Faulttolerant quantum computation with few qubits qutech. Pdf a note on threshold theorem of faulttolerant quantum. With this scheme it seems possible to reach the faulttolerant threshold. Faulttolerant architecture for quantum computation using.
In part 1, we cover results pertaining to magic state distillation, one of the. In short the theory of quantum computation and quantum information. Pdf faulttolerant quantum computation with few qubits. Bosonic codes for faulttolerant quantum computation example.
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. Faulttolerant quantum computation versus gaussian noise. Quantum error correction and fault tolerant quantum computing. The standard textbook, quantum computation and quantum information, by michael nielsen and isaac chuang is published. Demonstrating that this theory really works in practice is one of the great challenges facing contemporary science. Further elements of a faulttolerant q c ccomputation are shown in fig. Faulttolerant quantum computing in the pauli or clifford. The theory of faulttolerant quantum computation shows that properly encoded quantum information can be protected against decoherence and processed reliably with imperfect hardware 1. Consistency checks, like the parity of a bit string, work classically, but in the quantum world are simply not powerful enough. Checkpoints require stoping the computation at a 1. As far as faulttolerant quantum computing is concerned, again the first method was given by shor 65 who introduced the idea of. One optical pulse represents one logical qubit catbinomialgkp code efficient. 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 versus realistic noise.
Faulttolerant detection of a quantum error science. Quantum computation with topological codes from qubit to. Level reduction and the quantum threshold theorem 11. Blueprint for faulttolerant quantum computation with rydberg atoms 14 nov 2017 paywall with abstract. Reaching that point, however, will require quantum processors that are scalable and fault tolerant.
Highthreshold faulttolerant quantum computation with. Pdf faulttolerant quantum computation researchgate. A theory of faulttolerant quantum computation daniel gottesman. The result holds for a very general, not necessarily probabilistic noise model, for quantum particles with any number of states, and is also generalized to one dimensional quantum computers with only nearest neighbor interactions. There are lots of details which we need to pay attention to in. And given those constructions, we have essentially shown the threshold theorem for faulttolerant quantum computation in a far from rigorous manner, however. The number 15 was factored using 10 18 identical molecules, each containing seven active nuclear spins. Provides a comprehensive introduction to topological quantum codes and faulttolerant quantum computation with them. Faulttolerant quantum computation arijit ghosh roll no 03cs3007 advisors. Quantum computing recent advances in creating quantum processors comprising several tens of qubits bring the era of quantum advantage tantalizingly close.
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. Abstract it has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by. Parkerson department of computer science and computer engineering university of arkansas, fayetteville, ar 72701, usa email. Fault tolerant quantum computation with a new reversible gate d. A quantum computer can provide fast solution for certain computational problems e. Fault tolerant quantum computation with a new reversible. Faulttolerant quantum computation by anyons sciencedirect.
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. In a quantum computer, the basic gates are much more vulnerable to noise than classical transistors after all. 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. Pdf new limits on faulttolerant quantum computation. Pdf is faulttolerant quantum computation really possible. Faulttolerant quantum computation with longrange correlated noise dorit aharonov,1 alexei kitaev,2,3 and john preskill2 1school of computer science and engineering, hebrew university, jerusalem, israel 2institute for quantum information, california institute of technology, pasadena, california 91125, usa 3microsoft research, one microsoft way, redmond, washington 98052, usa. One must be able to compute without allowing the errors to propagate too much. Hybrid magic state distillation for universal faulttolerant quantum computation. Quantum science and technology paper open access faulttolerant, highlevel quantum circuits. Algorithms such as quantum factoring1 and quantum search2 illustrate the great theoretical promise of quantum computers.
I discuss a number of examples in more detail, including the. Holonomic surface codes for faulttolerant quantum computation. Faulttolerant quantum computation with few qubits npj. However, achieving faulttolerant quantum computation entails a signi. We will discuss one of these approaches which achieves faulttolerance which involves the use of concatenated quantum error correcting codes. Holonomic surface codes for fault t olerant quan tum computation jiang zhang, 1 simon j. Recently shor23 showed how to use quant urn codes in order to perform fault tolerant quantum computation when the noise rate, or. 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. We also take advantage of special code symmetries, and use pieceable fault tolerance.
