Quantum Computation and Quantum Information
Quantum Computation and Quantum Information is a textbook about quantum information science written by Michael Nielsen and Isaac Chuang, regarded as a standard text on the subject. It is informally known after the candies of that name; the book assumes minimal prior experience with quantum mechanics and with computer science, aiming instead to be a self-contained introduction to the relevant features of both. The focus of the text is on theory, rather than the experimental implementations of quantum computers, which are discussed more briefly; as of February 2018, the book has been cited over 31,000 times on Google Scholar. Chapter 1: Introduction and Overview Chapter 2: Introduction to Quantum Mechanics Chapter 3: Introduction to Computer Science Chapter 4: Quantum Circuits Chapter 5: The Quantum Fourier Transform and its Applications Chapter 6: Quantum Search Algorithms Chapter 7: Quantum Computers: Physical Realization Chapter 8: Quantum Noise and Quantum Operations Chapter 9: Distance Measures for Quantum Information Chapter 10: Quantum Error-Correction Chapter 11: Entropy and Information Chapter 12: Quantum Information Theory Appendix 1: Notes on Basic Probability Theory Appendix 2: Group Theory Appendix 3: The Solovay–Kitaev Theorem Appendix 4: Number Theory Appendix 5: Public Key Cryptography and the RSA Cryptosystem Appendix 6: Proof of Lieb's Theorem Bibliography Index Nielsen, Michael A..
Quantum Computation and Quantum Information. Cambridge: Cambridge University Press. ISBN 978-0-521-63503-5. OCLC 634735192. Nielsen, Michael A.. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press. ISBN 978-1-107-00217-3. OCLC 844974180
Economic inequality covers a wide variety of topics. It can refer to the distribution of wealth. Besides economic inequality between countries or states, there are important types of economic inequality between different groups of people. Important types of economic measurements focus on wealth and consumption. There are many methods for measuring economic inequality, with the Gini coefficient being a used one. Another type of measure is the Inequality-adjusted Human Development Index, a statistic composite index that takes inequality into account. Important concepts of equality include equity, equality of outcome, equality of opportunity. Research suggests. Whereas globalization has reduced global inequality, it has increased inequality within nations. In 1820, the ratio between the income of the top and bottom 20 percent of the world's population was three to one. By 1991, it was eighty-six to one. A 2011 study titled "Divided we Stand: Why Inequality Keeps Rising" by the Organisation for Economic Co-operation and Development sought to explain the causes for this rising inequality by investigating economic inequality in OECD countries.
Single-headed households in OECD countries have risen from an average of 15% in the late 1980s to 20% in the mid-2000s, resulting in higher inequality. Assortative mating refers to the phenomenon of people marrying people with similar background, for example doctors marrying doctors rather than nurses. OECD found out that 40% of couples where both partners work belonged to the same or neighbouring earnings deciles compared with 33% some 20 years before. In the bottom percentiles number of hours worked; the main reason for increasing inequality seems to be the difference between the demand for and supply of skills. Income inequality in OECD countries is at its highest level for the past half century; the ratio between the bottom 10 % and the top 10 % has increased to 1:9 in 25 years. There are tentative signs of a possible convergence of inequality levels towards a common and higher average level across OECD countries. With few exceptions, the wages of the 10% best-paid workers have risen relative to those of the 10% lowest paid.
A 2011 OECD study investigated economic inequality in Argentina, China, Indonesia and South Africa. It concluded that key sources of inequality in these countries include "a large, persistent informal sector, widespread regional divides, gaps in access to education, barriers to employment and career progression for women."A study by the World Institute for Development Economics Research at United Nations University reports that the richest 1% of adults alone owned 40% of global assets in the year 2000. The three richest people in the world possess more financial assets than the lowest 48 nations combined; the combined wealth of the "10 million dollar millionaires" grew to nearly $41 trillion in 2008. A January 2014 report by Oxfam claims that the 85 wealthiest individuals in the world have a combined wealth equal to that of the bottom 50% of the world's population, or about 3.5 billion people. According to a Los Angeles Times analysis of the report, the wealthiest 1% owns 46% of the world's wealth.
In January 2015, Oxfam reported that the wealthiest 1 percent will own more than half of the global wealth by 2016. An October 2014 study by Credit Suisse claims that the top 1% now own nearly half of the world's wealth and that the accelerating disparity could trigger a recession. In October 2015, Credit Suisse published a study which shows global inequality continues to increase, that half of the world's wealth is now in the hands of those in the top percentile, whose assets each exceed $759,900. A 2016 report by Oxfam claims that the 62 wealthiest individuals own as much wealth as the poorer half of the global population combined. Oxfam's claims have however been questioned on the basis of the methodology used: by using net wealth, the Oxfam report, for instance, finds that there are more poor people in the United States and Western Europe than in China. Anthony Shorrocks, the lead author of the Credit Suisse report, one of the sources of Oxfam's data, considers the criticism about debt to be a "silly argument" and "a non-issue … a diversion."
