Jun 30, 2010 topological quantum computation by zhenghan wang, 9780821849309, available at book depository with free delivery worldwide. Twists are defects corresponding to the endpoints of domain walls and are asso. Quantum simulation of topological majorana bound states and. A short introduction to topological quantum computation. Qa 22 mar 2016 on classification of modular categories by rank paul bruillard, siuhung ng, eric c. Topological quantum computation tqc is the name given to an alternative approach to quantum computation 8 where the elementary computational units are socalled anyonsrather than qubits. Pachos zhenghan wang 1 quantum information processing volume 11, pages 1969 1973 2012 cite this article. Topological quantum computation zhenghan wang microsoft research station q, cnsi bldg rm 2237, university of california, santa barbara, ca 931066105, u. In topological quantum computing, information is encoded in knotted.
Topological qubits are among the more baffling, and if practical, more promising ways to approach scalable quantum computing. It is called topological because of the particular properties of anyons, that are physically realisable as quasiparticles in topological systems. Aug 31, 2012 watch this 30second video for a brief summary of what kind of work the microsoft research connections team does. Kitaev, faulttolerant quantum computation by anyons. Topological quantum computation regional conference series in.
Topological quantum computation topological quantum computationtqc is a computational model built upon systems oftopological phases. Topological systems can serve as quantum memories or as quantum computers. Topological quantum computation zhenghan wang microsoft research station q, cnsi bldg rm 2237, university of. Magnets with nondiagonal braiding exist in theoryland. Submitted on 17 may 2017 v1, last revised 5 dec 2017 this. Microsoft research, one microsoft way, redmond, wa 98052. This book thus provides the first comprehensive description of the whole picture of topological quantum codes and quantum computation with them. Keeping highlevel and technical language to a minimum, the author adopts a pedagogical style, making the book accessible to nonspecialists and researchers from a variety of subdisciplines. They underlie the jones polynomial and arise in wittenchernsimons theory.
In this book, a variety of different topics are presented together for the first time, forming a thorough introduction to topological quantum computation. Topological quantum computation zhenghan wang ucsb math. The theory of quantum computation can be constructed from the abstract study of anyonic systems. Topological quantum computation american mathematical society.
Introduction to topological quantum computation pachos, jiannis k. Topological quantum computation by zhenghan wang, 9780821849309, available at book depository with free delivery worldwide. The search for nonabelian anyons in fractional quantum. Introduction to topological quantum computation by jiannis k. Other readers will always be interested in your opinion of the books youve read. Freedman, kitaev, and wang quantph0001071 also showed that a system of anyons can be simulated e. In this approach, information is stored in the lowest energy states of manyanyon systems and processed by.
This book expands the plan of the authors 2008 nsfcbms lectures on knots and topological quantum computing, and is intended as a primer for mathematically. Quantum computers should be capable of performing tasks that would be very difficult, if not impossible, with digital computers, such as finding the prime factors of large numbers, searching large databases, and simulating quantum systems. In this approach, information is stored in the lowest energy states of manyanyon systems and processed by braiding nonabelian anyons. Braiding defects in topological stabiliser codes can be used to faulttolerantly implement logical operations. Inside microsofts quest for a topological quantum computer. These braids form the logic gates that make up the computer. Quantum simulation of topological majorana bound states. Oct 21, 2016 microsoft has been working on topological quantum computing for more than a decade, for most of which the necessary qubits were hypothetical. On topological quantum computing with mapping class group. Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. Topological quantum computation is a crazy idea, but no less crazy than other ideas for quantum computing.
A topological quantum computer is a theoretical quantum computer that employs twodimensional quasiparticles called anyons, whose world lines pass around one another to form braids in a threedimensional spacetime i. Landau institute for theoretical physics, kosygina st. We introduce anyons at the systemindependent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions for encoding and processing quantum information. This book expands the plan of the authors 2008 nsfcbms lectures on knots. Larsen, and zhenghan wang proved that a topological quantum computer can, in principle, perform any computation that a conventional quantum computer can do, and vice versa. Wang department of physics and center of theoretical and computational physics, the university of hong kong, pokfulam road, hong kong, china received 2 april 2014. Mathematics of topological quantum computing american.
Introduction to topological quantum computation by jiannis. For additional information and updates on this book, visit. Additional material for the book american mathematical society. Temperley lieb recoupling theory and invariants of 3manifolds, princeton university press, annals studies 114, 1994 i zhenghan wang, topological quantum computation, cbms. Microsoft, purdue tackle topological quantum computer.
Universality is an important property that needs to be satis. Topological quantum computation topological quantum computation tqc is a computational model built upon systems oftopological phases. About microsoft research connections microsoft research. Topological quantum computation microsoft research. As described above, topological quantum computation is novel wa y to perform quantum computation which attempts to solv e the problem of decoherence at the chapter 1. The makings of topological systems, their properties and their computational power are presented in a pedagogical way. Topological quantum computation is a paradigm to build a large scale quantum. The particles necessary for it probably exist in the lab. Lomonaco jr topological quantum information theory i l. Cbms regional conference series in mathematics publication year 2010.
Topological quantum computation books pics download. Pdf mathematics of topological quantum computing semantic. Miniworkshop on topological quantum computation hangzhou, july 67, 2006. Larsen, and zhenghan wang proved that a topological quantum computer can, in principle. However, enormous scientific and engineering challenges must be overcome for scalable quantum computers to be realized. The computational answer is accessed by bringing anyons together and observing the result. The aim of these lectures is to explain these important results. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. Download pdf mathematicsofquantumcomputing free online. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. In this book, the author presents a variety of different topics developed together for the. The institute is located at 17 gauss way, on the university of california, berkeley campus, close to grizzly peak, on the.
The mathematical sciences research institute msri, founded in 1982, is an independent nonprofit mathematical research institution whose funding sources include the national science foundation, foundations, corporations, and more than 90 universities and institutions. Christian schmid, ady stern, david tong, zhenghan wang, harald weinfurter, witlef. Introduction to topological quantum computation pachos. Topological quantum computing topological phases of matter are quantum computers, and form the. Topological quantum computation kitaev 97, flw 00 time.
They underlie the jones polynomial and arise in wittenchern. Wang, a class of p, tinvariant topological phases of interacting electrons, annals of physics 310. Topological quantum computation zhenghan wang publication year. Pdf introduction to topological quantum computation. The interdisciplinary fields between quantum information and other fields of physics such as condensed matter physics and statistical physics are also explored in terms of the topological quantum codes. The advantage of a quantum computer based on quantum braids. The search for nonabelian anyons in fractional quantum hall systems the past five years xin wan zhejiang institute of modern physics, hangzhou. Mathematics of quantum computation download book pdf full. Watch this 30second video for a brief summary of what kind of work the microsoft research connections team does. In mathematical terms, these are unitary topological modular functors. Introduction to topological quantum computation university of leeds. May 29, 2010 topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories.
Introduction to topological quantum computation by j. Sep 21, 2012 introduction to topological quantum computation by j. At least thats what microsoft, purdue university, and three other universities are hoping after having recently signed a fiveyear agreement to develop a topological qubit based quantum computer. Pdf topological quantum computation download ebook for free. Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering.
The braiding and fusion of anyonic excitations in quantum hall electron liquids and 2dmagnets are modeled by modular functors, opening a new. A topological quantum computer is a theoretical quantum computer that employs. Buy topological quantum computation regional conference series in mathematics conference. Microsoft has been working on topological quantum computing for more than a decade, for most of which the necessary qubits were hypothetical.