Improved Machine Learning Algorithm for Predicting Ground State Properties
summary
A classical ML pipeline encodes geometric locality into a feature map, uses L1‑regularized regression (LASSO) plus classical shadows and proven bounds (spectral flow, Lieb‑Robinson) to approximate ground‑state observables of gapped local n‑qubit Hamiltonians with only O(log n) training samples, improving from prior polynomial sample requirements, and achieves O(n log n) runtime for training and prediction; numerical experiments on physical models up to 45 qubit numerics show the method predicts two‑body correlations with small datasets.
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chapters (17)
- 0:00Introduction
- 0:30Motivation
- 3:07Parameterization
- 4:38Ground State Properties
- 6:23Ground State Representation
- 9:57Efficient Classical Machine Learning
- 11:19Key Additional Assumption
- 17:27Does this have any implication on solving NPR problems
- 23:04Feature mapping
- 24:31Implementation
- 35:17Ideas behind the proof
- 37:04Proof
- 44:08Locality Properties
- 50:33Norm Inequality
- 53:30Proof Summary
- 54:45Numerical Experiments
- 55:50Numerical Results
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