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Hamiltonian property testing requires significant evolution time, researchers find

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Researchers have established lower bounds for Hamiltonian property testing, demonstrating that certain tasks require a significant amount of evolution time. Specifically, testing if a Hamiltonian is k-local or distinguishing it from a target Hamiltonian necessitates $\Omega(1/\varepsilon^2)$ total evolution time. This finding matches existing upper bounds and is the first time such lower bounds have been proven for Hamiltonian learning and testing problems, ruling out Heisenberg-limited scaling. The research also shows that amplitude estimation to a precision of $\varepsilon$ requires $\Omega(1/\varepsilon^2)$ total time evolution. AI

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Hamiltonian property testing requires significant evolution time, researchers find

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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Francisco Escudero Guti\'errez, Junseo Lee, Sebastian Zur ·

    Hamiltonian locality testing and certification do not achieve the Heisenberg limit

    arXiv:2610.03205v1 Announce Type: cross Abstract: We establish lower bounds for Hamiltonian property testing with access to the time-evolution operator but not its inverse. Each experiment may query the time-evolution operator multiple times, and distances between Hamiltonians ar…

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