As far as fault tolerant quantum computing is concerned, again the first method was given by shor 65 who. Get any books you like and read everywhere you want. Quantum computation, quantum theory and ai sciencedirect. Faulttolerant quantum computation with asymmetric baconshor. Chuang cambridge, 2000 in addition the book consistent quantum theory by r. Aharonov d, kitaev ay, preskill j 2006 faulttolerant quantum computation with longrange correlated noise. Fault tolerant quantum computation guest lecture for quantum computation mathm0023 dominic verdon school of mathematics, university of bristol dominic. The threshold theorem states that it is possible to create a. Download full coding theory and quantum computing book or read online anytime anywhere, available in pdf, epub and kindle. Since the threshold for faulttolerant quantum computation depends signicantly on the complexity of the.
In order to read online or download quantum computation and information full ebooks in pdf, epub, tuebl and mobi you need to create a free account. Pdf errorcorrection process has to be carried out periodically to prevent accumulation. Quantum computing jozef gruska quantum measurement has the effect of magnifying one of the outcomes of quantum superposition probabilistic, sequential only at this point do indeterminacy and probabilities e. We apply it to derive gates in the important collective decoherence model the decoherence mechanism expected to dominate in the solid state at very low temperatures, and. Quantum computation is not digital like conventional binary computation. Theory of fault tolerant quantum computation quantum computation. The theory of faulttolerant quantum computation tells us how to perform operations on states encoded in a quantum errorcorrecting code without compromising the codes ability to protect against errors. Quantum error correction and fault tolerant quantum computing. This paper deals with the construction one of such elementary quantum gate. Quantum computation a quantum computer performs computations with single atoms or other quantum objects and can solve some problems exponentially faster than a classical computer. The formalism we develop here connects dfss with the theory of stabilizer qeccs 11. The inspiration comes from two seemingly independent themes which appeared around 1997. Currently the best schemes for faulttolerant qc give a value of h. Quantum computer properties in theory 1 general purpose not limited to a single class of problems.
In order to use quantum errorcorrecting codes to improve the performance of a quantum computer, it is. The theory of quantum error correcting codes was designed to deal with a setting where we can encode our quantum information perfectly, then subject the qubits. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of faulttolerant quantum computation, instructing us how to. Click get books and find your favorite books in the online library. Griffiths cambridge 2002 is recommended for part i of the course.
This is the associated paper that will appear in the proceedings. We show that the limited set of faulttolerant operations used in standard stateinjection circuits can be realized within spekkens theory, and that state. I present a theory of faulttolerant operations on stabilizer codes based on symmetries of the code stabilizer. To overcome this, a different method first proposed by asher peres in 1985, such as the socalled threequbit bit flip. Sorry, we are unable to provide the full text but you may find it at the following locations. Quantum computing is an exciting new paradigm of computation using quantum bits qubits where quantum superposition can be exploited for exponential gains in processing power.
One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information in. 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. The entire content of the threshold theorem is that youre correcting errors faster than theyre created. The text book for the course will be quantum computation and quantum information by m. There are now numerous methods to deal with the problems we detail above. A quantum computer would also have profound applications for pure physics. Tqc covers all theoretical aspects of quantum information. Faulttolerant gate gadgets a gate gadget is fault tolerant if it satis. One was kitaevs idea of faulttolerant quantum computation by anyons ki1, and the other was freed. There are lots of details which we need to pay attention to in. 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. We also take advantage of special code symmetries, and use pieceable fault tolerance.
Currently the best schemes for faulttolerant qc give a value of h between 103 and 104. An introduction to and survey of the field of quantum computing. A gentle introduction eleanor rieffel and wolfgang polak. Devices that perform quantum information processing are known as quantum computers. Pdf quantum error correction and fault tolerant quantum. The argument against quantum computers, the quantum laws of.
