Fault tolerant quantum computation with nondeterministic entangling gates 16 mar 2018 paywall with abstract from the arxiv. Quantum information processing and quantum error correction. Even so, the study of faulttolerant clas s ical computing has a distinguished. Faulttolerant quantum computation by anyons sciencedirect.
In part 1, we cover results pertaining to magic state distillation, one of the. Such fault tolerant measurements will allow more frequent interrogations of the state of the logical qubit, ultimately leading to the implementation of more. A major event in the field was kitaevs proposal and realization of a theoretical fault tolerant quantum computation platform based on braiding topological defects of topological phases of matter. 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. Quantum computing is an exciting alternative model to classical computation. A typeset version of chapter 8 on fault tolerant quantum computation is not yet available.
Download it once and read it on your kindle device, pc, phones or tablets. A quantum computer can provide fast solution for certain computational problems e. Fibonacci scheme for fault tolerant quantum computation panos aliferis1 and john preskill2 1ibm watson research center, p. After learning about qecc, chapter 5 begins with the important topic of fault tolerant quantum computing ftqc. The remaining ingredients for a faulttolerant quantum computer are gates and measurements, which also happen to be straightforward to implement. In a quantum computer, the basic gates are much more vulnerable to noise than classical transistors after all. In the past three decades, the discovery of topological phases has not only engendered great interest among researchers in condensed matter physics but it has also attracted the interest of researchers working on quantum information, quantum materials and simulations, high energy. A faulttolerant oneway quantum computer sciencedirect.
We demonstrate a faulttolerant errordetection scheme that suppresses spreading of ancilla errors by a. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Is probabilitistic,universal, fault tolerant quantum. Fibonacci scheme for faulttolerant quantum computation. Pdf faulttolerant quantum computation researchgate. Find materials for this course in the pages linked along the left. Technical roadmap for faulttolerant quantum computing.
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. Consistency checks, like the parity of a bit string, work classically, but in the quantum world are simply not powerful enough. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information in. In short the theory of quantum computation and quantum information deals with the tasks of computing and information processing that can be accomplished using small systems which follow the fundamental laws of quantum mechanics. Workshop on topological phase transitions and new developments. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of faulttolerant quantum computation. Such computation is faulttolerant by its physical nature. Faulttolerant quantum computing in the pauli or clifford. Today ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. Quantum error correction and fault tolerant quantum computing. The threshold theorem states that it is possible to create a quantum computer to perform an arbitrary.
With a given noise model, can one still reliably compute. 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 introduction to faulttolerant quantum computation and its. Faulttolerant architecture for quantum computation using.
Cancel the membership at any time if not satisfied. 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. Divincenzo2, 1columbia university, 1214 amsterdam avenue, mc. For the background of quantum computing in general, we refer the reader to the related articles in this volume as well as the book by nielsen andchuang 56.
We also take advantage of special code symmetries, and use pieceable fault tolerance. Towards faulttolerant quantum computing with trapped ions. 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. The qc c is a scheme for universal quantum computation by onequbit measurements on cluster states. Checkpoints require stoping the computation at a 1. Box 218, yorktown heights, new york 10598, usa 2institute for quantum information, california institute of technology, pasadena, california 91125, usa. Faulttolerant quantum computation arijit ghosh roll no 03cs3007 advisors. Faulttolerant detection of a quantum error science. 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. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Quantum computing faulttolerant detection of a quantum error. Improving the overhead of fault tolerant quantum computation with magic state distillation joe ogorman and earl campbell. Here we describe a fault tolerant version of the oneway quantum computer qc c.
Graphical proofs for faulttolerant quantum computation abstract. From qubit to topological faulttolerance springerbriefs in mathematical physics book 8 kindle edition by fujii, keisuke. Readings quantum computation mathematics mit opencourseware. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information. The paper goes even further and claims it is possible. An important objective is to nd quantum algorithms that are signi cantly faster than any classical algorithm solving the same problem. The paper probabilistic fault tolerant universal quantum computation and sampling problems in continuous variables douce et al. The work provides a good reference for quantum computation and quantum information courses, allowing for students to become familiar with major points on the quantum information theoretical aspects of topological quantum computation and the advantages of topological quantum computation for quantum noise resistance. Quantum error correction and faulttolerance quantiki.
