Quantum State Reconstruction Through Online Shadow Tomography: Theoretical Framework and Simulation Results

Abstract

The purpose of this research work is to learn the quantum states in an ideal environments analytically, computationally, and graphically. The analysis starts with the learning of quantum states in identity channels with the help of the Regularized Follow the Leader (RFTL) algorithm. Our machine will try to learn the states based on the previous information, which is called the online learning model. The objective of this problem is to minimize regret by utilizing a learning algorithm that successively anticipates quantum states through observed measurements and losses. We have to produce many copies of quantum state ρ to perform analysis on them, which indicates the use of the shadow tomography approach in an ideal situation. Our goal is to learn the shadow of the state ρ by using a series of measurement operators that have two outcomes in nature. Aaronson et al. [1] developed an online setting for a non-realizable case, where the maximum possible loss is O( √ Tn) for the best possible state up to T−measurements . It is noteworthy that this outcome is an extension of the Aaronson PAC-like findings [2].

GANIT J. Bangladesh Math. Soc. 43.1 (2023) 65-74