Heisenberg-limited Hamiltonian learning is achievable with any constant minimum evolution time T per query, attaining optimal 1/ε total-time scaling for logarithmically sparse Hamiltonians.
For convenience, define a unitary𝑉satisfying𝑉(𝑃 𝑥 ⊗𝐼)|Φ⟩=|𝑥⟩for all𝑥
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Heisenberg-limited Hamiltonian learning without short-time control
Heisenberg-limited Hamiltonian learning is achievable with any constant minimum evolution time T per query, attaining optimal 1/ε total-time scaling for logarithmically sparse Hamiltonians.