Quantum computation with topological codes from qubit to. In part 1, we cover results pertaining to magic state distillation, one of the. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of faulttolerant quantum computation. Fault tolerant quantum computing robert rogers, thomas sylwester, abe pauls 1 introduction 1. However, formatting rules can vary widely between applications and fields of interest or study. It provides indepth coverage on the most important class of codes discovered to date. From the purely theoretical point of view, this problem has been solved due to shors discovery of faulttolerant quantum computation 2, with subsequent improvements 3, 4, 5, 6. For the fault tolerant scheme of quantum computation described in this paper we require a quantum code with the following three properties. 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. Fibonacci scheme for faulttolerant quantum computation. Faulttolerant quantum computation arijit ghosh roll no 03cs3007 advisors.
One must be able to compute without allowing the errors to propagate too much. From the journals of the american physical society. Topological codes support a variety of approaches to fault tolerant computation, the theoretical sophistication of. Faulttolerant quantum computation with constant error rate. Faulttolerant quantum computation semantic scholar. 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. Quantum computation is the eld that investigates the computational power and other properties of computers based on quantum mechanical principles.
An introduction to quantum error correction and faulttolerant. Faulttolerant quantum error detection science advances. Blueprint for faulttolerant quantum computation with rydberg atoms 14 nov 2017 paywall with abstract. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information.
With a given noise model, can one still reliably compute. Consistency checks, like the parity of a bit string, work classically, but in the quantum world are simply not powerful enough. Our first result looks at limitations on the simplest implementation of faulttolerant operations, transversality. 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. And given those constructions, we have essentially shown the threshold theorem for faulttolerant quantum computation in a far from rigorous manner, however. An important objective is to nd quantum algorithms that are signi cantly faster than any classical algorithm solving the same problem. One important problem is decoherence and systematic errors in unitary transformations which occur in real quantum systems. Pdf faulttolerant quantum computation researchgate. The procedures could enable testing more sophisticated protected circuits in smallscale quantum devices. There are lots of details which we need to pay attention to in. The discovery of quantum error correction has greatly improved the long term prospects for quantum computing technology. Faulttolerant quantum computation perimeter institute.
The field of topological quantum computation pursues phases of matter supporting emergent particles known as nonabelian anyons to ultimately realize scalable, intrinsically fault tolerant. 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. The garland science website is no longer available to access and you have been automatically redirected to. Is probabilitistic,universal, fault tolerant quantum. All instructor resources see exceptions are now available on our instructor hub. A faulttolerant oneway quantum computer sciencedirect. 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. 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. Quantum computing1the processing of information according to the fundamental laws of physicsoffers a means to solve efficiently a small. Quantum computation and quantum information 10th anniversary ed. Physical realization of a quantum computer is a big challenge for scientists.
The detailed explanations of classical concepts such as data compression and encoding help put the quantum analogues in context. 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 impossible. Divincenzo2, 1columbia university, 1214 amsterdam avenue, mc. Box 218, yorktown heights, new york 10598, usa received 15 october 2004. 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. Interest in quantum computation has since been growing. The remaining ingredients for a faulttolerant quantum computer are gates and measurements, which also happen to be straightforward to implement. For example, one can run many copies of a classical calculation in parallel, periodically using majority gates to catch and correct faults. Errors are most often local perturbations, but topological invariants encoding information would be immune to all but the most odious. The subject encapsulates one of the greatest hurdles in creating a useful quantum computer. An introduction to faulttolerant quantum computation and its. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Introduction to quantum computation and information. From qubit to topological faulttolerance springerbriefs in mathematical physics book 8 kindle edition by fujii, keisuke.
Sudebkumar prasant pal abstract quantum computing is an exciting alternative model to classical computation. We demonstrate a faulttolerant errordetection scheme that suppresses spreading of ancilla errors by a. Such computation is faulttolerant by its physical nature. Here, a very detailed analysis is presented for syndrome extraction and shor state preparation. Faulttolerant quantum computation with constant error. Box 218, yorktown heights, new york 10598, usa 2institute for quantum information, california institute of technology, pasadena, california 91125, usa. Faulttolerant quantum computation by anyons nasaads. A twodimensional quantum system with anyonic excitations can be considered as a quantum computer. Faulttolerant quantum computation with few qubits npj. Fibonacci scheme for fault tolerant quantum computation panos aliferis1 and john preskill2 1ibm watson research center, p. 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.
Faulttolerant quantum computation with a softdecision. Jul 23, 2015 aharonov d, kitaev ay, preskill j 2006 fault tolerant quantum computation with longrange correlated noise. Download it once and read it on your kindle device, pc, phones or tablets. Such fault tolerant measurements will allow more frequent interrogations of the state of the logical qubit, ultimately leading to the implementation of more. Faulttolerant quantum computation introduction to quantum. Presents the most efficient way to update the progress made after nielsenchuangs textbook was published in 2000. 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.
Level reduction and the quantum threshold theorem 11. Therefore, given the ability to perform faulttolerant clifford group operations, faulttolerant measurements, and to prepare the encoded. Provides a comprehensive introduction to topological quantum codes and faulttolerant quantum computation with them. 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. Riding bosonic qubits towards faulttolerant quantum computation.
