Predicting Many Properties of a Quantum System from Very Few Measurements

Explore a comprehensive lecture on quantum state prediction and measurement techniques in this talk by Richard Kueng from Caltech. Delve into the intricacies of quantum state tomography, shadow tomography, and the main question of predicting multiple properties of a quantum system from limited measurements. Examine the process of predicting single and multiple linear properties, and understand the general results and specific examples involving global and local Clifford circuits. Analyze numerical runtime comparisons and discover the concept of classical shadows and their asymptotic optimality. Gain valuable insights into quantum protocols, testing, and quantum PCPs through this in-depth presentation from the Simons Institute.

Intro
Table of Contents
Quantum state tomography
Shadow tomography
Main question
Predicting a single linear property
Predicting many linear properties
General result
Example l: global Clifford circuits
Example 1: local Clifford circuits
Numerics I+II: runtime comparison
Classical shadows: asymptotic optimality