Adaptive Learning of Quantum Hamiltonians
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Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Keywords: Hamiltonian Learning, Quantum Learning Theory, Iterative Scaling, Convergence, Quasi-Newton Methods, Anderson Mixing
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Abstract: The challenge of learning representations for quantum Hamiltonian systems resides at the intersection of quantum information and learning theory. Viewed through the lens of learning theory, this task can be regarded as the non-commutative counterpart to learning graphical models. In our research, we design and analyze adaptive learning algorithms, including the quantum iterative scaling algorithm (QIS) and gradient descent (GD), for the Hamiltonian inference problem using adaptive Gibbs state oracles. Our principal technical contribution centers on the thorough analysis of their convergence rates, involving the establishment of both lower and upper bounds on the spectrum of the Jacobian matrix for each iteration of these algorithms. Furthermore, we explore quasi-Newton methods to enhance the performance of both QIS and GD. Specifically, we propose the use of Anderson mixing and the L-BFGS method for QIS and GD, respectively. These quasi-Newton techniques exhibit remarkable efficiency gains, resulting in orders of magnitude improvements in performance.
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Submission Number: 5716
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