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An introduction to quantum error correction and faulttolerant quantum computation
, 2009
"... Abstract. Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. ..."
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Abstract. Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers.
Noise Threshold for a FaultTolerant TwoDimensional Lattice Architecture
 Quant. Inf. Comp
"... We consider a model of quantum computation in which the set of operations is limited to nearestneighbor interactions on a 2D lattice. We model movement of qubits with noisy SWAP operations. For this architecture we design a faulttolerant coding scheme using the concatenated [[7, 1, 3]] Steane code ..."
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Cited by 24 (2 self)
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We consider a model of quantum computation in which the set of operations is limited to nearestneighbor interactions on a 2D lattice. We model movement of qubits with noisy SWAP operations. For this architecture we design a faulttolerant coding scheme using the concatenated [[7, 1, 3]] Steane code. Our scheme is potentially applicable to iontrap and solidstate quantum technologies. We calculate a lower bound on the noise threshold for our local model using a detailed failure probability analysis. We obtain a threshold of 1.85×10 −5 for the local setting, where memory error rates are onetenth of the failure rates of gates, measurement, and preparation steps. For the analogous nonlocal setting, we obtain a noise threshold of 3.61×10 −5. Our results thus show that the additional SWAP operations required to move qubits in the local model affect the noise threshold only moderately.
Level reduction and the quantum threshold theorem
 PH.D. THESIS, CALTECH, 2007, EPRINT ARXIV:QUANTPH/0703230
, 2007
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Faulttolerant quantum dynamical decoupling
 Phys. Rev. Lett. 95
, 2005
"... Abstract: We review our work concerning a method of decoherence control via concatenated dynamical decoupling (DD) pulses. These recursively nested DD pulse sequences exhibit a faulttolerance threshold similar to that of concatenated quantum error correcting codes. We briefly discuss how quantum lo ..."
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Abstract: We review our work concerning a method of decoherence control via concatenated dynamical decoupling (DD) pulses. These recursively nested DD pulse sequences exhibit a faulttolerance threshold similar to that of concatenated quantum error correcting codes. We briefly discuss how quantum logic gates can be incorporated into this framework.
ACCURACY THRESHOLD FOR POSTSELECTED QUANTUM COMPUTATION
, 2008
"... We prove an accuracy threshold theorem for faulttolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated errordetecting code ..."
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Cited by 14 (2 self)
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We prove an accuracy threshold theorem for faulttolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated errordetecting code and the preparation is aborted if an error is detected. The proof applies to independent stochastic noise but (in contrast to proofs of the quantum accuracy threshold theorem based on concatenated errorcorrecting codes) not to stronglycorrelated adversarial noise. Our rigorously established lower bound on the accuracy threshold, 1.04 × 10 −3, is well below Knill’s numerical estimates.
Approaches to Quantum Error Correction
 SÉMINAIRE POINCARÉ
, 2005
"... We have persuasive evidence that a quantum computer would have extraordinary power. But will we ever be able to build and operate them? A quantum computer will inevitably interact with its environment, resulting in decoherence and the decay of the quantum information stored in the device. It is the ..."
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We have persuasive evidence that a quantum computer would have extraordinary power. But will we ever be able to build and operate them? A quantum computer will inevitably interact with its environment, resulting in decoherence and the decay of the quantum information stored in the device. It is the great technological (and theoretical) challenge to combat decoherence. And even if we can suitably isolate our quantum computer from its surroundings, errors in the quantum gates themselves will pose grave difficulties. Quantum gates (as opposed to classical gates) are unitary transformations chosen from a continuous set; they cannot be implemented with perfect accuracy and the effects of small imperfections in the gates will accumulate, leading to an eventual failure of the computation. Any reasonable correctionscheme must thus protect against small unitary errors in the quantum gates as well as against decoherence. Furthermore we must not ignore that the correction and recovery procedure itself can introduce new errors; successful faulttolerant quantum computation must also deal with this issue. The purpose of this account is to give an overview of the main approaches to quantum error correction. There exist several excellent reviews of the subject, which the interested reader may consult (see [Pre98b],[Pre99], [NC00], [KSV02], [Ste99, Ste01] and more recently [Got05]).
How quantum computers can fail
, 2006
"... Abstract We propose and discuss two postulates on the nature of errors in highly correlated noisy physical stochastic systems. The first postulate asserts that errors for a pair of substantially correlated elements are themselves substantially correlated. The second postulate asserts that in a nois ..."
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Abstract We propose and discuss two postulates on the nature of errors in highly correlated noisy physical stochastic systems. The first postulate asserts that errors for a pair of substantially correlated elements are themselves substantially correlated. The second postulate asserts that in a noisy system with many highly correlated elements there will be a strong effect of error synchronization. These postulates appear to be damaging for quantum computers. * Research supported in part by an NSF grant, by an ISF Bikura grant, and by a BSF grant. I am grateful to Dorit Aharonov, Michael BenOr, Greg Kuperberg and John Preskill for fruitful discussions and to many colleagues for helpful comments.
Quantum Computers: Noise Propagation and Adversarial Noise Models
, 2009
"... In this paper we consider adversarial noise models that will fail quantum error correction and faulttolerant quantum computation. We describe known results regarding highrate noise, sequential computation, and reversible noisy computation. We continue by discussing highly correlated noise and the ..."
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In this paper we consider adversarial noise models that will fail quantum error correction and faulttolerant quantum computation. We describe known results regarding highrate noise, sequential computation, and reversible noisy computation. We continue by discussing highly correlated noise and the “boundary, ” in terms of correlation of errors, of the “threshold theorem. ” Next, we draw a picture of adversarial forms of noise called (collectively) “detrimental noise.” Detrimental noise is modeled after familiar properties of noise propagation. However, it can have various causes. We start by pointing out the difference between detrimental noise and standard noise models for two qubits and proceed to a discussion of highly entangled states, the rate of noise, and general noisy quantum systems. Research supported in part by an NSF grant, an ISF grant, and a BSF grant.
Accuracy threshold for postselected quantum computation
 Quantum Information and Computation
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