A provable exponential quantum-classical learning separation is established for predicting expectation values of time-evolved quantum states under unknown low-intersection Hamiltonians, assuming BQP ⊄ P/poly.
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Low-energy eigenstates of a spin chain allow a neural network to reconstruct the Hamiltonian accurately, while mid-spectrum eigenstates do not, defining a spectral 'learnability' gap.
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Provable learning separation for predicting time-evolution of quantum many-body systems
A provable exponential quantum-classical learning separation is established for predicting expectation values of time-evolved quantum states under unknown low-intersection Hamiltonians, assuming BQP ⊄ P/poly.
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Information in Many-body Eigenstates: A Question of Learnability
Low-energy eigenstates of a spin chain allow a neural network to reconstruct the Hamiltonian accurately, while mid-spectrum eigenstates do not, defining a spectral 'learnability' gap.