Improved machine learning algorithm for predicting ground state properties

Lewis, L. H.; Huang, Hsin-Yuan; Tran, Viet T.; Lehner, S.; Kueng, Richard; Preskill, John

doi:10.48550/arxiv.2301.13169

Cited by 1 publication

(1 citation statement)

References 33 publications

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“…Other than the above-mentioned approach, recently a combination of structural assumptions on quantum states with the classical shadow has been found to achieve better sample complexity for estimating observables. It has been shown that exponential improvements in the sample complexity hold for some specific quantum states such as high-temperature Gibbs states of commuting Hamiltonians or outputs of shallow circuits [34]; quantum Gibbs states of non-commuting Hamiltonians with exponential decay of correlations [35]; ground states of gapped local Hamiltonians [36]. Thus, there is another room for improvements to reduce the variance of the estimation in practice.…”

Section: Estimator Of the Negative Qce: Classical Shadow Approachmentioning

confidence: 99%

Quantum information criteria for model selection in quantum state estimation

Yano,

Yamamoto

2023

J. Phys. A: Math. Theor.

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Quantum state estimation (or state tomography) is an indispensable task in quantum information processing. Because full state tomography that determines all elements of the density matrix is computationally demanding, one usually takes the strategy of assuming a certain model of quantum states and identifying the model parameters. However, it is difficult to make a valid assumption given little prior knowledge on a quantum state of interest, and thus we need a reasonable model selection method for quantum state estimation. Actually, in the classical statistical estimation theory, several types of information criteria have been established and widely used in practice for appropriately choosing a classical statistical model. In this study, we propose quantum information criteria for evaluating the quality of the estimated quantum state in terms of the quantum relative entropy, which is a natural quantum analogue of the classical information criterion defined in terms of Kullback–Leibler divergence. In particular, we derive two quantum information criteria depending on the type of estimator for the quantum relative entropy; one uses the log-likelihood and the other uses the classical shadow. The general role of information criteria is to predict the performance of an estimated model for unseen data, although it is a function of only sampled data; this generalization capability of the proposed quantum information criteria is evaluated in numerical simulations.

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Section: Estimator Of the Negative Qce: Classical Shadow Approachmentioning

confidence: 99%