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:稳定子模拟可高效模拟仅包含克利福德门的重要类别的量子电路。但是,所有现有的扩展该模拟到包括非克利福德门的任意量子电路的方法都受到指数时间的限制。在本研究中,我们通过提出一种新的方法,以牺牲精度为代价,在任意量子电路上实现高效的稳定子模拟,我们的关键思想是将量子态的指数和表示压缩为一个单独的抽象元素,覆盖所有出现的元素。这使我们可以引入抽象稳定子模拟器,通过过度抽象电路操作(包括克利福德门、非克利福德门和(内部)测量)的效果,高效地操作抽象元素。我们在一个名为Abstraqt的工具中实现了我们的抽象模拟器,并实验证明Abstraqt能够建立现有技术无法处理的电路属性。