Heisenberg-limited Hamiltonian learning is achievable with any constant minimum evolution time T per query, attaining optimal 1/Ξ΅ total-time scaling for logarithmically sparse Hamiltonians.
From the previous section, we have|supp π (ππ)| β€4 π, which becomes exponential inπ
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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/Ξ΅ total-time scaling for logarithmically sparse Hamiltonians.