It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking. Over a decade has passed since this monumental accomplishment yet no book length pedagogical presentation of this important theory exists. Technical roadmap for faulttolerant quantum computing. Faulttolerant detection of a quantum error science. Click download or read online button to quantumerrorcorrectionandfaulttolerantquantumcomputing book pdf for free now. In this paper we provide a basic introduction of the core ideas and theories surrounding fault tolerant quantum computation. A faulttolerant oneway quantum computer sciencedirect. For the fault tolerant scheme of quantum computation described in this paper we require a quantum code with the following three properties. Faulttolerant quantum computation introduction to quantum. The garland science website is no longer available to access and you have been automatically redirected to. Quantum error correction and faulttolerance quantiki. To achieve large scale quantum computers and communication networks it is essential not only to overcome noise in stored quantum information, but also in general faulty quantum operations. In the context of stabilizer codes, i will discuss a number of known codes, the capacity of a quantum channel, bounds on quantum codes, and fault tolerant quantum computation. Faulttolerant architecture for quantum computation using.

Improving the overhead of faulttolerant quantum computation with magic state distillation joe ogorman and earl campbell. Numerous and frequentlyupdated resource results are available from this search. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking topological aharonovbohm. Physical realization of a quantum computer is a big challenge for scientists. The discovery of quantum error correction has greatly improved the long term prospects for quantum computing technology. Fault tolerant quantum computing the fault tolerant 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. For example, one can run many copies of a classical calculation in parallel, periodically using majority gates to catch and correct faults. Sudebkumar prasant pal abstract quantum computing is an exciting alternative model to classical computation. It may be possible to incorporate intrinsic fault tolerance into the design of.

Fibonacci scheme for faulttolerant 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. In short the theory of quantum computation and quantum information. Unitary transformations can be performed by moving the excitations around each other. California institute of technology, pasadena, ca 91125, usa. Divincenzo2, 1columbia university, 1214 amsterdam avenue, mc. A twodimensional quantum system with anyonic excitations can be considered as a quantum computer. Fibonacci scheme for faulttolerant quantum computation. In part 1, we cover results pertaining to magic state distillation, one of the. An important objective is to nd quantum algorithms that are signi cantly faster than any classical algorithm solving the same problem. Faulttolerant quantum computation versus realistic noise.

Use features like bookmarks, note taking and highlighting while reading quantum computation with topological codes. Measurements can be performed by joining excitations in pairs and observing the result of fusion. This encoded universality paradigm offers potential simplifications in quantum computer design since it does away with the need to perform singlequbit rotations. Fault tolerant quantum computation with high threshold. An introduction to quantum error correction and faulttolerant. Improving the overhead of fault tolerant quantum computation with magic state distillation joe ogorman and earl campbell. Quantumerrorcorrectionandfaulttolerantquantumcomputing download quantumerrorcorrectionandfaulttolerantquantumcomputing ebook pdf or read online books in pdf, epub, and mobi format. Fault tolerant quantum computation versus realistic noise. However, formatting rules can vary widely between applications and fields of interest or study. The paper probabilistic fault tolerant universal quantum computation and sampling problems in continuous variables douce et al.

Reichardt university of southern california 21th annual conference on quantum information processing january 15 19, 2018 at the tu delft arxiv. Quantum computation with topological codes from qubit to. The 7qubit code is much studied because its properties make it particularly wellsuited to fault tolerant quantum computation. Fault tolerance is the study of reliable computation using unreliable components. Recently shor23 showed how to use quant urn codes in order to perform fault tolerant quantum computation when the noise rate, or the fault probability each time. Preskill, john 1998 fault tolerant quantum computers. There are copious worked examples, and all exercises have full solutions given at the rear of the book their treatment of more mainstream parts of quantum information is clear, concise and comprehensive. Recently shor23 showed how to use quant urn codes in order to perform fault tolerant quantum computation when the noise rate, or. 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. Faulttolerant quantum computation by anyons sciencedirect. Quantum error correction and fault tolerant quantum. However, considering the fault tolerance, the overhead of the quantum computer increases exponentially.

Riding bosonic qubits towards faulttolerant quantum computation. Faulttolerant quantum computation with high threshold in two. Resource cost of fault tolerant quantum computing in hybrid quantum computers and linearoptical quantum computers ying li, peter c. But the coding is inefficient and requires many quantum bits 10,11,12, which results in physically unwieldy fault tolerant quantum circuits 10,11,12,14,15,16,17,18. No part of this book may be reproduced in any form by any electronic or mechanical means including. 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. Industrialists expressed a demand for a technical roadmap which explains the complex concepts of faulttolerant quantum computing for a broad audience, and to identify the potential applications for a small quantum computer. Such computation is fault tolerant by its physical nature. Resource cost of faulttolerant quantum computing in hybrid quantum computers and linearoptical quantum computers ying li, peter c. Quantum error correction and fault tolerant quantum computing.

