This content will become publicly available on December 14, 2024
 Award ID(s):
 2226908
 NSFPAR ID:
 10492300
 Publisher / Repository:
 The ThirtySeventh Annual Conference on Neural Information Processing Systems (NeurIPS 2023)
 Date Published:
 Journal Name:
 The ThirtySeventh Annual Conference on Neural Information Processing Systems (NeurIPS 2023)
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Implicit solvent models divide solvation free energies into polar and nonpolar additive contributions, whereas polar and nonpolar interactions are inseparable and nonadditive. We present a feature functional theory (FFT) framework to break this
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INTRODUCTION Solving quantum manybody problems, such as finding ground states of quantum systems, has farreaching consequences for physics, materials science, and chemistry. Classical computers have facilitated many profound advances in science and technology, but they often struggle to solve such problems. Scalable, faulttolerant quantum computers will be able to solve a broad array of quantum problems but are unlikely to be available for years to come. Meanwhile, how can we best exploit our powerful classical computers to advance our understanding of complex quantum systems? Recently, classical machine learning (ML) techniques have been adapted to investigate problems in quantum manybody physics. So far, these approaches are mostly heuristic, reflecting the general paucity of rigorous theory in ML. Although they have been shown to be effective in some intermediatesize experiments, these methods are generally not backed by convincing theoretical arguments to ensure good performance. RATIONALE A central question is whether classical ML algorithms can provably outperform nonML algorithms in challenging quantum manybody problems. We provide a concrete answer by devising and analyzing classical ML algorithms for predicting the properties of ground states of quantum systems. We prove that these ML algorithms can efficiently and accurately predict groundstate properties of gapped local Hamiltonians, after learning from data obtained by measuring other ground states in the same quantum phase of matter. Furthermore, under a widely accepted complexitytheoretic conjecture, we prove that no efficient classical algorithm that does not learn from data can achieve the same prediction guarantee. By generalizing from experimental data, ML algorithms can solve quantum manybody problems that could not be solved efficiently without access to experimental data. 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Our proof of this result builds on recent developments in quantum information theory, computational learning theory, and condensed matter theory. Furthermore, under the widely accepted conjecture that nondeterministic polynomialtime (NP)–complete problems cannot be solved in randomized polynomial time, we prove that no polynomialtime classical algorithm that does not learn from data can match the prediction performance achieved by the ML algorithm. In a related contribution using similar proof techniques, we show that classical ML algorithms can efficiently learn how to classify quantum phases of matter. In this scenario, the training data consist of classical representations of quantum states, where each state carries a label indicating whether it belongs to phase A or phase B . The ML algorithm then predicts the phase label for quantum states that were not encountered during training. The classical ML algorithm not only classifies phases accurately, but also constructs an explicit classifying function. Numerical experiments verify that our proposed ML algorithms work well in a variety of scenarios, including Rydberg atom systems, twodimensional random Heisenberg models, symmetryprotected topological phases, and topologically ordered phases. CONCLUSION We have rigorously established that classical ML algorithms, informed by data collected in physical experiments, can effectively address some quantum manybody problems. These rigorous results boost our hopes that classical ML trained on experimental data can solve practical problems in chemistry and materials science that would be too hard to solve using classical processing alone. Our arguments build on the concept of a succinct classical representation of quantum states derived from randomized Pauli measurements. 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