Performance analysis of multi-shot shadow estimation

نویسندگان

چکیده

Shadow estimation is an efficient method for predicting many observables of a quantum state with statistical guarantee. In the multi-shot scenario, one performs projective measurement on sequentially prepared K times after same unitary evolution, and repeats this procedure xmlns:mml="http://www.w3.org/1998/Math/MathML">M rounds random sampled unitary. As result, there are xmlns:mml="http://www.w3.org/1998/Math/MathML">MK measurements in total. Here we analyze performance shadow which characterized by variance estimating expectation value some observable xmlns:mml="http://www.w3.org/1998/Math/MathML">O. We find that addition to shadow-norm xmlns:mml="http://www.w3.org/1998/Math/MathML">‖O‖shadow introduced \cite{huang2020predicting}, also related another norm, denote it as cross-shadow-norm mathvariant="normal">Xw. For both Pauli Clifford measurements, show upper bounds particular, figure out exact formula under measurements. Our work gives theoretical guidance application estimation.

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ژورنال

عنوان ژورنال: Quantum

سال: 2023

ISSN: ['2521-327X']

DOI: https://doi.org/10.22331/q-2023-06-29-1044