Faulttolerant quantum computation with constant error. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of faulttolerant quantum computation. A central insight used in the theory of faulttolerant quan. In order to use quantum errorcorrecting codes to improve the performance of a quantum computer, it is necessary to be able to perform operations faulttolerantly on encoded states. Quantum computing for computer architects, second edition. Quantum computation is an emerging field whose goal is to design effectively atomic sized computers which. Interest in quantum computation has since been growing.
Pdf faulttolerant quantum computation researchgate. Pdf theory of decoherencefree faulttolerant universal. A topological quantum computer should allow intrinsically faulttolerant quantum computation, but there remains uncertainty about how such a computer can be implemented. Assume that the group g12 contains all matrices of the form 1 however, we would like to point out that the automorphism group of the quantum hamming code of length 15 was used to aid faulttolerant quantum i a. Theory of decoherencefree faulttolerant universal quantum. Errors occur independently on qubits, gates, measurements, with no spatial or temporal correlations 1. In particular, the initial chapters offer a simple and selfcontained introduction.
Pdf universal faulttolerant quantum computation with only. Institute for quantum information, california institute of technology, pasadena, california 91125, usa received 9 november 2012. The positions will be supervised by joseph emerson andor joel wallman. Pdf leveraging automorphisms of quantum codes for fault. Faulttolerant quantum computation theory and practice vuillot, christophe doi 10. The formalism we develop here connects dfss with correlated errors, there exist subspaces of the systems the theory of stabilizer qeccs 11. This volume also includes a selection of special topics. While in theory this is possible, the reality today is that quantum computers have yet to achieve these types of results. This is the fourteenth in a series of conferences that aims to bring together the leading researchers in the areas of quantum computation, quantum communication and quantum cryptography. Faulttolerant quantum computation with few qubits npj quantum. Theory of faulttolerant quantum computation caltech authors.
In the first part, we present the theory ofquantum errorcorrecting codes qeccs and, in particular, two. In this paper we provide a basic introduction of the core ideas and theories surrounding faulttolerant quantum computation. Universal faulttolerant quantum computation in the presence of spontaneous emission and collective dephasing, phys. And given those constructions, we have essentially shown the threshold theorem for faulttolerant quantum computation in a far from rigorous manner, however. Raussendorf and coauthors develop these ideas in the measurementbased quantum computation framework. The argument against quantum computers, the quantum. Theory of decoherencefree faulttolerant universal quantum computation j.
In quantum computing and quantum information theory, the clifford gates are the elements of the clifford group, a set of mathematical transformations which effect permutations of the pauli operators. Bennett and peter shor 52 pages this is a survey on quantum information theory which will appear in the ieee transactions on information theory october, 1998. Apr 16, 2009 to build a quantum computer which behaves correctly in the presence of errors, we also need a theory of faulttolerant quantum computation, instructing us how to perform quantum gates on qubits which are encoded in a quantum errorcorrecting code. Stateinjection schemes of quantum computation in spekkens. Graphical proofs for fault tolerant quantum computation. Theory of faulttolerant quantum computation nasaads. Quantum bits qubits have basis states labelled by 0 and 1 but can also be in superpositions or entangled states. Pdf quantum computation and information download full. To architect such systems, one must understand what it takes to design and model a balanced, faulttolerant quantum computer architecture. Abstract it has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. This is the theory of faulttolerant quantum computation. Pdf coding theory and quantum computing download full.
Pdf a note on threshold theorem of faulttolerant quantum. An introduction to quantum error correction and faulttolerant. Quantum error correction and faulttolerance quantiki. Universal faulttolerant quantum computation on decoherence. In this chapter, we discuss the basic theory of quantum errorcorrecting codes, faulttolerant quantum computation, and the threshold theorem. This allows a straightforward determination of which operations can be performed faulttolerantly on a given code.