Measurements can be performed by joining excitations in pairs and observing the result of fusion. Terhal and christophe vuillot jara institute for quantum information, rwth aachen university, 52056 aachen, germany dated. Fibonacci scheme for faulttolerant quantum computation panos aliferis1 and john preskill2 1ibm watson research center, p. The practicality of fault tolerant quantum computing proposals is investigated by considering the entanglement of local and global errors. However, it is still challenging to experimentally generate the gkp qubit with the required squeezing level, 14. A twodimensional quantum system with anyonic excitations can be considered as a quantum computer.
Intro to faulttolerant quantum computing from the perspective of the classical community, 7 pages. Pdf hybrid magic state distillation for universal fault. Faulttolerant quantum computation and the threshold theorem. The goal of faulttolerant quantum computing is to operate a largescale quantum computer reliably, even though the components of the.
In quantum computing, the quantum threshold theorem proved by michael ben or and dorit. The inspiration comes from two seemingly independent themes which appeared around 1997. Faulttolerant quantum computation caltech division of. Physical realization of a quantum computer is a big challenge for scientists. Presents the most efficient way to update the progress made after nielsenchuangs textbook was published in 2000. Faulttolerant quantum computation with high threshold in. The steep road towards robust and universal quantum computation earl t. Related content lattice surgery translation for quantum computation. Box 218, yorktown heights, new york 10598, usa 2institute for quantum information, california institute of technology, pasadena, california 91125, usa received 30 september 2008.
Pdf errorcorrection process has to be carried out periodically to prevent accumulation of errors in faulttolerant quantum computation. Fault tolerance is the study of reliable computation using unreliable components. To implement faulttolerant quantum computation with continuous variables, the gottesmankitaevpreskill gkp qubit has been recognized as an important technological element. An important objective is to nd quantum algorithms that are signi cantly faster than any classical algorithm solving the same problem. Title faulttolerant quantum computation on logical. Pdf the socalled threshold theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum. Development of quantum hardware towards faulttolerant. Faulttolerant quantum computation with constant error. Faulttolerant quantum computation with nondeterministic entangling gates 16 mar 2018 paywall with abstract from the arxiv. A novel basis and a new constructive proof of universality for shors basis. Fault tolerant quantum computation guest lecture for quantum computation mathm0023 dominic verdon school of mathematics, university of bristol dominic.
Faulttolerant quantum computation with asymmetric bacon. Such computation is faulttolerant by its physical nature. No measurements, or classical operations, are required during the quantum computation. 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. 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. Introduction the theory of quantum computers assures us that quantum algorithms can solve certain. Roads towards faulttolerant universal quantum computation. Every lecture is accompanied by readings that support and expand on what was covered in the lecture. Fault tolerance in quantum computation mavilla hima bindhu, california state university abstract.
Qk one of the big challenges in quantum computing today is to perform nearly perfect gate operations. Unitary transformations can be performed by moving the excitations around each other. With trapped ions, initialization, readout, and singlequbit operations have al. Interest in quantum computation has since been growing. The main achievement in the theory of faulttolerant quantum computation is the threshold theorem. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure.
Find materials for this course in the pages linked along the left. A note on threshold theorem of faulttolerant quantum computation 25 jun 2010. Faulttolerant quantum computation with few qubits npj quantum. Kitaev, 2008 as a theoretical physics student, on the one hand im interested on an entire class of problems related to quantum information theory, including aspects of classical and quantum cryptography, as well as the computational complexity.
With the underlying architectures of these processors based on superconducting qubits laid out in a twodimensional array, socalled. Fibonacci scheme for faulttolerant quantum computation. Campbell department of physics and astronomy, university of she. Quantum computation is the eld that investigates the computational power and other properties of computers based on quantummechanical principles.
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