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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.
A meetinthemiddle algorithm for fast synthesis of depthoptimal quantum circuits. arXiv:1206.0758v2 [quantph
, 2012
"... Abstract We present an algorithm for computing depthoptimal decompositions of logical operations, leveraging a meetinthemiddle technique to provide a significant speedup over simple brute force algorithms. As an illustration of our method we implemented this algorithm and found factorizations ..."
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Abstract We present an algorithm for computing depthoptimal decompositions of logical operations, leveraging a meetinthemiddle technique to provide a significant speedup over simple brute force algorithms. As an illustration of our method we implemented this algorithm and found factorizations of the commonly used quantum logical operations into elementary gates in the Clifford+T set. In particular, we report a decomposition of the Toffoli gate over the set of Clifford and T gates. Our decomposition achieves a total T depth of 3, thereby providing a 40% reduction over the previously best known decomposition for the Toffoli gate. Due to the size of the search space the algorithm is only practical for small parameters, such as the number of qubits, and the number of gates in an optimal implementation.
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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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.
Errordetectionbased quantum fault tolerance against discrete Pauli noise
, 2006
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Aoneway quantum computer
 Physics Review Letters
, 2001
"... oneway quantum computer—a nonnetwork model of ..."
Automated Generation of Layout and Control for Quantum Circuits
 In Proc. of ACM Intl. Conf. on Computing Frontiers
, 2007
"... We present a computeraided design flow for quantum circuits, complete with automatic layout and control logic extraction. To motivate automated layout for quantum circuits, we investigate gridbased layouts and show a performance variance of four times as we vary grid structure and initial qubit pl ..."
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Cited by 10 (3 self)
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We present a computeraided design flow for quantum circuits, complete with automatic layout and control logic extraction. To motivate automated layout for quantum circuits, we investigate gridbased layouts and show a performance variance of four times as we vary grid structure and initial qubit placement. We then propose two polynomialtime design heuristics: a greedy algorithm suitable for small, congestionfree quantum circuits and a dataflowbased analysis approach to placement and routing with implicit initial placement of qubits. Finally, we show that our dataflowbased heuristic generates better layouts than the stateoftheart automated gridbased layout and scheduling mechanism in terms of latency and potential pipelinability, but at the cost of some area. 1
Faulttolerant quantum computation for local leakage faults
 2005, quantph/0511065. THRESHOLD AGAINST BIASED NOISE 11
"... We provide a rigorous analysis of faulttolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage faults by using socalled leakage reduction units such as quantum teleportation. We describe ways to limit the use of leakage reduction ..."
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Cited by 9 (2 self)
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We provide a rigorous analysis of faulttolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage faults by using socalled leakage reduction units such as quantum teleportation. We describe ways to limit the use of leakage reduction while keeping the quantum circuits faulttolerant. We also show that measurementbased computation is inherently tolerant against leakage faults. 1
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]).