Physics 219 course information caltech particle theory. Faulttolerant quantum computation semantic scholar. Flag faulttolerant error correction with arbitrary. Fault tolerant quantum computation versus realistic noise. An introduction to quantum error correction and fault. It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically.
However, these obstacles may not be as formidable as originally believed. 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. There are lots of details which we need to pay attention to in. I demonstrate that faulttolerant universal computation is possible for any stabilizer code. Proceedings of 35th annual symposium on fundamentals of computer science focs96. Quantum error correction and faulttolerance quantiki. Jun 16, 2007 latency in fault tolerant quantum computing with local, twodimensional architecture.
Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. This allows a straightforward determination of which operations can be performed faulttolerantly on a given code. Introduction the theory of quantum computers assures us that quantum algorithms can solve certain. We analytically estimate how the threshold will depend on a scale parameter r which characterizes the scaleup in the size of the circuit due to encoding. I present a general theory of fault tolerant operations based on symmetries of the code stabilizer.
Find materials for this course in the pages linked along the left. Faulttolerant quantum computation in the 21st century. An introduction to quantum error correction and faulttolerant. An introduction to faulttolerant quantum computation and. Steane in 5, the fault tolerant behavior for the concatenated sevenqubit css 7,1,3 code for the local and nonlocal model. In our analysis, we focus on concatenated coding and the threshold result. Fault tolerance in quantum computation mavilla hima bindhu, california state university abstract. Therefore, given the ability to perform faulttolerant clifford group operations, faulttolerant measurements, and to prepare the encoded. A quantum computer can provide fast solution for certain computational problems e. Unitary transformations can be performed by moving the excitations around each other. This is not to say that the strategy of using a large code once so that logical failure rates are small enough. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information in a superposition of states in a quantum computer making long computations. Fault tolerant quantum computing robert rogers, thomas sylwester, abe pauls 1 introduction 1. Quantum error correction quantum physics, quantum information.
The best quantum computing books five books expert. Posts for the topic threshold theorem for fault tolerant quantum computation a blog written by quantum researchers for quantum researchers and those interested in their work. This is called faulttolerant quantum computation and it is an essential condition for implementing a quantum computer. Measurements can be performed by joining excitations in pairs and observing the result of fusion. A critical component of any quantum errorcorrecting scheme is detection of errors by using an ancilla system. A theory of faulttolerant quantum computation arxiv. I discuss a number of examples in more detail, including the five qubit. Quantum error correction and fault tolerant quantum.
Checkpoints require stoping the computation at a 1. All instructor resources see exceptions are now available on our instructor hub. Consistency checks, like the parity of a bit string, work classically, but in the quantum world are simply not powerful enough. Fault tolerant quantum computation with nondeterministic entangling gates 16 mar 2018 paywall with abstract from the arxiv. In the first part, we present the theory ofquantum errorcorrecting codes. A typeset version of chapter 8 on faulttolerant quantum computation is not yet available. Quantum error correction and fault tolerant quantum computing. 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 fault tolerantly on encoded states. For any quantum computation with t gates, we show how to build a polynomial size quantum circuit that tolerates o1logsup ct amounts of inaccuracy and decoherence per gate, for some constant c. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Faulttolerant quantum computation by anyons sciencedirect. Fault tolerant quantum computation with few qubits rui chao ben w. Our first result looks at limitations on the simplest implementation of faulttolerant operations, transversality. Local faulttolerant quantum computation microsoft research.
Introduction to fault tolerant quantum computation fact. Thequantumcomputerpuzzle american mathematical society. Enter your mobile number or email address below and well send you a link to download the free kindle app. Roads towards faulttolerant universal quantum computation. Fault tolerance is the study of reliable computation using unreliable components. Faulttolerant quantum computation with constant error.
In short the theory of quantum computation and quantum information. Faulttolerant quantum computation with few qubits npj. Eastinknill theorem 2009 a universal set of quantum gates cannot be achieved using only transversal gates i. The practicality of fault tolerant quantum computing proposals is investigated by considering the entanglement of local and global errors. There is a straightforward generalization of the class of stabilizer codes to ddimensional systems, and i will discuss the theory of fault tolerant computation using such codes. Theory of quantum computation, communication and cryptography. I imagine they will probably revise it again in 2020 but again, i imagine, the revisions will be minimal. Such computation is fault tolerant by its physical nature.
