Robust and Efficient Hamiltonian Learning

doi:10.22331/q-2023-06-29-1045

Robust and Efficient Hamiltonian Learning

2023-06-29

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DOI：10.22331/q-2023-06-29-1045

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With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the interaction, i.e., to learn the Hamiltonian, which determines both static and dynamic properties of the system. Conventional Hamiltonian learning methods either require costly process tomography or adopt impractical assumptions, such as prior information on the Hamiltonian structure and the ground or thermal states of the system. In this work, we present a robust and efficient Hamiltonian learning method that circumvents these limitations based only on mild assumptions. The proposed method can efficiently learn any Hamiltonian that is sparse on the Pauli basis using only short-time dynamics and local operations without any information on the Hamiltonian or preparing any eigenstates or thermal states. The method has a scalable complexity and a vanishing failure probability regarding the qubit number. Meanwhile, it performs robustly given the presence of state preparation and measurement errors and resiliently against a certain amount of circuit and shot noise. We numerically test the scaling and the estimation accuracy of the method for transverse field Ising Hamiltonian with random indynamics of large quantum systems.

Keywords:

RESTRICTED ISOMETRY PROPERTY

QUANTUM PROCESS

COMPLEXITY

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Robust and Efficient Hamiltonian Learning

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