Andras Gilyen: On preparing ground states of gapped Hamiltonians

Опубликовано 1 февраля 2017, 1:28

"A frustration-free local Hamiltonian has the property that its ground state minimises the energy of all terms simultaneously. In general, deciding whether a Hamiltonian is frustration-free is a hard problem, but the Quantum Lovász Local Lemma (QLLL) provides a sufficient condition for it. A natural question is whether there is an efficient way to prepare a frustration-free state under the conditions of the QLLL. Previous results showed that the answer is positive if all local terms commute.

In this work we improve on the previous constructive results by designing an algorithm that works efficiently for non-commuting terms as well, assuming that the system is ``strongly"" gapped -- i.e., the system and all its subsystems are poly-gapped. Also, our analysis works under the most general form of QLLL, known as Shearer's bound. Moreover, similarly to the previous results, our algorithm has the charming feature that it uses only local measurement operations corresponding to the Hamiltonian terms."