Oxfam's 2017 report says the top eight billionaires have as much wealth as the bottom half of the global population, that rising inequality is suppressing wages, as businesses are focused on delivering higher returns to wealthy owners and executives. In 2018, the Oxfam report said that the wealth gap continued to widen in 2017, with 82% of global wealth generated going to the wealthiest 1%; the 2019 Oxfam report said that the poorest half of the human population has been losing wealth at the same time that a billionaire is minted every two days. According to PolitiFact, the top 400 richest Americans "have more wealth than half of all Americans combined." According to The New York Times on July 22, 2014, the "richest 1 percent in the United States now own more wealth than the bottom 90 percent". Inherited wealth may help explain why many Americans who have become rich may have had a "substantial head start". In September 2012, according to the Institute for Policy Studies (I
OCLC Online Computer Library Center, Incorporated d/b/a OCLC is an American nonprofit cooperative organization "dedicated to the public purposes of furthering access to the world's information and reducing information costs". It was founded in 1967 as the Ohio College Library Center. OCLC and its member libraries cooperatively produce and maintain WorldCat, the largest online public access catalog in the world. OCLC is funded by the fees that libraries have to pay for its services. OCLC maintains the Dewey Decimal Classification system. OCLC began in 1967, as the Ohio College Library Center, through a collaboration of university presidents, vice presidents, library directors who wanted to create a cooperative computerized network for libraries in the state of Ohio; the group first met on July 5, 1967 on the campus of the Ohio State University to sign the articles of incorporation for the nonprofit organization, hired Frederick G. Kilgour, a former Yale University medical school librarian, to design the shared cataloging system.
Kilgour wished to merge the latest information storage and retrieval system of the time, the computer, with the oldest, the library. The plan was to merge the catalogs of Ohio libraries electronically through a computer network and database to streamline operations, control costs, increase efficiency in library management, bringing libraries together to cooperatively keep track of the world's information in order to best serve researchers and scholars; the first library to do online cataloging through OCLC was the Alden Library at Ohio University on August 26, 1971. This was the first online cataloging by any library worldwide. Membership in OCLC is based on use of services and contribution of data. Between 1967 and 1977, OCLC membership was limited to institutions in Ohio, but in 1978, a new governance structure was established that allowed institutions from other states to join. In 2002, the governance structure was again modified to accommodate participation from outside the United States.
As OCLC expanded services in the United States outside Ohio, it relied on establishing strategic partnerships with "networks", organizations that provided training and marketing services. By 2008, there were 15 independent United States regional service providers. OCLC networks played a key role in OCLC governance, with networks electing delegates to serve on the OCLC Members Council. During 2008, OCLC commissioned two studies to look at distribution channels. In early 2009, OCLC negotiated new contracts with the former networks and opened a centralized support center. OCLC provides bibliographic and full-text information to anyone. OCLC and its member libraries cooperatively produce and maintain WorldCat—the OCLC Online Union Catalog, the largest online public access catalog in the world. WorldCat has holding records from private libraries worldwide; the Open WorldCat program, launched in late 2003, exposed a subset of WorldCat records to Web users via popular Internet search and bookselling sites.
In October 2005, the OCLC technical staff began a wiki project, WikiD, allowing readers to add commentary and structured-field information associated with any WorldCat record. WikiD was phased out; the Online Computer Library Center acquired the trademark and copyrights associated with the Dewey Decimal Classification System when it bought Forest Press in 1988. A browser for books with their Dewey Decimal Classifications was available until July 2013; until August 2009, when it was sold to Backstage Library Works, OCLC owned a preservation microfilm and digitization operation called the OCLC Preservation Service Center, with its principal office in Bethlehem, Pennsylvania. The reference management service QuestionPoint provides libraries with tools to communicate with users; this around-the-clock reference service is provided by a cooperative of participating global libraries. Starting in 1971, OCLC produced catalog cards for members alongside its shared online catalog. OCLC commercially sells software, such as CONTENTdm for managing digital collections.
