Robust and Efficient Hamiltonian Learning
Author:
Yu Wenjun12, Sun Jinzhao34, Han Zeyao5, Yuan Xiao2
Affiliation:
1. QICI, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China 2. Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China 3. Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK 4. Quantum Advantage Research, Beijing 100080, China 5. School of Physics, Peking University, Beijing 100871, China
Abstract
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 interaction strengths and molecular Hamiltonians, both with varying sizes and manually added noise. All these results verify the robustness and efficacy of the method, paving the way for a systematic understanding of the dynamics of large quantum systems.
Publisher
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Subject
Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics
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