Howard Mark, Campbell Earl
Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom.
Phys Rev Lett. 2017 Mar 3;118(9):090501. doi: 10.1103/PhysRevLett.118.090501.
Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. First, we show that robustness of magic is a well-behaved magic monotone that operationally quantifies the classical simulation overhead for a Gottesman-Knill-type scheme using ancillary magic states. Our framework subsequently finds immediate application in the task of synthesizing non-Clifford gates using magic states. When magic states are interspersed with Clifford gates, Pauli measurements, and stabilizer ancillas-the most general synthesis scenario-then the class of synthesizable unitaries is hard to characterize. Our techniques can place nontrivial lower bounds on the number of magic states required for implementing a given target unitary. Guided by these results, we have found new and optimal examples of such synthesis.
受大多数容错量子计算方案对其需求的推动，我们为魔态制定了一种资源理论。首先，我们表明魔性的鲁棒性是一种行为良好的魔单调量，它从操作上量化了使用辅助魔态的戈特斯曼 - 基尔型方案的经典模拟开销。我们的框架随后在使用魔态合成非克利福德门的任务中立即得到应用。当魔态与克利福德门、泡利测量和稳定子辅助量子比特穿插出现时（这是最一般的合成场景），可合成酉算子的类别很难刻画。我们的技术可以为实现给定目标酉算子所需的魔态数量给出非平凡的下界。受这些结果的指导，我们找到了此类合成的新的最优示例。
