Short Proofs of Linear Growth of Quantum Circuit Complexity
Zhi Li
TL;DR
This paper provides two concise proofs that the complexity of quantum gates constructed from random circuits grows linearly with the number of gates, and discusses a discrete complexity growth version.
Contribution
It introduces two short proofs of linear growth of quantum circuit complexity and explores a discrete variant of this growth.
Findings
Quantum gate complexity grows linearly with circuit size
Two short proofs of the linear growth result
Discussion of a discrete complexity growth model
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Quantum Information and Cryptography