稳定剂范围不是倍增性的
Stabilizer extent is not multiplicative
摘要：
Gottesman-Knill定理指出，Clifford电路作用于稳定器状态可以在经典计算机上有效地模拟。最近，这一结果已被推广到涵盖输入，接近相干叠加的congramically许多稳定状态。经典仿真的运行时间由稳定器范围控制，该范围粗略地测量需要多少稳定器状态来近似状态。一个重要的公开问题是在张量积下判定区间是否是乘法的。如果答案是肯定的，那么就可以得到一种计算乘积输入范围的有效算法，而如果答案是否定的，那么就意味着存在一种更有效的经典算法来模拟大规模的量子线路。在这里，我们以否定的方式回答这个问题。我们的结果如下从非常一般的属性的一组稳定状态，如有一个大小，规模在维度上呈次指数级，因此可以很容易地适应其他资源理论的类似结构。
英文摘要：
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.
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