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Efficient and robust estimation of many-qubit Hamiltonians

Author

Listed:
  • Daniel Stilck França

    (University of Copenhagen
    Univ Lyon, ENS Lyon, UCBL, CNRS, Inria, LIP)

  • Liubov A. Markovich

    (Delft University of Technology
    Universiteit Leiden)

  • V. V. Dobrovitski

    (Delft University of Technology)

  • Albert H. Werner

    (University of Copenhagen
    University of Copenhagen)

  • Johannes Borregaard

    (Delft University of Technology
    Harvard University)

Abstract

Characterizing the interactions and dynamics of quantum mechanical systems is an essential task in developing quantum technologies. We propose an efficient protocol based on the estimation of the time-derivatives of few qubit observables using polynomial interpolation for characterizing the underlying Hamiltonian dynamics and Markovian noise of a multi-qubit device. For finite range dynamics, our protocol exponentially relaxes the necessary time-resolution of the measurements and quadratically reduces the overall sample complexity compared to previous approaches. Furthermore, we show that our protocol can characterize the dynamics of systems with algebraically decaying interactions. The implementation of the protocol requires only the preparation of product states and single-qubit measurements. Furthermore, we improve a shadow tomography method for quantum channels that is of independent interest and discuss the robustness of the protocol to various errors. This protocol can be used to parallelize the learning of the Hamiltonian, rendering it applicable for the characterization of both current and future quantum devices.

Suggested Citation

  • Daniel Stilck França & Liubov A. Markovich & V. V. Dobrovitski & Albert H. Werner & Johannes Borregaard, 2024. "Efficient and robust estimation of many-qubit Hamiltonians," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-023-44012-5
    DOI: 10.1038/s41467-023-44012-5
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    References listed on IDEAS

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    1. Sepehr Ebadi & Tout T. Wang & Harry Levine & Alexander Keesling & Giulia Semeghini & Ahmed Omran & Dolev Bluvstein & Rhine Samajdar & Hannes Pichler & Wen Wei Ho & Soonwon Choi & Subir Sachdev & Marku, 2021. "Quantum phases of matter on a 256-atom programmable quantum simulator," Nature, Nature, vol. 595(7866), pages 227-232, July.
    2. Frank Arute & Kunal Arya & Ryan Babbush & Dave Bacon & Joseph C. Bardin & Rami Barends & Rupak Biswas & Sergio Boixo & Fernando G. S. L. Brandao & David A. Buell & Brian Burkett & Yu Chen & Zijun Chen, 2019. "Quantum supremacy using a programmable superconducting processor," Nature, Nature, vol. 574(7779), pages 505-510, October.
    3. M. D. Shulman & S. P. Harvey & J. M. Nichol & S. D. Bartlett & A. C. Doherty & V. Umansky & A. Yacoby, 2014. "Suppressing qubit dephasing using real-time Hamiltonian estimation," Nature Communications, Nature, vol. 5(1), pages 1-6, December.
    4. Pascal Scholl & Michael Schuler & Hannah J. Williams & Alexander A. Eberharter & Daniel Barredo & Kai-Niklas Schymik & Vincent Lienhard & Louis-Paul Henry & Thomas C. Lang & Thierry Lahaye & Andreas M, 2021. "Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms," Nature, Nature, vol. 595(7866), pages 233-238, July.
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