Unitary transformations can be performed by moving the excitations around each other. Quantum annealing, simulator and universal computing pdfvideo. Pdf developing a robust approach to implementing non. Kitaev, shen and vyalyi, classical and quantum computation thorough treatment. Similar work has been performed for kitaev s honeycomb model by lahtinen and pachos 16, who examined the. You need to know how to multiply matrices to understand the basic operations of a quantum computer. Intro to faulttolerant quantum computing suggested reading. Qubits composed of holes could be the trick to build faster, larger quantum computers. Classical and quantum computation american mathematical society. Included are a complete proof of the solovay kitaev theorem with accurate algorithm complexity bounds, approximation of unitary operators by circuits of doubly logarithmic depth. Inpart v, we describe quantum algorithms for simulating the dynamics of quantum systems. We also discuss an application of quantum simulation to an algorithm for linear systems.
Kaye, laflamme and mosca, an introduction to quantum computing introductory. All necessary information from computing theory and quantum mechanics is contained in 2 and 3. Timeline of quantum computing and communication wikipedia. In fact, this is what feynman originally had imagined. Kitaev explores the mysterious behavior of quantum systems and their implications. Measurements can be performed by joining excitations in pairs and observing the result of fusion.
Previously, it has been shown that kitaev s model for. Vly i klassiqeskiei kvantovye vyqisleni mcnmoqero,moskva,1999 translated from the russian by lester j. Preskill and ogburn, topological quantum computation 1997. Quantum error correction with imperfect gates springerlink. The inspiration comes from two seemingly independent themes which appeared around 1997. Quantum simulation of fermionic systems presents a. Researchers gather numerical evidence of quantum chaos in. Jan 01, 2003 a twodimensional quantum system with anyonic excitations can be considered as a quantum computer. In this talk, we will present the work on the generalization of kitaev model for quantum groupoids and discuss its ground states. Sergey bravyi and alexei kitaev, quantum invariants of 3manifolds and quantum computation, unpublished. Taylor joint quantum institute, university of maryland, college park, md 20742, and national institute of standards and technology, gaithersburg, md 20899 quantum computation provides a unique opportunity to explore new regimes. Essentially, the program presented in this paper translates a desired operation into the machine code of a quantum computer and therefore acts as a quantum compiler.
Taylor joint quantum institute, university of maryland, college park, md 20742, and national institute of standards and technology, gaithersburg, md 20899 quantum computation provides a unique opportunity to explore new regimes of. A twodimensional medium that supports abelian anyons has a topological. The purpose of this research is to create an efficient program that demonstrates the process of the solovay kitaev theorem using various universal gate sets. This paper is a gentle but rigorous introduction to quantum computing intended for dis. Two physicists bet over a quantum computing moon shot wired. His main contribution was the concept of topological quantum computation, a scheme where quantum information is protected from errors due to special properties of the underlying physical system, which are generally related to topology. We also provide the faulttolerant construction of single qubit unitaries by solovay kitaev algorithm. First united states government workshop on quantum computing is organized by nist in gaithersburg, maryland, in autumn. Quantum compiler for topological quantum computation fsu.
Kitaevs quantum double model as an error correcting code. These braids form the logic gates that make up the computer. The bravyikitaev transformation for quantum computation. The majorana zero modes in the kitaev chain are an example of nonabelian anyons where braiding operations can be used to perform quantum gates. Such intriguing phenomena are not only of great fundamental relevance in themselves, but also hold promise for quantum computing and quantum information. Emulating quantum teleportation of a majorana zero mode qubit. Benenti, casati and strini, principles of quantum computation, v. In mathematical terms, these are unitary topological modular functors.
To operate a large scale quantum computer reliably we will need to. He suggested in 1982 that quantum computers might have fundamentally more powerful computational abilities than conventional ones basing his conjecture on the extreme difficulty encountered in computing the result of quantum mechanical processes on conventional computers, in. Efficient unitary approximations in quantum computing. Quantum simulation of the hexagonal kitaev model with. First proposed in 1997 by russianamerican physicist alexei kitaev, a topological quantum computer represents information in clusters of electrons, known as nonabelian anyons, inside a material. Pdf quantum simulation of kitaev honeycomb model on ibm qx. Among different types of qsls, the exactly solvable kitaev model is attracting much attention, with most proposed candidate materials, e. An introduction to quantum information and quantum circuits. Phase estimation was originally due to kitaev 111, and was put in a broader context by.
