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Adaptive estimation of quantum observables

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Ariel Shlosberg1,2, Andrew J. Jena3,4, Priyanka Mukhopadhyay3,4, Jan F. Haase3,5,6, Felix Leditzky3,4,7,8, and Luca Dellantonio3,5,9

1JILA, University of Colorado and National Institute of Standards and Technology, Boulder, CO 80309, USA
2Department of Physics, University of Colorado, Boulder, CO 80309, USA
3Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada
4Department of Combinatorics & Optimization, University of Waterloo, Waterloo, ON N2L 3G1, Canada
5Department of Physics & Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
6Institute of Theoretical Physics and IQST, Universität Ulm, D-89069 Ulm, Germany
7Department of Mathematics and IQUIST, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA
8Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada
9Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom

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Abstract

The accurate estimation of quantum observables is a critical task in science. With progress on the hardware, measuring a quantum system will become increasingly demanding, particularly for variational protocols that require extensive sampling. Here, we introduce a measurement scheme that adaptively modifies the estimator based on previously obtained data. Our algorithm, which we call AEQuO, continuously monitors both the estimated average and the associated error of the considered observable, and determines the next measurement step based on this information. We allow both for overlap and non-bitwise commutation relations in the subsets of Pauli operators that are simultaneously probed, thereby maximizing the amount of gathered information. AEQuO comes in two variants: a greedy bucket-filling algorithm with good performance for small problem instances, and a machine learning-based algorithm with more favorable scaling for larger instances. The measurement configuration determined by these subroutines is further post-processed in order to lower the error on the estimator. We test our protocol on chemistry Hamiltonians, for which AEQuO provides error estimates that improve on all state-of-the-art methods based on various grouping techniques or randomized measurements, thus greatly lowering the toll of measurements in current and future quantum applications.

Quantum systems, as opposed to classical ones, are irreversibly destroyed every time they are measured. This has deep implications when one wants to extract information from a quantum system. For instance, when one must estimate the average value of an observable, it is often required to repeat the whole experiment several times. Depending on the measurement strategy employed, the requirements to achieve the same precision vary considerably. In this work, we propose a new approach that considerably lowers the resources on the hardware. Our strategy is adaptive, in the sense that learns and improves the measurement allocation while data is being acquired. Furthermore, it allows for estimating both the average and the error affecting the desired observable at the same time. Compared with other state-of-the-art approaches, we demonstrate consistent and considerable improvement in the accuracy of estimation when our protocol is employed.

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Cited by

[1] Andreas Elben, Steven T. Flammia, Hsin-Yuan Huang, Richard Kueng, John Preskill, Benoît Vermersch, and Peter Zoller, “The randomized measurement toolbox”, Nature Reviews Physics 5 1, 9 (2023).

[2] Zachary Pierce Bansingh, Tzu-Ching Yen, Peter D. Johnson, and Artur F. Izmaylov, “Fidelity overhead for non-local measurements in variational quantum algorithms”, arXiv:2205.07113, (2022).

[3] Masaya Kohda, Ryosuke Imai, Keita Kanno, Kosuke Mitarai, Wataru Mizukami, and Yuya O. Nakagawa, “Quantum expectation-value estimation by computational basis sampling”, Physical Review Research 4 3, 033173 (2022).

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[6] Bojia Duan and Chang-Yu Hsieh, “Hamiltonian-based data loading with shallow quantum circuits”, Physical Review A 106 5, 052422 (2022).

[7] Daniel Miller, Laurin E. Fischer, Igor O. Sokolov, Panagiotis Kl. Barkoutsos, and Ivano Tavernelli, “Hardware-Tailored Diagonalization Circuits”, arXiv:2203.03646, (2022).

[8] Francisco Escudero, David Fernández-Fernández, Gabriel Jaumà, Guillermo F. Peñas, and Luciano Pereira, “Hardware-efficient entangled measurements for variational quantum algorithms”, arXiv:2202.06979, (2022).

[9] William Kirby, Mario Motta, and Antonio Mezzacapo, “Exact and efficient Lanczos method on a quantum computer”, arXiv:2208.00567, (2022).

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The above citations are from SAO/NASA ADS (last updated successfully 2023-01-26 13:33:05). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2023-01-26 13:33:03: Could not fetch cited-by data for 10.22331/q-2023-01-26-906 from Crossref. This is normal if the DOI was registered recently.

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