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 two qubits, the Bell states are |𝜎00⟩= 1√ 2(|00⟩+|11⟩),|𝜎 01⟩= 1√ 2(|00⟩ − |11⟩),|𝜎 10⟩= 1√ 2(|01⟩+|10⟩),|𝜎 11⟩= 1√ 2(|01⟩ − |10⟩)
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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.