Quantum computing stack exchange is a question and answer site for engineers, scientists, programmers, and computing professionals interested in quantum computing. Mcmahon, quantum computing explained new undergraduateoriented text. Mochon, anyons from nonsolvable groups are sufficient for universal. A topological quantum computer is a theoretical quantum computer proposed by russianamerican physicist alexei kitaev in 1997. The rst ideas of quantum computing were established in the early eighties, but during the last years the great advances in mathematics, materials science, and computer science have turned quantum computing from a theory into a reality. Vyalyi, booktitlegraduate studies in mathematics, year2002. This idea was first floated by kitaev in connection to surface codes for quantum error. Jul 09, 1997 a twodimensional quantum system with anyonic excitations can be considered as a quantum computer. Kitaev chain is an example of a new class of quantum critical phenomena, the topological phase transition. Researchers gather numerical evidence of quantum chaos in the sachdevye kitaev model. This theory is sufficiently complete, simple and selfcontained. Jul 31, 2017 kitaev originally constructed his quantum double model based on finite groups and anticipated the extension based on hopf algebras, which was achieved later by buerschaper, etc.
Ibm unveils its first commercial quantum computer, the ibm q system one, designed by ukbased map project office and universal design studio and manufactured by goppion nike dattani and coworkers decode dwaves pegasus architecture and make its description open to the public austrian physicists demonstrate selfverifying, hybrid, variational quantum simulation of lattice models in. Researchers gather numerical evidence of quantum chaos in the. Introduction to topological quantum computation theoretical. Kitaev s topological quantum computing, algorithms. The book is an introduction to a new rapidly developing topic. Mar 09, 2021 quantum computing and the entanglement frontier if you know the probability of one alternative, and you know the probability of another, then you can add those together and find the probability that one or the other occurred. There is a unique quantum model of computing or a physical quantum field theory can be efficiently simulated by quantum computers. The braiding and fusion of anyonic excitations in quantum hall electron liquids and 2dmagnets are modeled by modular functors, opening a new.
Pdf solovaykitaev approximations of special orthogonal. Thanks for contributing an answer to quantum computing stack exchange. Quantum computing is the use of quantum phenomena such as superposition and. A twodimensional quantum system with anyonic excitations can be considered as a quantum computer. Among other interesting topics are toric codes and their relation to the anyon approach to quantum computing. The effective pseudospin interactions making up such quantum simulators are found to be proportional to the dipoledipole interaction between the trapped ions, and are mediated by motion that can be driven by statedependent forces. Classical and quantum computation graduate studies in. Jan 16, 2018 mathematics of topological quantum computing. Mar 25, 2021 here we perform a quantum simulation of topological quantum computing, by teleporting a qubit encoded in the majorana zero modes of a kitaev chain. It is widely believed that kitaev s quantum double models satisfy tqo1 and tqo2.
They underlie the jones polynomial and arise in wittenchernsimons theory. This relation is rooted in the fact that the basic playground of qprocessing is the complex space hn generated by the set bnof binary vectors of length n, which is the basic arena of classical computation. Quantum computing with ion traps, quantum computing with nmr, quantum computing with photons, quantum computing with microwaves, can one quantum compute with excitons. A quantum algorithm for computing the unit group of an arbitrary degree number field, with kirsten eisentrager, alexei kitaev, and fang song, stoc 2014. Pdf from ising model to kitaev chain an introduction to. Quantum computing lecture 3 anuj dawar principles of quantum mechanics 2 what is quantum mechanics quantum mechanics is a framework for the development of physical theories. According to solovay kitaev theorem it is possible to approximate any unitary quantum gate by sequence of gates from small set of another gates. An introduction to quantum computing algorithms elementary introduction to algorithms. Quantum computing is not difficult, but simply different. It gives an example of a quantum speedup without entanglement. In this general article, we map the onedimensional transverse field quantum ising model of ferromagnetism to kitaev s onedimensional pwave superconductor, which has its application in faulttolerant topological quantum computing. Schedule sep 29, 2020 towards topological quantum computing with kitaev materials jason alicea, caltech cite as.
