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A more accurate measurement model for fault-tolerant quantum computing.

机译：用于容错量子计算的更精确的测量模型。

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摘要

Aliferis, Gottesman and Preskill [1, 2] reduce a non-Markovian noise model to a local noise model, under assumptions on the smallness of the norm of the system-bath interaction. They also prove constructively that given a local noise model, it is possible to simulate an ideal quantum circuit with size L and depth D up to any accuracy, using circuit constructed out of noisy gates from the Boykin set [3] with size L' = O(L(logL)a) and depth D' = O(D( logD)b), where a and b are constants that depend on the error correction code that we choose and the design of the fault-tolerant architecture, in addition to more assumptions [1, 2]. These two results combined give us a fault-tolerant threshold theorem for non-Markovian noise, provided that the strength of the effective local noise model is smaller than a positive number that depends on the fault-tolerant architecture we choose. However the ideal measurement process may involve a strong system-bath interaction which necessarily gives a local noise model of large strength. We refine the reduction of the non-Markovian noise model to the local noise model such that this need not be the case, provided that system-bath interactions from the non-ideal operations is sufficiently small. We make all assumptions that [1, 2] has already made, in addition to a few more assumptions to obtain our result. We also give two specific instances where the norm of the fault gets suppressed by some paramater other than the norm of the system-bath interaction. These include the large ratio of the norm of the ideal Hamiltonian to the norm of the perturbation, and frequency of oscillation of the perturbation. We hence suggest finding specific phenomenological models of noise that exhibit these properties.
机译：Aliferis，Gottesman和Preskill [1，2]在系统-浴相互作用的范式较小的假设下，将非马尔可夫噪声模型简化为局部噪声模型。他们也有建设性地证明，给定局部噪声模型，可以使用由Boykin集合[3]的噪声门构成的大小为L'=的L到D深度的任意精度的理想量子电路。 O（L（logL）a）和深度D'= O（D（logD）b），其中a和b是取决于我们选择的纠错码和容错体系结构设计的常数更多的假设[1，2]。如果有效局部噪声模型的强度小于正数（取决于我们选择的容错体系结构），那么这两个结果的组合将为我们提供非马尔可夫噪声的容错阈值定理。但是，理想的测量过程可能涉及强大的系统与浴之间的相互作用，这必然会给出强度较大的局部噪声模型。我们将非马尔可夫噪声模型的简化细化为局部噪声模型，使得这种情况不必如此，只要来自非理想操作的系统与浴之间的相互作用足够小。除了获得我们结果的一些其他假设外，我们还进行[1，2]已经做出的所有假设。我们还给出了两个特定的实例，其中故障规范被系统-浴相互作用规范之外的某些参数所抑制。这些因素包括理想哈密顿量范数与扰动范数的较大比率，以及扰动的振荡频率。因此，我们建议找到表现出这些特性的特定噪声现象学模型。

著录项

  • 作者

    Ouyang, Yingkai.;

  • 作者单位

    University of Waterloo (Canada).;

  • 授予单位 University of Waterloo (Canada).;
  • 学科 Applied Mathematics.
  • 学位 M.Math.
  • 年度 2009
  • 页码 64 p.
  • 总页数 64
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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