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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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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.
Upper Bounds on the Noise Threshold for Faulttolerant Quantum Computing
, 2008
"... We prove new upper bounds on the tolerable level of noise in a quantum circuit. We consider circuits consisting of unitary kqubit gates each of whose input wires is subject to depolarizing noise of strength p, as well as arbitrary onequbit gates that are essentially noisefree. We assume that the ..."
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We prove new upper bounds on the tolerable level of noise in a quantum circuit. We consider circuits consisting of unitary kqubit gates each of whose input wires is subject to depolarizing noise of strength p, as well as arbitrary onequbit gates that are essentially noisefree. We assume that the output of the circuit is the result of measuring some designated qubit in the final state. Our main result is that for p> 1 − Θ(1 / √ k), the output of any such circuit of large enough depth is essentially independent of its input, thereby making the circuit useless. For the important special case of k = 2, our bound is p> 35.7%. Moreover, if the only allowed gate on more than one qubit is the twoqubit CNOT gate, then our bound becomes 29.3%. These bounds on p are notably better than previous bounds, yet are incomparable because of the somewhat different circuit model that we are using. Our main technique is the use of a Pauli basis decomposition, which we believe should lead to further progress in deriving such bounds. 1
Logic synthesis for faulttolerant quantum computers. arXiv preprint arXiv:1310.7290
, 2013
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permission. ESTIMATING THE RESOURCES FOR QUANTUM COMPUTATION WITH THE QuRE TOOLBOX
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Towards a Geometrodynamic Entropic Approach to Quantum Entanglement and the Perspectives on Quantum Computing
, 2013
"... Abstract: On the basis of the Fisher Bohm Entropy, we outline here a geometric approach to quantum information. In particular, we review the spinspin correlation and berry Phase, and study the processes of coherence and decoherence in terms of the number of thermal microstates of the qubits system ..."
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Abstract: On the basis of the Fisher Bohm Entropy, we outline here a geometric approach to quantum information. In particular, we review the spinspin correlation and berry Phase, and study the processes of coherence and decoherence in terms of the number of thermal microstates of the qubits system c © Electronic Journal of Theoretical Physics. All rights reserved.
Accuracy threshold for postselected quantum computation
 Quantum Information and Computation
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Ognyan OreshkovDedication To Iskra ii Acknowledgements
, 2008
"... Todd A. Brun for his guidance and support throughout the years of our work together. He has been a great advisor and mentor! I am deeply indebted to him for introducing me to the field of quantum information science and helping me advance in it. From him I learned not only how to do research, but al ..."
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Todd A. Brun for his guidance and support throughout the years of our work together. He has been a great advisor and mentor! I am deeply indebted to him for introducing me to the field of quantum information science and helping me advance in it. From him I learned not only how to do research, but also numerous other skills important for the career of a scientist, such as writing, giving presentations, or communicating professionally. I highly appreciate the fact that he was always supportive of any research direction I wanted to undertake, never exerted pressure on my work, and was available to give me advice or encouragement every time I needed them. This provided for me the optimal environment to develop and made my work with him a wonderful experience. I am also greatly indebted to Daniel A. Lidar who has had an enormous impact on my work. He provided inspiration for many of the studies presented in this thesis. I have learned tons from my discussions with him and from his courses on open quantum systems and quantum error correction. His interest in what I do, the lengthy email discussions we had, and his invitations to present my research at his group meetings,