Another good book with more of a little yellow book experience is classical and quantum computation by kitaev, shen and vyalyi. The reading of the second part can begin with the theory of onetoone quantum codes 8. Pdf spin liquids are quantum phases of matter in which the interacting spins exhibit longrange entanglement and do not order even at absolute zero. Quantum computing people school of mathematics georgia. Classical and quantum computation by alexander shen, alexei kitaev, and mikhail n. Such computation is faulttolerant by its physical nature. If you find a better way of capturing carbon by designing a better catalyst, or you can design pharmaceuticals that have new effects, materials that have presebtation properties. Its invention sparked a tremendous interest in quantum computers. Here we show that there is much more to quantum computing by exploring some of the many quantum algorithms that have been developed over the past twenty ve years. Actual physical theories, such as quantum electrodynamics are. Topological quantum computing for beginners john preskill, caltech kitp 7 june 2003. Kitaev, fermionic quantum computation, annals of physics. Towards topological quantum computing with kitaev materials. But avoid asking for help, clarification, or responding to other answers.
A short introduction to topological quantum computation. Professor kitaev works in the field of quantum computation and related areas of theoretical physics. Seeley et al 2012 the bravyi kitaev transformation for quantum computation of electronic structure aharanov et al 2007 adiabatic quantum computation is equivalent to standard quantum computation kandala et al 2017 hardwareefficient variational quantum eigensolver for small molecules and quantum magnets. Faulttolerant quantum computation by anyons sciencedirect.
Classical and quantum computation request pdf researchgate. Isaac chuang and yoshihisa yamamoto scientist propose a quantum optical realization of a quantum computer to implement deutschs algorithm. Jan 04, 2001 the theory of quantum computation can be constructed from the abstract study of anyonic systems. Magic states institute for quantum science and technology. Later, when the qof qprocessing is interpreted as genuine quantum feature, the.
Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. An introduction to quantum computing, without the physics siam. E cient unitary approximations in quantum computing. The jordanwigner transformation allows for representation of a fermionic operator by on qubit operations.
Quantum computation contents university of bristol. Topological quantum computation is an approach to storing and. Measurement and teleportation based quantum computation. Pdf from ising model to kitaev chain an introduction. Quantum computation and quantum information project euclid. Pdf classical and quantum computation semantic scholar. The birth of topological quantum computation took place when alexei kitaev 16 made. Introduction to quantum computing universite parissaclay. The bravyikitaev transformation for quantum computation of. Third, as largescale quantum computing devices are experimentally realized, it may be possible to build a kitaev feynman clock as a quantum simulator. Classical and quantum computation, kitaev, shen and vyalyi.
Developing a robust approach to implementing nonabelian anyons and topological quantum computing in a modified kitaev honeycomb lattice model haitan xu and j. The canonical reference for learning quantum computing is the textbook quantum computation and quantum information by nielsen and chuang. Mar 03, 2021 quantum computing and the entanglement frontier and before we started recording you mentioned working with him. Dec 28, 1996 quantum computer more precisely, a quantum scheme appears in 4. It states four mathematical postulates that a physical theory must satisfy. Inpart vi, we discuss adiabatic quantum computing, a general approach to solving optimization prob. Quantum simulation of fermionic systems presents a speci. The use of quantum computers to perform classically intractable quantum chemistry calculations is often cited as one of the principal uses of emerging quantum technology. Nielsen, the solovaykitaev algorithm, quantum infor. Kitaev freedman kitaev, faulttolerant quantum computation by anyons 1997.
We do not expect any background knowledge in quantum computing, nor in quantum physics. Mar 03, 2021 topological quantum computation based on anyons is a promising approach to achieve faulttolerant quantum computing. Lecture notes quantum information science media arts. Mathematics of topological quantum computing inspire. This would rigorously justify the inherit faulttolerance of kitaev s models for topological quantum computing. Abstract for topological quantum computing for beginners, by john preskill i will describe the principles of faulttolerant quantum computing, and explain why topological approaches to fault tolerance seem especially promising. In contrast, for example, to topological quantum computing in fractional quantum hall systems where even the ground state of the system is subject to debate, our models are exactly solvable and simple.
Quantum simulation of the hexagonal kitaev model with trapped. The main idea of quantum computing relies on the physical device where the information is stored. The theory of quantum computation can be constructed from the abstract study of anyonic systems. Rotation relation in solovaykitaev quantum computing. Kitaev feynman clock for unitary evolution might be extendable to open quantum systems. The aim of this work is to introduce the solovay kitaev theorem for readers without prior knowledge in quantum mechanics or quantum computation. One was kitaev s idea of faulttolerant quantum computation by anyons ki1, and the other was freed.
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