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OP-9454Status unassessedQuantum information

Learning Hamiltonians using only long time evolutions

Learning Hamiltonians using only long time evolutions — original question and dated source context.

Historical source; current status unassessedAs of 2024-10-27Source & evidence ↓
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Problem statement

Let H=∑a=1mλaEaH=\sum_{a=1}^m\lambda_a E_a be an nn-qubit geometrically local Hamiltonian, where EaE_a are known constant-support Pauli products and −1≤λa≤1-1\leq\lambda_a\leq1. Learn its coefficients to additive error ε\varepsilon, given access only to ρ↦e−iHtρeiHt\rho\mapsto e^{-iHt}\rho e^{iHt} for t>100t>100. Is time-efficient learning possible, and can it achieve total evolution time O(log⁡(n)/ε)O(\log(n)/\varepsilon)?

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Progress & source assessment

Historical source dated 2024-10-27. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date.

References
  1. [1]Chen, Cotler, Huang, Li and Tang, Some Open Problems in Quantum Learning, FOCS 2024 workshop, slide 10 link
  2. [2]Ewin Tang, 2025 follow-up formulation and context link

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