# The detectability lemma and quantum gap amplification

@inproceedings{Aharonov2009TheDL, title={The detectability lemma and quantum gap amplification}, author={D. Aharonov and I. Arad and Zeph Landau and U. Vazirani}, booktitle={STOC '09}, year={2009} }

The quantum analogue of the constraint satisfaction problem is the fundamental physics question of finding the minimal energy state of a local Hamiltonian --- each term of the Hamiltonian specifies a local constraint whose violation contributes to the energy of the given quantum state. However, in general it is not meaningful to ask for the probability that a given quantum state violates at least one constraint; the difficulty being that the terms of the Hamiltonian do not commute. We show how… Expand

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