Two-Qubit Circuit Depth and the Monodromy Polytope
Two-Qubit Circuit Depth and the Monodromy Polytope
复制标题
二量子位电路深度和单峰多面体
作者：
E. C. Peterson;G. Crooks;Robert S. Smith
对于包含所有单量子位门的本机门集，我们应用辛几何的结果来分析在固定数量的门内可访问的双量子位程序的空间。这些技术产生了这个子空间作为凸多面体的显式描述，由一系列线性不等式本身通过有限计算表示。我们在各种熟悉的例子中完全描述了这个不等式族，因此我们强调了“XY-族”的某个成员，该子空间特别大，即许多双量子位程序允许将其表达为低深度电路。
For a native gate set which includes all single-qubit gates, we apply results from symplectic geometry to analyze the spaces of two-qubit programs accessible within a fixed number of gates. These techniques yield an explicit description of this subspace as a convex polytope, presented by a family of linear inequalities themselves accessible via a finite calculation. We completely describe this family of inequalities in a variety of familiar example cases, and as a consequence we highlight a certain member of the ``XY--family' for which this subspace is particularly large, i.e., for which many two-qubit programs admit expression as low-depth circuits.