Eisert J
Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany and Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany.
Phys Rev Lett. 2021 Jul 9;127(2):020501. doi: 10.1103/PhysRevLett.127.020501.
Notions of circuit complexity and cost play a key role in quantum computing and simulation where they capture the (weighted) minimal number of gates that is required to implement a unitary. Similar notions also become increasingly prominent in high energy physics in the study of holography. While notions of entanglement have in general little implications for the quantum circuit complexity and the cost of a unitary, in this work, we discuss a simple such relationship when both the entanglement of a state and the cost of a unitary take small values, building on ideas on how values of entangling power of quantum gates add up. This bound implies that if entanglement entropies grow linearly in time, so does the cost. The implications are twofold: It provides insights into complexity growth for short times. In the context of quantum simulation, it allows us to compare digital and analog quantum simulators. The main technical contribution is a continuous-variable small incremental entangling bound.
电路复杂度和成本的概念在量子计算和模拟中起着关键作用，它们用于描述实现一个酉矩阵所需的（加权）最少门数量。类似的概念在高能物理的全息研究中也日益突出。虽然一般来说，纠缠的概念对量子电路复杂度和酉矩阵的成本影响不大，但在这项工作中，我们基于量子门纠缠能力值如何累加的思想，讨论了一种简单的关系，即当一个态的纠缠和一个酉矩阵的成本都取小值时的关系。这个界限意味着，如果纠缠熵随时间线性增长，那么成本也会如此。其影响是双重的：它为短时间内的复杂度增长提供了见解。在量子模拟的背景下，它使我们能够比较数字和模拟量子模拟器。主要技术贡献是一个连续变量的小增量纠缠界限。
