In mathematical terms, these are unitary topological modular functors. Larsen, and wang 63 proved that for certain types of nonabelian. Nonabelian anyons and topological quantum computation s. Magnets with nondiagonal braiding exist in theoryland. Quantum simulation of topological majorana bound states and. Quantum computation a classical computer as a device that operates on states built from a. First we provide an introduction to anyons and topological models. Topological quantum computation topological quantum computationtqc is a computational model built upon systems oftopological phases. Introduction to topological quantum computation by jiannis. 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.
A short introduction to topological quantum computation. 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. Topological quantum computers quantum information encoded in state of anyons. Topological quantum computers are equivalent in computational power to other standard models of quantum computation, in particular to the quantum circuit model and to the quantum turing machine model.
Chuang, cambridge university press 2000 pach introduction to topological quantum computation, j. Topological quantum computation kitaev 97, flw 00 time. Quantum mechanics in the 20th century development of quantum mechanics and using it to describe bulk matter. Topological quantum computation topological quantum computation tqc is a computational model built upon systems oftopological phases. Quantum information and quantum computation, zhejiang. C191 final presentation paolo zoccante, william leibzon. May 29, 2010 topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. This 10th anniversary edition includes an introduction from the authors setting the work in context. Microsoft, purdue tackle topological quantum computer. Microsoft and purdue work on scalable topological quantum. Chuang, cambridge university press 2000 introduction to topological quantum computation, j. Lecture notes on quantum information and quantum computation.
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. Topological quantum computation is a crazy idea, but no less crazy than other ideas for quantum computing. Wang, a modular functor which is universal for quantum computation. So we mainly cite original references, expository surveys, and books.
It is called topological because of the particular properties of anyons, that are physically realisable as quasiparticles in topological systems. Topological quantum computation regional conference series in. Freedman, kitaev, and wang quantph0001071 also showed that a system of anyons can be simulated e. Redundancy equivalence between states hamiltonian protects information 67 4. 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. Landau institute for theoretical physics, kosygina st. Quantum computation and quantum information nielson. David mermin, quantum computer science, cambridge university press, 2007 general books. Quantum simulation of topological majorana bound states. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. For readers interested in the physics of topological. Physical system for complete quantum computation are abelians anyons on a lattice they could be quantum hall effect excitations. Pachos, cambridge university press 2012 topological quantum computation, zhenghan.
Inside microsofts quest for a topological quantum computer. Quantum computation and quantum information by nielsen. The theory of quantum computation can be constructed from the abstract study of anyonic systems. Michael nielsen was born in brisbane, australia in 1974, and was educated at the university of queensland, obtaining postgraduate degrees in mathematics and physics, before being awarded his phd in physics at the university of new mexico in 1998. Pachos, cambridge university press 2012 wang topological quantum computation, zhenghan wang, american mathematical society 2010. In topological quantum computation one aims to make use of quantum. Topological quantum computation zhenghan wang microsoft research station q, cnsi bldg rm 2237, university of california, santa barbara, ca 931066105, u. Apr 09, 2018 professor kang wang ucla presents his invited lecture on chiral majorana and topological quantum computing at the kavli futures symposium on the frontiers of condensed matter physics, hosted. Oct 21, 2016 inside microsofts quest for a topological quantum computer alex bocharov explains why the company is hoping to build qubits out of particles that some scientists think might not even exist.
In particular we consider the properties of anyons and their relation to topological quantum computation. Dec 09, 2010 buy quantum computation and quantum information. Elusive majorana particle takes major step towards quantum. These lectures are from the 2014 princeton summer school on condensed matter physics psscmp. One of the most cited books in physics of all time, quantum computation and quantum information remains the best textbook in this exciting field of science. Jun 12, 2017 arxiv topological quantum computation. Atomic, molecular and solid state physics, lasers, electronics. 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. Chuang, quantum computation and quantum information, cambridge university press, 2000. Jun 30, 2010 topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. They underlie the jones polynomial and arise in wittenchernsimons theory. Kitaev, faulttolerant quantum computation by anyons. In topological quantum computing, information is encoded in knotted quantum.
In this approach, information is stored in the lowest energy states of manyanyon systems and processed by braiding nonabelian anyons. Kang wang on chiral majorana and topological quantum computing. They underlie the jones polynomial and arise in wittenchern. That is, any of these models can efficiently simulate any of the others. Dec 09, 2010 quantum computation and quantum information. Building a common language since this school aims to be accessible to people who dont necessarily have a background in quantum mechanics or computer science, well spend the first day building a common. The braiding and fusion of anyonic excitations in quantum hall electron liquids and 2dmagnets are modeled by modular functors, opening a new. Nielsen, michael and a great selection of related books, art and collectibles available now at. Universality is an important property that needs to be satis.
A longwinded introduction on the history of this field the original string theorist 1867. Topological quantum computation with gapped boundaries. Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. Topological quantum computation sits at the triple juncture of quantum topology, quantum physics, and quantum computation. Kang wang on chiral majorana and topological quantum. The aim of these lectures is to explain these important results.
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. Introduction to topological quantum computing steven h. Introduction to topological quantum computation by jiannis k. Quantum computation and quantum information by chuang, isaac.
These braids form the logic gates that make up the computer. Topological quantum computation zhenghan wang ucsb math. This pedagogical introduction to topological quantum computation includes the following parts. Topological quantum computation microsoft research. Buy topological quantum computation regional conference series in mathematics conference board. This book expands on the authors cbms lectures on knots and topological quantum computing and is. The particles necessary for it probably exist in the lab. In other words, the braiding not only proves the existence of majoranas, but also provides the mechanism by which they could serve as the basis of a qubit for a topological quantum computer. In this book, a variety of different topics are presented together for the first time, forming a thorough introduction to topological quantum computation. May 31, 2017 topological qubits are among the more baffling, and if practical, more promising ways to approach scalable quantum computing. Further information and materials can be found on the website. 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. Download for offline reading, highlight, bookmark or take notes while you read quantum computation and quantum information. Dec 09, 2010 one of the most cited books in physics of all time, quantum computation and quantum information remains the best textbook in this exciting field of science.
Larsen, and zhenghan wang proved that a topological quantum computer can, in principle, perform any computation that a conventional quantum computer can. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to. Part ii quantum computation 171 4 quantum circuits 171 4. Clearwater, explorations in quantum computing, springerverlag, 1998.
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