Quantum error correction and fault tolerant quantum computing. Each ion provided one physical qubit in the form of a pair of states in the hyperfinesplit 2 s 12 ground level with an energy difference of 12. Fault tolerant quantum computational models from topological quantum field theories ee376a winter 2019 milind jagota, alec lau. Use features like bookmarks, note taking and highlighting while reading quantum computation with topological codes. Your instructor credentials will not grant access to the hub, but existing and new users may request access here. A typeset version of chapter 8 on faulttolerant quantum computation is not yet available. In short the theory of quantum computation and quantum information. Furthermore, encoded quantum information can be processed without serious propagation of errors. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information in.
There is also an updated though incomplete version of chapter 4, prepared in 2001. Improving the overhead of fault tolerant quantum computation with magic state distillation joe ogorman and earl campbell. Such computation is fault tolerant by its physical nature. Topological quantum computation provides a beautiful solution to this problem.
In the first part, we present the theory of quantum errorcorrecting codes qeccs and in particular two important classes of qeccs, namely the socalled css codes and stabilizer codes. Quantum error correction and fault tolerant quantum. Nov 18, 2019 the remaining ingredients for a fault tolerant quantum computer are gates and measurements, which also happen to be straightforward to implement. Quantum error correction and faulttolerance quantiki. Checkpoints require stoping the computation at a 1. Additional material is available in the form of handwritten notes. Faulttolerant detection of a quantum error science. Unitary transformations can be performed by moving the excitations around each other.
Faulttolerant quantum computation by anyons caltechauthors. Over a decade has passed since this monumental accomplishment yet no book length pedagogical presentation of this important theory exists. Faulttolerant quantum computation via exchange interactions. 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. Resource cost of fault tolerant quantum computing in hybrid quantum computers and linearoptical quantum computers ying li, peter c. Here we provide an overview of the ingredients leading to fault tolerant quantum computation ftqc. Introduction to fault tolerant quantum computation fact. Fault tolerant quantum computation with nondeterministic entangling gates 16 mar 2018 paywall with abstract from the arxiv.
A critical component of any quantum errorcorrecting scheme is detection of errors by using an ancilla system. Over a decade has passed since this monumental accomplishment yet no booklength pedagogical presentation of this important theory exists. Citeseerx document details isaac councill, lee giles, pradeep teregowda. This encoded universality paradigm offers potential simplifications in quantum computer design since it does away with the need to perform singlequbit rotations. A faulttolerant system for stopping leaks in quantum. Faulttolerant quantum computation by anyons sciencedirect. Blueprint for faulttolerant quantum computation with rydberg atoms 14 nov 2017 paywall with. Quantum computing faulttolerant detection of a quantum. Such faulttolerant measurements will allow more frequent interrogations of the state of the logical qubit, ultimately leading to the implementation of more. Faulttolerant universal computation is possible with four extra qubits, 19 in total. Combined with the twoqubit fault tolerant errordetection and errorcorrection methods in chao and reichardt, this means that substantial quantum calculations can be implemented fault tolerantly in a quantum device with fewer than 20 physical qubits.
This book constitutes the thoroughly refereed postconference proceedings of the 5th conference on theory of quantum computation, communication, and cryptography, tqc 2010, held in leeds, uk, in april 2010. Faulttolerant quantum computation with quantum errorcorrecting codes has been considerably developed over the past decade. Quantum error correction and fault tolerant quantum computing offers the first fulllength exposition on the realization of a theory once thought impossible. Aharonov d, kitaev ay, preskill j 2006 faulttolerant quantum computation with longrange correlated noise. A typeset version of chapter 8 on fault tolerant quantum computation is not yet available. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information in a. Written primarily for undergraduate students in physics, mathematics, computer science, and related disciplines, this introductory text is also suitable for researchers interested in. Eastinknill theorem 2009 a universal set of quantum gates cannot be achieved using only transversal gates i. Fault tolerance is the study of reliable computation using unreliable components. However, there are still difficult issues, particularly on the resource requirement. In a breakthrough, knill has constructed a novel fault tolerance.
Riding bosonic qubits towards faulttolerant quantum. However, considering the fault tolerance, the overhead of the quantum computer increases exponentially. The paper probabilistic fault tolerant universal quantum computation and sampling problems in continuous variables douce et al. Filling this gap, elements of quantum computation and quantum communication gives a clear, selfcontained introduction to quantum computation and communication. After learning about qecc, chapter 5 begins with the important topic of fault tolerant quantum computing ftqc. It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Preskill, john 1998 faulttolerant quantum computers. In a quantum computer, the basic gates are much more vulnerable to noise. In quantum computing, the quantum threshold theorem proved by michael ben or and dorit. California institute of technology, pasadena, ca 91125, usa.
Measurements can be performed by joining excitations in pairs and observing the result of fusion. The paper goes even further and claims it is possible. A quantum computer can provide fast solution for certain computational problems e. There is also an updated though incomplete version of chapter 4, prepared in. The only way a quantum computer can work is if its logical qubits are constantly monitored by ancillary qubits, which ensure logical errors are detected and corrected before they can affect the computation, said yale postdoctoral associate serge rosenblum, colead author of a new study published in the journal science. Fault tolerant quantum computing robert rogers, thomas. 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. Please join the simons foundation and our generous member organizations in supporting arxiv during our giving campaign september 2327. 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.
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