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OP-9456Status unassessedQuantum information

Does amplitude estimation require the inverse unitary?

Does amplitude estimation require the inverse unitary? — original question and dated source context.

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

Estimate ∣⟨0∣U∣0⟩∣2|\langle0|U|0\rangle|^2 to error ε\varepsilon with constant high success probability for an unknown dd-dimensional unitary UU. Access to UU and U†U^\dagger allows O(1/ε)O(1/\varepsilon) uses via amplitude estimation, whereas independent sampling uses O(1/ε2)O(1/\varepsilon^2). Prove a separation between forward-only access and access to both directions, for sufficiently large dd.

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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 12 link
  2. [2]Ewin Tang, 2025 follow-up formulation and context link

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