This thesis contains the results of research projects broadly related to the pursuit of universal fault tolerant quantum computation. Here, a very detailed analysis is presented for syndrome extraction and shor state preparation. One important problem is decoherence and systematic errors in unitary transformations which occur in real quantum systems. Faulttolerant quantum computation with a softdecision. Pdf fault tolerant computation on ensemble quantum computers. Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. 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. A faulttolerant system for stopping leaks in quantum. Sudebkumar prasant pal abstract quantum computing is an exciting alternative model to classical computation. Steane in 5, the faulttolerant behavior for the concatenated sevenqubit css 7,1,3 code for the local and nonlocal model. Such computation is faulttolerant by its physical nature. The subject encapsulates one of the greatest hurdles in creating a useful quantum computer. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical operations. Topological codes support a variety of approaches to fault tolerant computation, the theoretical sophistication of which has evolved over time.
Faulttolerant quantum computation arijit ghosh roll no 03cs3007 advisors. And given those constructions, we have essentially shown the threshold theorem for faulttolerant quantum computation in a far from rigorous manner, however. The yale team solves this problem by making its system fault tolerant meaning that errors in the ancillary qubits arent able to leak over to the logical qubits. 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. Quantum computing faulttolerant detection of a quantum error. Fault tolerance is the property that enables a system to continue operating properly in the event of the failure of or one or more faults within some of its components. Quantum computation and quantum information, cambridge university press. I discuss a number of examples in more detail, including the. A theory of faulttolerant quantum computation daniel gottesman. Benor, faulttolerant quantum computation with constant error, proc. We demonstrate a faulttolerant errordetection scheme that suppresses spreading of ancilla errors by a. Revised selected papers lecture notes in computer science 5906 childs, andrew, mosca, michele on.
Fibonacci scheme for fault tolerant quantum computation panos aliferis1 and john preskill2 1ibm watson research center, p. Box 218, yorktown heights, new york 10598, usa 2institute for quantum information, california institute of technology, pasadena, california 91125, usa. Faulttolerant universal computation is possible with four extra qubits, 19 in total. Faulttolerant quantum computing the faulttolerant quantum computing roadmap aims for a fullstack scalable quantum computing system, including the qubit circuits, the control electronics, and the software layers such as compilers. Fault tolerant computing is not essentially needed to solve a problem. Even when the gates used to perform these operations are noisy, the quantum computation must be tolerable to the errors. Faulttolerant quantum computation by anyons caltechauthors. Measurements of qubits in an individual computer cannot be. 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. Such faulttolerant measurements will allow more frequent interrogations of the state of the logical qubit, ultimately leading to the implementation of more. In order to build a large quantum computer, we will almost certainly need to encode the qubits using quantum errorcorrecting codes and encode the quantum circuits using fault tolerant protocols. Faulttolerant quantum computation with constant overhead. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information.
From the purely theoretical point of view, this problem has been solved due to shors discovery of faulttolerant quantum computation, with subsequent improvements. This thesis takes another look at several aspects of stabilizer code quantum errorcorrection to discover solutions to the practical problems of choosing a code, using it to correct errors, and performing faulttolerant operations. Buy this book on publishers site reprints and permissions. Quantum computation and information is one of the most exciting. In order to use quantum errorcorrecting codes to improve the performance of a quantum computer, it is. In quantum computing, the quantum threshold theorem or quantum fault tolerance theorem, proved by michael benor and dorit aharonov along with other. California institute of technology, pasadena, ca 91125 abstract in order to use quantum errorcorrecting codes to actually improve the performance of a quantum computer, it is necessary to be able to performoperations faulttolerantly on encoded states.
Faulttolerant detection of a quantum error science. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. In quantum computing, the quantum threshold theorem or quantum faulttolerance theorem, proved by michael benor and dorit aharonov along with other. Faulttolerant quantum computation a dynamical systems approach. Proceedings of the 37th symposium on foundations of computer science focs. Fault tolerant quantum computation by anyons inspirehep. After learning about qecc, chapter 5 begins with the important topic of fault tolerant quantum computing ftqc.
