the Author Noson F. Yanofsky is an Assistant Professor in the Department of Computer and Information Science at Brooklyn College, City University of New York and of the Computer Department in The Graduate Center of CUNY.

Mirco A. Mannucci, Ph. He also serves as Adjunct Professor of Computer Science at George Mason University and the University of Maryland. This is amazing introductory book! By Jun Won Lee I am studying quantum computing by myself. Before this book, I studied this field with other school's class website. Even though the slide and on-line documents I obtained is great, it was hard to understand by just reading! This book is totally different from other books. It focued on people who are weak to mathematics and have little knowledge of quantum computing. Even some chapters are still hard because of the nature of this field , most chapters are so well written that you can read lying on the couch and feel like you read some kind of story.

Since I have been in the technical field for a while, I am a CS PhD student studying Data Mining and Machine Learning , this book is one of very rarely well written books containing sufficient depth but keeping simplicity. For anyone who wish to start to study Quantum Computing WITHOUT much pain, this is THE book. Viewpoint of a self-guided explorer of quantum computing By Arnab Chakraborty Good points about the book: 1 The authors focus on the "what"'s and "how"'s rather than the "why"'s. They do not waste time with nitty gritty details of quantum physics.

The book is true to it title, and delves directly into the practical details of quantum computing. In this respect this book is a welcome exception among a plethora of similarly titled book that end up bombarding the readers with alpha particles and magical photons, and leave the quantum computing topics only vaguely explained. Just as classical computing is not about understanding semiconductors, quantum computing is not about chasing photons. This book makes this very clear. Though I skipped most of the exercises during my firsr reading, these helped me to consolidate my understanding during subsequent readings. This book is ideal for self-guided study.

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Report Quantum computing for computer scientists pdf download. The book is intended primarily for computer scientists who know nothing about quantum theory, but will also be of interest to physicists who want to learn the theory of quantum computation, and philosophers of science interested in quantum foundational issues. In the application to bit commitment in Section 6. It takes years to develop such intuition. So r is also a multiple of 6 less than PDF Download Quantum Computing for Computer Scientists, by Noson S. Mannucci The multidisciplinary field of quantum computing strives to exploit some of the uncanny aspects of quantum mechanics to expand our computational horizons.