Thrifty Shadow Estimation: Re-using Quantum Circuits and Bounding Tails

Watch a conference talk from TQC 2023 exploring the statistical efficiency of randomized shadow estimation in quantum computing, focusing on a new variant called thrifty shadow estimation. Learn how reusing quantum circuits instead of generating new ones for each measurement affects protocol efficiency, with analysis showing maximum effectiveness when sampling Haar random unitaries and minimum effectiveness with Clifford circuits. Discover an efficiently simulable family of quantum circuits based on approximate t-designs that bridges these extremes, while examining tail bounds and comparing median-of-means estimation with standard mean estimation. Delivered at the 18th Conference on the Theory of Quantum Computation, Communication and Cryptography at the University of Aveiro, this technical presentation draws from research published on arXiv and advances theoretical understanding of practical quantum computing implementations.