Retrieving Non-Linear Features from Noisy Quantum States

The framework of recovering the high-order quantum information given copies of noisy states

Abstract

Accurately estimating high-order moments of quantum states is an elementary precondition for many crucial tasks in quantum computing, such as entanglement spectroscopy, entropy estimation, spectrum estimation and predicting non-linear features from quantum states. But in reality, inevitable quantum noise prevents us from accessing the desired value. In this paper, we address this issue by systematically analyzing the feasibility and efficiency of extracting high-order moments from noisy states. We first show that there exists a quantum protocol capable of accomplishing this task if and only if the underlying noise channel is invertible. We then establish a method for deriving protocols that attain optimal sample complexity using quantum operations and classical post-processing only. Our protocols, in contrast to conventional ones, incur lower overheads and avoid sampling different quantum operations due to a novel technique called observable shift, making the protocols strong candidates for practical usage on current quantum devices. The proposed method also indicates the power of entangled protocols in retrieving high-order information, whereas in the existing methods, entanglement does not help. Our work contributes to a deeper understanding of how quantum noise could affect high-order information extraction and provides guidance on how to tackle it.

Publication
arXiv.2309.11403
Mingrui Jing
Mingrui Jing
PhD Student

I obtained my BS and MS degrees in physics from the University of Melbourne. My research interests include distributed quantum computing, quantum entanglement and quantum machine learning.

Lei Zhang
Lei Zhang
PhD Student

I obtained my BMath in AMath, CO & joint PMath from the University of Waterloo. My research interests include quantum information theory and quantum machine learning.

Xin Wang
Xin Wang
Associate Professor

The main focus of my research is to better understand the limits of information processing with quantum systems and the power of quantum artificial intelligence.