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On the natural gradient for variational quantum eigensolver
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The variational quantum eigensolver is a hybrid algorithm composed of quantum state driving and classical parameter optimization, for finding the ground state of a given Hamiltonian. The natural gradient method is an optimization method taking into account the geometric structure of the parameter space. Very recently, Stokes et al. developed the general method for employing the natural gradient for the variational quantum eigensolver. This paper gives some simple case-studies of this optimization method, to see in detail how the natural gradient optimizer makes use of the geometric property to change and improve the ordinary gradient method.
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Cited by 2 Pith papers
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Benchmarking a wide range of optimisers for solving the Fermi-Hubbard model using the variational quantum eigensolver
A 372-instance numerical benchmark of VQE for Fermi-Hubbard finds Momentum and Adam with finite differences achieve the best accuracy, while SPSA and CMAES minimize function calls.
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Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise
A generalization bound for noisy parameterized quantum classifiers is derived from quantum Fisher information, parameter-space volume, and sample size, with local refinements claimed to tighten it.
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