论文标题
稳定范围不是乘法
Stabilizer extent is not multiplicative
论文作者
论文摘要
Gottesman-Knill定理指出，可以在经典计算机上有效地模拟作用于稳定器状态的Clifford电路。最近，该结果已被普遍覆盖接近对数上许多稳定剂状态的连贯叠加的输入。经典模拟的运行时间受稳定范围的控制，该稳定范围大致衡量了需要多少稳定态才能近似状态。一个重要的开放问题是确定在张量产品下是否具有乘法的程度。肯定的答案将产生一种用于计算产品输入程度的有效算法，而负面结果意味着存在更有效的经典算法，用于模拟LargesCale量子电路。在这里，我们以负面的方式回答这个问题。我们的结果来自稳定器态的非常通用的属性，例如具有在维度中缩放的大小，因此很容易适应其他资源理论的类似构造。
The Gottesman-Knill theorem states that a Clifford circuit acting on stabilizer states can be simulated efficiently on a classical computer. Recently, this result has been generalized to cover inputs that are close to a coherent superposition of logarithmically many stabilizer states. The runtime of the classical simulation is governed by the stabilizer extent, which roughly measures how many stabilizer states are needed to approximate the state. An important open problem is to decide whether the extent is multiplicative under tensor products. An affirmative answer would yield an efficient algorithm for computing the extent of product inputs, while a negative result implies the existence of more efficient classical algorithms for simulating largescale quantum circuits. Here, we answer this question in the negative. Our result follows from very general properties of the set of stabilizer states, such as having a size that scales subexponentially in the dimension, and can thus be readily adapted to similar constructions for other resource theories.
