IAS CMT/QFT Group Meeting

Abstract: In this talk, I will introduce a new framework of quantum convolution to study stabilizer states and magic states in discrete-variable systems. Within this convolutional framework, we find that the stabilizer states play a similar role to Gaussian distribution in classical probability theory.  Additionally, we propose a protocol, called the quantum convolution-swap test, to perform stabilizer testing for quantum states and gates.  Based on this protocol, we introduce “magic entropy” to quantify magic in quantum states and gates, in a way which may be measurable experimentally. This talk is based on the joint works with Weichen Gu, and Arthur Jaffe(PNAS120(25)2023, arXiv: 2302.08423, arXiv:2306.09292).