Constraints on magic state protocols from the statistical mechanics of Wigner negativity
Constraints on magic state protocols from the statistical mechanics of Wigner negativity
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DOI：
10.1038/s41534-022-00551-1
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发表时间：
2021-06
影响因子：
7.6
通讯作者：
Nikolaos Koukoulekidis;D. Jennings
中科院分区：
文献类型：
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作者：
Nikolaos Koukoulekidis;D. Jennings
幻态是实现泛容错量子计算的关键。幻态理论试图通过单调性来量化这种计算元素，并确定如何将这些状态有效地转化为有用的形式。在这里，我们开发了一个统计力学框架的基础上的优势，以描述维格纳负魔态的奇素数维量子处理下的克利福德电路。我们表明，优化使我们既可以量化的维格纳表示的混乱，并推导出魔术蒸馏的上限。这些界限被证明是比其他界限，如从mana和thauma，更严格，并可用于将硬件物理，如温度依赖性和系统哈密顿。我们还表明，一个子集的单发雷尼熵保持良好的定义准分布，在数据处理方面是完全有意义的，可以获得负值，信号魔术。我们发现，一个神奇的状态的mana是这些Rényi熵的发散的措施，作为一个接近Wigner分布的香农熵，并讨论如何蒸馏下界可以在此设置。这种对拟分布的优化可以在其他非经典性的研究中找到应用，并在经典统计力学的背景下提出了一些非平凡的问题。
Magic states are key ingredients in schemes to realize universal fault-tolerant quantum computation. Theories of magic states attempt to quantify this computational element via monotones and determine how these states may be efficiently transformed into useful forms. Here, we develop a statistical mechanical framework based on majorization to describe Wigner negative magic states for qudits of odd prime dimension processed under Clifford circuits. We show that majorization allows us to both quantify disorder in the Wigner representation and derive upper bounds for magic distillation. These bounds are shown to be tighter than other bounds, such as from mana and thauma, and can be used to incorporate hardware physics, such as temperature dependence and system Hamiltonians. We also show that a subset of single-shot Rényi entropies remain well-defined on quasi-distributions, are fully meaningful in terms of data processing and can acquire negative values that signal magic. We find that the mana of a magic state is the measure of divergence of these Rényi entropies as one approaches the Shannon entropy for Wigner distributions, and discuss how distillation lower bounds could be obtained in this setting. This use of majorization for quasi-distributions could find application in other studies of non-classicality, and raises nontrivial questions in the context of classical statistical mechanics.