The complexity of a quantum gate, defined as the minimal number of elementary gates to build it, is an important concept in quantum information and computation. It is shown recently that the complexity of quantum gates built from random quantum circuits almost surely grows linearly with the number of building blocks. In this article, we provide two short proofs of this fact. We also discuss a discrete version of quantum circuit complexity growth.
@article{arxiv.2205.05668,
title = {Short Proofs of Linear Growth of Quantum Circuit Complexity},
author = {Zhi Li},
journal= {arXiv preprint arXiv:2205.05668},
year = {2022}
}