This stops being the case for a quantum channel in which, due to the nocloning theorem, it is no longer possible to repeat a single qubit three times. Quantum information theory postscript postscript or pdf, by charles h. Topics addressed include quantum algorithms, models of quantum computation, quantum complexity theory, simulation of quantum systems, quantum cryptography, quantum communication, quantum estimation and measurement, quantum noise, quantum coding theory, faulttolerant quantum computing, and entanglement theory. An introduction to quantum error correction and fault. Fault tolerant quantum computation with a new reversible gate. The stabilizer formalism for quantum codes also illustrates the relationships to classical coding theory, particularly classical codes over gf4, the finite field with four elements.
An invitation to new quantum technologies quantum information and computation summer school research seminar, university of queensland, australia ppt html. Later, when the qof qprocessing is interpreted as genuine quantum feature, the. Universal faulttolerant computation on decoherencefree subspaces d. In short the theory of quantum computation and quantum information. Two postdoctoral positions are available at the institute for quantum computing, university of waterloo, in the area of quantum computing theory, with particular emphasis on methods for characterizing and validating quantum computing errors qcvv, erroraware complication strategies and faulttolerant quantum computation. The repetition code works in a classical channel, because classical bits are easy to measure and to repeat. Faulttolerant quantum computation quantum information and computation summer school, university of queensland, australia ppt html. Whaley1 departments of chemistry1, physics2 and mathematics3, university of california, berkeley. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of fault tolerant quantum computation, instructing us how to.
It is shown that in both cases universal quantum computation which always preserves the dfs natural faulttolerant computation can be performed using only twobody interactions. Quantum computing1the processing of information according to the fundamental laws of physicsoffers a means to solve efficiently a small but significant set of classically intractable problems. This allows a straightforward determination of which operations can be performed faulttolerantly on a. Theory of faulttolerant quantum computation quantum computation. State injection promotes faulttolerant quantum circuits, which are usually limited to the classically ef. In order to use quantum errorcorrecting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations faulttolerantly on encoded states. Consistency checks, like the parity of a bit string, work classically, but in the quantum world are simply not powerful enough. This book constitutes the thoroughly refereed postworkshop proceedings of the third workshop on theory of quantum computation, communication, and cryptography, tqc 2008, held in tokyo, japan, in januaryfebruary 2008. Various important aspects of quantum computation and information are covered in depth, starting from the foundations the basic concepts of computational complexity, energy, entropy.
A talk on faulttolerant quantum computation, delivered at the workshop on quantum information science. Quantum world classical world quantum computation is deterministic highly exponentially parallel unitary described by. The notion was introduced by daniel gottesman and is named after the mathematician william kingdon clifford. It is known that topological quantum computation can be implemented with limited quasiparticle braiding capabilities, in fact using only a single mobile quasiparticle, if the. Pdf universal faulttolerant quantum computation with. Faulttolerant quantum computation with constant error rate.
Checkpoints require stoping the computation at a 1. Theory of quantum computation, communication and cryptography. Sudebkumar prasant pal abstract quantum computing is an exciting alternative model to classical computation. I present a general theory of faulttolerant operations based on symmetries of the code stabilizer. A theory of faulttolerant quantum computation arxiv vanity.
Quantum information processing is the result of using the physical reality that quantum theory tells us about for the purposes of performing tasks that were previously thought impossible or infeasible. Quantum computers, being in the theoretical level of modeling, have attracted lots of attention in the past few years. Postdoctoral fellowship characterizing and validating. By their very nature, quantum computers would take exponentially. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of fault tolerant quantum computation. The center piece of this theory is the threshold theorem, which we will sketch below. The goal of this lecture is to provide architectural abstractions for the design of a quantum computer and to explore the systemslevel challenges in achieving scalable, faulttolerant quantum computation. It describes the quantum factoring algorithm and briefly sketches the basics of quantum error correction and quantum fault tolerant computation. Faulttolerant quantum computation arijit ghosh roll no 03cs3007 advisors.
Under certain assumptions about the on the threshold for faulttolerant quantum computation symmetry of the noise processes, most notably spatially 9. Create free account to access unlimited books, fast download and ads free. Quantum error correcting subsystem codes and faulttolerant. It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically.
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