Surface code implementation of block code state distillation.
TL;DR: It is found that, using the best available techniques, for parameters of practical interest, block code state distillation does not always lead to lower overhead, and, when it does, the overhead reduction is typically less than a factor of three.
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Abstract: State distillation is the process of taking a number of imperfect copies of a particular quantum state and producing fewer better copies. Until recently, the lowest overhead method of distilling states produced a single improved [formula: see text] state given 15 input copies. New block code state distillation methods can produce k improved [formula: see text] states given 3k + 8 input copies, potentially significantly reducing the overhead associated with state distillation. We construct an explicit surface code implementation of block code state distillation and quantitatively compare the overhead of this approach to the old. We find that, using the best available techniques, for parameters of practical interest, block code state distillation does not always lead to lower overhead, and, when it does, the overhead reduction is typically less than a factor of three.
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Citations
Roads towards fault-tolerant universal quantum computation
TL;DR: In this article, the authors proposed a fault-tolerant logical qubit architecture for quantum computers, which uses high-dimensional quantum codes in a modular architecture, but need to be explored further.
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TL;DR: A comprehensive mathematical theory of the stabilizerRank and the related approximate stabilizer rank is developed and a suite of classical simulation algorithms with broader applicability and significantly improved performance over the previous state-of-the-art are presented.
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TL;DR: Gidney et al. as mentioned in this paper presented an approximate cost of factoring integers and computing discrete logarithms in finite fields on a quantum computer by combining techniques from Shor 1994, Griffiths-Niu 1996 and Zalka 2006.
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TL;DR: In this paper, the authors considered a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis.
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