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.
Optimal short-time measurements for hamiltonian learning
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Establishes n^{Ω(k)} lower bounds for learning k-local Hamiltonians from time evolution, including single-coefficient and effective Hamiltonian learning, via a new connection to Boolean function analysis.
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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.
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Lower Bounds for Learning Hamiltonians from Time Evolution
Establishes n^{Ω(k)} lower bounds for learning k-local Hamiltonians from time evolution, including single-coefficient and effective Hamiltonian learning, via a new connection to Boolean function analysis.