IQIM Virtual Seminar, April 17, 2020 - Hsin-Yuan (Robert) Huang

Speaker: Hsin-Yuan (Robert) Huang, Graduate student, Vidick/Preskill groups
Title: Predicting Many Properties of a Quantum System from Very Few Measurements
Abstract:
Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties: order log(M) measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods. (This work will appear on Nature Physics and the arXiv link is at arxiv.org/abs/2002.08953)

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From few measurements there has to be mistakes in the overall outcome . It is like being told there is a room full of furniture you have never seen and do not know the type of furniture therein . You describe the furniture with a few known ideas but wen you enter the room you realize you have left out many pieces of furniture that a key to the setting. :O)