The standard circuit model of quantum computing requires a universal set of quantum logic gates for the implementation of arbitrary quantum operations. Quantum computation with topological codes from qubit to. And given those constructions, we have essentially shown the threshold theorem for faulttolerant quantum computation in a far from rigorous manner, however. Daniel gottesman april 28, 2020 graphical proofs for. A critical component of any quantum errorcorrecting scheme is detection of errors by using an ancilla system. For the quantum computer to function efficiently, each layer must issue instructions. Additional material is available in the form of handwritten notes. 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. Riding bosonic qubits towards faulttolerant quantum. Here, a very detailed analysis is presented for syndrome extraction and shor state preparation.
Faulttolerant universal computation is possible with four extra qubits, 19 in total. However, considering the fault tolerance, the overhead of the quantum computer increases exponentially. This thesis contains the results of research projects broadly related to the pursuit of universal fault tolerant quantum computation. Fault tolerant computation and fault tolerant data storage are largely similar in that the recovery operations dominate the dynamics.
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. For example, one can run many copies of a classical calculation in parallel, periodically using majority gates to catch and correct faults. Choosing the rules of quantum physics as the physical basis for constructing models of computation allows for solving certain computational problems more efficiently as in models based on classical physics. I demonstrate that faulttolerant universal computation is possible for any stabilizer code.
Fault tolerance is the study of reliable computation using unreliable components. Quantum error correction and fault tolerant quantum. Fault tolerant quantum computation with nondeterministic gates. The theory of fault tolerant 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. Faulttolerant holonomic quantum computation in surface codes. Overhead and noise threshold of faulttolerant quantum error. It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Resource cost of fault tolerant quantum computing in hybrid quantum computers and linearoptical quantum computers ying li, peter c. Proceedings of 35th annual symposium on fundamentals of computer science focs96. Cluster states consist of qubits arranged on a two or threedimensional lattice and may be created by a nearestneighbor ising interaction. A note on threshold theorem of fault tolerant quantum computation 25 jun 2010. From the purely theoretical point of view, this problem has been solved due to shors discovery of faulttolerant quantum computation, with subsequent improvements. There are lots of details which we need to pay attention to in.
In short the theory of quantum computation and quantum information. The procedures could enable testing more sophisticated protected circuits in smallscale quantum devices. Furthermore, encoded quantum information can be processed without serious propagation of errors. Unitary transformations can be performed by moving the excitations around each other. Level reduction and the quantum threshold theorem 11. An introduction to quantum error correction and fault.
There is also an updated though incomplete version of chapter 4, prepared in 2001. Faulttolerant quantum computation with few qubits npj. Such computation is fault tolerant by its physical nature. The garland science website is no longer available to access and you have been automatically redirected to.
It was once widely believed that quantum computation would never become a reality. Instead of a quantum computer where the fundamental units are 2dimensional qubits, we can consider a quantum computer made up of ddimensional systems. Sunday, 27 april 2008 towards fault tolerant quantum computing with trapped ions. Faulttolerant quantum computation with few qubits npj quantum. Faulttolerant quantum computation with higherdimensional. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps. Here we provide an overview of the ingredients leading to fault tolerant quantum computation ftqc. The present treatment is thorough for the case of data storage, and it is argued in sec.
Quantum computation is the eld that investigates the computational power and other properties of computers based on quantum mechanical principles. One important problem is decoherence and systematic errors in unitary transformations which occur in real quantum systems. Interest in quantum computation has since been growing. Physical realization of a quantum computer is a big challenge for scientists. Faulttolerant quantum computation with constant error. Quantum information processing and quantum error correction is a selfcontained, tutorialbased introduction to quantum information, quantum computation, and quantum. All instructor resources see exceptions are now available on our instructor hub. Over a decade has passed since this monumental accomplishment yet no book length pedagogical presentation of this important theory exists. California institute of technology, pasadena, ca 91125, usa. An introduction to quantum error correction and faulttolerant. Here, we develop an architecture for quantum computation using electrically controlled semiconductor spins by extending the lossdivincenzo scheme and by combining actively protected quantum. Sudebkumar prasant pal abstract quantum computing is an exciting alternative model to classical computation. Introduction to quantum computation and information.
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