Universal quantum computation with the ν=5/2 fractional quantum Hall state
Universal quantum computation with the ν=5/2 fractional quantum Hall state
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DOI：
10.1103/physreva.73.042313
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发表时间：
2006-04-01
影响因子：
2.9
通讯作者：
Bravyi, S
中科院分区：
文献类型：
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作者：
Bravyi, S
我们考虑拓扑量子计算（TQC）与一个特定的类的任意子，被认为是存在于分数量子霍尔效应状态在朗道能级填充分数nu=5/2。由于描述这些任意子统计的辫群表示在计算上并不通用，因此不能直接应用标准的TQC技术。我们建议使用非常嘈杂的非拓扑操作，如任意子之间的直接短程相互作用来模拟一组通用的门。假设所有TQC操作都得到完美实施，我们证明非拓扑操作的阈值错误率在14%以上。模拟具有L个门的量子电路所需的非拓扑计算元件的总数为L（ln L）（3）。
We consider topological quantum computation (TQC) with a particular class of anyons that are believed to exist in the fractional quantum Hall effect state at Landau-level filling fraction nu=5/2. Since the braid group representation describing the statistics of these anyons is not computationally universal, one cannot directly apply the standard TQC technique. We propose to use very noisy nontopological operations such as direct short-range interactions between anyons to simulate a universal set of gates. Assuming that all TQC operations are implemented perfectly, we prove that the threshold error rate for nontopological operations is above 14%. The total number of nontopological computational elements that one needs to simulate a quantum circuit with L gates scales as L(ln L)(3).