Stabilizer simulation can efficiently simulate an important class of quantum circuits consisting exclusively of Clifford gates. However, all existing extensions of this simulation to arbitrary quantum circuits including non-Clifford gates suffer from an exponential runtime. In this work, we address this challenge by presenting a novel approach for efficient stabilizer simulation on arbitrary quantum circuits, at the cost of lost precision. Our key idea is to compress an exponential sum representation of the quantum state into a single abstract summand covering (at least) all occurring summands. This allows us to introduce an abstract stabilizer simulator that efficiently manipulates abstract summands by over-abstracting the effect of circuit operations including Clifford gates, non-Clifford gates, and (internal) measurements. We implemented our abstract simulator in a tool called Abstraqt and experimentally demonstrate that Abstraqt can establish circuit properties intractable for existing techniques.

翻译：稳定子模拟可以有效模拟仅包含Clifford门的重要量子电路类别。然而，现有将该模拟方法扩展至含非Clifford门的任意量子电路的所有方案，均面临指数级运行时间问题。针对这一挑战，本文提出一种高效稳定子模拟任意量子电路的新方法，其代价是精度损失。我们的核心思想是将量子状态的指数求和表示压缩为单个抽象求和项，该求和项能够至少覆盖所有实际存在的求和项。由此，我们引入了一种抽象稳定子模拟器，通过过度抽象电路操作（包括Clifford门、非Clifford门以及内部测量）的影响，高效操控抽象求和项。我们在名为Abstraqt的工具中实现了该抽象模拟器，并通过实验证明，Abstraqt能够建立现有技术无法处理的电路性质。