van Dam Wim, Howard Mark
Department of Computer Science, University of California, Santa Barbara, California 93106, USA.
Phys Rev Lett. 2009 Oct 23;103(17):170504. doi: 10.1103/PhysRevLett.103.170504.
We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect nonstabilizer gates. We prove that for all unitary single-qubit gates there exists a tight depolarizing noise threshold that determines whether the gate enables universal quantum computation or if the gate can be simulated by a mixture of Clifford gates. This exact threshold is determined by the Clifford polytope spanned by the 24 single-qubit Clifford gates. The result is in contrast to the situation wherein nonstabilizer qubit states are used; the thresholds in that case are not currently known to be tight.
我们研究通用门集在失去量子计算能力之前能够容忍多少噪声。具体而言，除了不完美的非稳定器门之外，我们考察具有完美稳定器操作的电路。我们证明，对于所有酉单比特门，都存在一个严格的退极化噪声阈值，该阈值决定了该门是支持通用量子计算，还是可以由克利福德门的混合态来模拟。这个精确的阈值由24个单比特克利福德门所跨越的克利福德多胞体决定。该结果与使用非稳定器量子比特态的情况形成对比；在那种情况下，目前尚不知道阈值是否严格。
