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OP-9455Status unassessedQuantum information

System-size lower bounds for Hamiltonian learning

System-size lower bounds for Hamiltonian learning — original question and dated source context.

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

For learning an nn-qubit local Hamiltonian from real-time evolution to coefficient error ε\varepsilon, must the total evolution time depend on nn? Can one prove a lower bound of order log⁡(n)/ε\log(n)/\varepsilon, beyond the Ω(1/ε)\Omega(1/\varepsilon) bound stated in the 2024 source? Is dependence on the one-spin energy max⁡i∈[n]∑a: i∈supp⁡(Ea)∥λaEa∥\max_{i\in[n]}\sum_{a:\,i\in\operatorname{supp}(E_a)}\|\lambda_aE_a\| necessary? See the preceding source slide for the learning model.

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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 11 link

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