The issue of fault tolerance is central to the future of quantum computation. A note on threshold theorem of fault tolerant quantum computation 25 jun 2010. Riding bosonic qubits towards faulttolerant quantum. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking topological aharonovbohm interactions to process quantum information. 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. In a breakthrough, knill has constructed a novel fault tolerance. Quantum computation with topological codes springerlink. Introduction to quantum computation and information. The basic concepts and powerful tools for understanding topological fault tolerant quantum computation, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurementbased quantum computation, are also introduced in 4. 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. The paper goes even further and claims it is possible. Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and controlling a single effective exchange interaction and possibly a global magnetic field. In the context of stabilizer codes, i will discuss a number of known codes, the capacity of a quantum channel, bounds on quantum codes, and faulttolerant quantum computation. Blueprint for faulttolerant quantum computation with rydberg atoms 14 nov 2017 paywall with.

Preskill, john 1998 faulttolerant quantum computers. Your instructor credentials will not grant access to the hub, but existing and new users may request access here. Most studies of fault tolerance until now 14 have focused on deriving fault tolerance in a setting where gates between any two qubits can be executed instantaneously, i. Download it once and read it on your kindle device, pc, phones or tablets. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus. 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. From the journals of the american physical society. As the quantum computing field is gaining momentum, a small quantum computer with 10 200 qubits is on the horizon. This thesis contains the results of research projects broadly related to the pursuit of universal faulttolerant quantum computation. All instructor resources see exceptions are now available on our instructor hub.

Faulttolerant quantum computation with constant error rate. And given those constructions, we have essentially shown the threshold theorem for faulttolerant quantum computation in a far from rigorous manner, however. Quantum computation and quantum information 10th anniversary ed. In quantum computing, the quantum threshold theorem proved by michael ben or and dorit. One must be able to compute without allowing the errors to propagate too much. Provides a comprehensive introduction to topological quantum codes and faulttolerant quantum computation with them. For the faulttolerant scheme of quantum computation described in this paper we require a quantum code with the following three properties. The paper thus provides a self contained and complete proof for universal fault tolerant quantum computation. Considerably extended version of our stoc paper containing the threshold result quantph9611025 subjects. Given a qecc, we can attempt to supplement it with protocols for performing fault tolerant operations. Level reduction and the quantum threshold theorem 11.

Nov 18, 2019 the remaining ingredients for a fault tolerant quantum computer are gates and measurements, which also happen to be straightforward to implement. Box 218, yorktown heights, new york 10598, usa 2institute for quantum information, california institute of technology, pasadena, california 91125, usa received 30 september 2008. I discuss a number of examples in more detail, including the. Faulttolerant quantum computation arijit ghosh roll no 03cs3007 advisors. Faulttolerant quantum computation with constant error. Scalable quantum computers require a farreaching theory of faulttolerant quantum computation. Packed with over 40 realworld problems, 35 field exercises, and 17 workedout examples, this book is the essential resource for any researcher interested in entering the quantum field as well as for those who want to understand how the unexpected realization of quantum computing is possible. With a given noise model, can one still reliably compute.

It is useful to list the assumptions which are put into the model. A gentle introduction eleanor rieffel and wolfgang polak. 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. This paper thus provides a selfcontained and complete proof of universal faulttolerant quantum computation in the presence of local. 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. Such computation is faulttolerant by its physical nature. In a quantum computer, the basic gates are much more vulnerable to noise. Quantum computation is the eld that investigates the computational power and other properties of computers based on quantummechanical principles.

To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of faulttolerant quantum computation. However, achieving faulttolerant quantum computation entails a signi. We will not be able to discuss the threshold theorem under the most restrictive of all assumptions which. But the coding is inefficient and requires many quantum bits 10,11,12, which results in physically unwieldy faulttolerant quantum circuits 10,11,12,14,15,16,17,18. Fibonacci scheme for fault tolerant quantum computation panos aliferis1 and john preskill2 1ibm watson research center, p. Faulttolerant quantum computation with few qubits rui chao ben w. Presents the most efficient way to update the progress made after nielsenchuangs textbook was published in 2000. These concepts underly the theoretical framework of largescale quantum computation and communications and are the driving force for many recent experimental efforts to construct small to medium sized arrays of controllable quantum bits. This paper thus provides a selfcontained and complete proof of universal faulttolerant quantum. Provides a comprehensive introduction to topological quantum codes and fault tolerant quantum computation with them. Faulttolerant quantum computation with high threshold in.

The remaining ingredients for a faulttolerant quantum computer are gates and measurements, which also happen to be straightforward to implement. 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. Blueprint for faulttolerant quantum computation with rydberg atoms 14 nov 2017 paywall with abstract. Box 218, yorktown heights, new york 10598, usa received 15 october 2004.

Such faulttolerant measurements will allow more frequent interrogations of the state of the logical qubit, ultimately leading to the implementation of more quantum operations and more complex entangled quantum circuits. Is probabilitistic,universal, fault tolerant quantum. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware. From qubit to topological faulttolerance springerbriefs in mathematical physics book 8 kindle edition by fujii, keisuke.

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