Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits

• URL: http://arxiv.org/abs/2412.18973v1
• Date: Wed, 25 Dec 2024 19:23:29 GMT
• Title: Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits
• Authors: Katherine Van Kirk, Christian Kokail, Jonathan Kunjummen, Hong-Ye Hu, Yanting Teng, Madelyn Cain, Jacob Taylor, Susanne F. Yelin, Hannes Pichler, Mikhail Lukin,
• Abstract summary: We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting quantum observables. Exploiting tensor network techniques, our algorithm outputs a set of shallow measurement circuits. Results indicate that DSS can also benefit many larger algorithms requiring estimation of multiple non-commuting observables.
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• Abstract: Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting observables, using shallow circuits to rotate into measurement bases. Exploiting tensor network techniques to ensure polynomial scaling of classical resources, our algorithm outputs a set of shallow measurement circuits that approximately minimizes the sample complexity of estimating a given set of Pauli strings. We numerically demonstrate systematic improvement, in comparison with state-of-the-art techniques, for energy estimation of quantum chemistry benchmarks and verification of quantum many-body systems, and we observe DSS's performance consistently improves as one allows deeper measurement circuits. These results indicate that in addition to being an efficient, low-depth, stand-alone algorithm, DSS can also benefit many larger quantum algorithms requiring estimation of multiple non-commuting observables.

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