Efficient and robust estimation of many-qubit Hamiltonians

• Published in: Nature communications Vol. 15; no. 1; p. 311
• Main Authors: Stilck França, Daniel, Markovich, Liubov A., Dobrovitski, V. V., Werner, Albert H., Borregaard, Johannes
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 08-01-2024; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/483/3926; 639/766/483/481; Dynamics; Estimation; Hamiltonian functions; Humanities and Social Sciences; Interpolation; Learning; Mathematical analysis; Mechanical systems; multidisciplinary; Physics; Polynomials; Protocol; Quantum mechanics; Quantum Physics; Qubits (quantum computing); Robustness; Science; Science (multidisciplinary); Tomography
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-023-44012-5

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.
Learning Hamiltonians or Lindbladians of quantum systems from experimental data is important for characterization of interactions and noise processes in quantum devices. Here the authors propose an efficient protocol based on estimating time derivatives using multiple temporal sampling points and robust polynomial interpolation.