Technical roadmap for faulttolerant quantum computing. Instead of a quantum computer where the fundamental units are 2dimensional qubits, we can consider a quantum computer made up of ddimensional systems. For example, one can run many copies of a classical calculation in parallel, periodically using majority gates to catch and correct faults. In a quantum computer, the basic gates are much more vulnerable to noise than. One of the main difficulties of realizing quantum computation is that decoherence tends to destroy the. In ensemble or bulk quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Your instructor credentials will not grant access to the hub, but existing and new users may request access here. If its operating quality decreases at all, the decrease is proportional to the severity of the failure, as compared to a naively designed system, in which even a small failure can cause total breakdown.
In quantum computation, each operation must be performed on the encoded states. With a given noise model, can one still reliably compute. In large scale distributed systems, fault tolerant computing is important because each module may not be always reliable. Fault tolerant computing ieee conferences, publications. Quantum computation and quantum information is a book to return to. Then you can start reading kindle books on your smartphone, tablet, or computer no kindle device required. However, it is useful to execute a computing correctly. A faulttolerant computational procedure ensures that errors do not multiply and spread. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the. Abstractwe apply a dynamical systems approach to con.
This report aims to show the technical steps needed to build a fully functional quantum computer. Proceedings of the twentyninth annual acm symposium on theory of computingmay 1997. We are interested in questions such as which resources are required to achieve a quantum computational advantage, how to utilize such resources in practice, and how to characterize and control noise throughout a computation. Physical realization of a quantum computer is a big challenge for scientists. Readings quantum computation mathematics mit opencourseware. To use a quantum errorcorrecting code to improve the performance of a noisy quantum computer, we need to be able to do operations on encoded states without causing the uncontrollable spread of errors consider the controllednot, a very simple and common twoqubit operation. Over a decade has passed since this monumental accomplishment yet no book length pedagogical presentation of this important theory exists. Improving the overhead of fault tolerant quantum computation with magic state distillation joe ogorman and earl campbell. Fibonacci scheme for faulttolerant quantum computation. I discuss a number of examples in more detail, including the fivequbit. The garland science website is no longer available to access and you have been automatically redirected to. Faulttolerant quantum computation perimeter institute. Over a decade has passed since this monumental accomplishment yet no booklength pedagogical presentation of this important theory exists. Among recent developments, the recent paper 12 has shown how fault tolerant quantum computation with constant multiple overhead can be obtained, and quantum ldpc codes are an essential component.
In part 1, we cover results pertaining to magic state distillation, one of the. Threshold theorem for faulttolerant quantum computation. Reichardt university of southern california 21th annual conference on quantum information processing. Thaker dd, metodi ts, cross aw, chuang il, chong ft 2006 quantum memory hierarchies. Fault tolerant quantum computing robert rogers, thomas.
Scalable quantum computers require a farreaching theory of faulttolerant quantum computation. Interest in quantum computation has since been growing. Fault tolerant computing in computational field model. Resource cost of fault tolerant quantum computing in hybrid quantum computers and linearoptical quantum computers ying li, peter c. We analyze and study the effects of locality on the faulttolerance threshold for quantum computation.
A note on threshold theorem of fault tolerant quantum computation 25 jun 2010. The procedures could enable testing more sophisticated protected circuits in smallscale quantum devices. An arbitrary quantum circuit can be simulated using imperfect gates, provided these gates are close to the ideal ones up to a constant precision. Critical noise parameters for faulttolerant quantum computation. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of faulttolerant quantum computation. We carry out a detailed seminumerical threshold analysis for concatenated coding using the sevenqubit. Experimentalists are getting better and better at building qubits, but no matter how hard they try, their qubits will never be perfect. Faulttolerant quantum computation with quantum errorcorrecting codes has been considerably developed over the past decade. Faulttolerant quantum computation with higherdimensional. The goal of faulttolerant quantum computing is to simulate accurately the ideal quantum circuit model using the imperfect noisy gates that can be executed by an actual device assuming the noise is not too strong. Fault tolerance prevents faulty ancillary qubits from collapsing the logical quantum state. I present a general theory of faulttolerant operations based on symmetries of the code stabilizer.
The threshold theorem states that it is possible to create a quantum computer to perform an arbitrary. In this paper we improve this result and show how to perform fault tolerant quantum computation in the presence of constant noise rate, which is what one might. However, there are still difficult issues, particularly on the resource requirement. Fault tolerant computation refers to computation in the. They revised it after 10 years, but the revisions were minimal. As far as faulttolerant quantum computing is concerned, again the first method was. Fault tolerant quantum computation guest lecture for quantum computation mathm0023 dominic verdon school of mathematics, university of bristol dominic.
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