Frustrated local Hamiltonians can sometimes be steered into their ground-state manifold via discrete local measurement steps, and when they cannot, local steering is bounded by a 'glass floor' set by the smallest eigenvalue of local reduced density matrices.
Commuting Pauli Hamiltonians are n-qubit Hamiltonians of the form H = P i H (i), where each term H (i) belongs to the Pauli group and satisfies [ H (i), H(j)] = 0 for all i, j
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State Engineering of Unsteerable Hamiltonians
Frustrated local Hamiltonians can sometimes be steered into their ground-state manifold via discrete local measurement steps, and when they cannot, local steering is bounded by a 'glass floor' set by the smallest eigenvalue of local reduced density matrices.