Efficient and robust estimation of many-qubit Hamiltonians

Daniel Stilck França (), Liubov A. Markovich, V. V. Dobrovitski, Albert H. Werner and Johannes Borregaard
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Daniel Stilck França: University of Copenhagen
Liubov A. Markovich: Delft University of Technology
V. V. Dobrovitski: Delft University of Technology
Albert H. Werner: University of Copenhagen
Johannes Borregaard: Delft University of Technology

Nature Communications, 2024, vol. 15, issue 1, 1-11

Abstract: 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.

Date: 2024
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DOI: 10.1038/s41467-023-44012-5

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