nu=5/2分数量子霍尔态的普适量子计算
Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State
摘要：
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的统计的辫群表示在计算上不是普适的，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。假设所有的TQC操作都完美地实现，我们证明了非拓扑操作的阈值错误率在14%以上。模拟具有$L$门的量子线路所需的非拓扑计算元件的总数按比例缩放为$L(\log L)^3$。
英文摘要：
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 statistics of these anyons is not computationally universal, one cannot directly apply the standard TQC technique. We propose to use very noisy non-topological operations such as direct short-range interaction 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 non-topological operations is above 14%. The total number of non-topological computational elements that one needs to simulate a quantum circuit with $L$ gates scales as $L(\log L)^3$.
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