In this article, we will introduce a method for estimating density matrix states using quantum shadow tomography. Quantum tomography is a technique for measuring the density matrix of a state and estimating the state using the fact that its elements can be represented by the direct product of Pauli operators [1]. This method was expected to be used to accurately estimate the density matrix in order to correctly estimate the state in noisy systems. However, this method cannot be applied to large-scale systems because the density matrix is expressed as a linear combination of ﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>4</mn><mi>n</mi></msup></mrow><annotation encoding="application/x-tex">4^n</annotation></semantics></math>4n﻿ Pauli matrix direct products for the number of qubits n used. Therefore, this method was developed to estimate the density matrix with a smaller number of observations. Quantum shadow tomography is a method of estimating the density matrix by editing the states in such a way that they can be successfully estimated with fewer observations. In the method of the paper, the density matrix is calculated separately for the diagonal and non-diagonal terms to reduce the number of observations. As a result, the density matrix in the GHZ state could be calculated with high accuracy. This method can be implemented in a circuit using a tensor network. So, I am planning to implement it when I get a chance. https://arxiv.org/pdf/2102.10132.pdf [1] https://qiita.com/SamN/items/ecbae603041317511969

Introduction of paper: Hamiltonian-Driven Shadow Tomography of Quantum States.

Hikaru Wakaura