It offers the bibliographic discovery system WorldCat Discovery, which allows for library patrons to use a single search interface to access an institution's catalog, database subscriptions and more. OCLC has been conducting research for the library community for more than 30 years. In accordance with its mission, OCLC makes its research outcomes known through various publications; these publications, including journal articles, reports and presentations, are available through the organization's website. OCLC Publications – Research articles from various journals including Code4Lib Journal, OCLC Research, Reference & User Services Quarterly, College & Research Libraries News, Art Libraries Journal, National Education Association Newsletter; the most recent publications are displayed first, all archived resources, starting in 1970, are available. Membership Reports – A number of significant reports on topics ranging from virtual reference in libraries to perceptions about library funding. Newsletters – Current and archived newsletters for the library and archive community.
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Michael Aaron Nielsen is a quantum physicist, science writer, computer programming researcher living in San Francisco. In 2004 Nielsen was characterized as Australia's "youngest academic" and secured a Federation Fellowship at the University of Queensland, he worked at the Los Alamos National Laboratory, as the Richard Chace Tolman Prize Fellow at Caltech, a Senior Faculty Member at the Perimeter Institute for Theoretical Physics. Nielsen obtained his PhD in physics in 1998 at the University of New Mexico. With Isaac Chuang he is the co-author of a popular textbook on quantum computing. In 2007, Nielsen announced a marked shift in his field of research: from quantum information and computation to “the development of new tools for scientific collaboration and publication”; this work includes "massively collaborative mathematics" projects like the Polymath project with Timothy Gowers. Besides writing books and essays, he has given talks about Open Science, he was a member of the Working Group on Open Data in Science at the Open Knowledge Foundation.
In 2015 Nielsen published the online textbook Neural Networks and Deep Learning. The same year he joined the Recurse Center as a Research Fellow. Since 2017 Nielsen works as a Research Fellow at Y Combinator Research.. Nielsen, Michael A. Reinventing Discovery: The New Era of Networked Science. Princeton, N. J: Princeton University Press. ISBN 0-691-14890-2; this book is based on themes that are covered in his essay on the Future of Science. Nielsen, Michael A.. Neural Networks and Deep Learning. Determination Press
Ingram Olkin was a professor emeritus and chair of statistics and education at Stanford University and the Stanford Graduate School of Education. He is known for developing statistical analysis for evaluating policies in education, for his contributions to meta-analysis, statistics education, multivariate analysis, majorization theory. Olkin was born in 1924 in Connecticut, he received a B. S. in mathematics at the City College of New York, an M. A. from Columbia University, his Ph. D. from the University of North Carolina. Olkin studied with Harold Hotelling. Olkin's advisor was S. N. Roy and his Ph. D. thesis was "On distribution problems in multivariate analysis" submitted in 1951. Olkin died from complications of colorectal cancer at his home in Palo Alto, California on April 28, 2016, aged 91. Olkin was awarded the first Elizabeth Scott Award from the American Statistical Association for his achievements in supporting women in statistics. In 1962 he was elected as a Fellow of the American Statistical Association.
In 1984, he was President of the Institute of Mathematical Statistics. Olkin is a Guggenheim and Lady Davis Fellow, with an honorary doctorate from De Montfort University. Olkin has written many books including Statistical methods for meta-analysis, Probability theory, Education in a Research University. Olkin's coauthors include Larry V. Hedges. Olkin has written two books with Albert W. Marshall, Inequalities: Theory of Majorization and its Applications and Life distributions: Structure of nonparametric and parametric families. In nonparametric statistics and decision theory, Olkin wrote Selecting and ordering populations: A new statistical methodology with Jean Dickinson Gibbons and Milton Sobel. Ingram was Editor of the Annals of Mathematical Statistics and served as the first editor of the Annals of Statistics, both published by the Institute of Mathematical Statistics, he was a primary force in the founding of the Journal of Educational Statistics, published with the American Statistical Association.
Olkin was an editor with the mathematics journal, Linear Algebra and its Applications, has been active in supporting a series of international conferences on matrix theory, linear algebra, statistics. Golbeck, Amanda L.. Leadership and Women in Statistics. Chapman & Hall/CRC Press. ISBN 978-1482236446. Hedges, Larry V.. Statistical methods for meta-analysis. Boston: Academic Press. ISBN 978-0-12-336380-0. Marshall, Albert W.. Derman, Holt and Winston. "Probability Models and Application", with L. Gleser and C. Derman, Prentice Hall. A tribute to Marshall and Olkin's book "Inequalities: Theory of Majorization and its Applications" Ingram from Stanford University Ingram Olkin at the Mathematics Genealogy Project Ingram Olkin Marshall–Olkin exponential distribution
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to