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.
We begin with Duhamel’s principle, which provides a convenient way to express and bound𝑒−𝑖𝑋𝑡 𝑒𝑖𝑌 𝑡
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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.