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<https://discovery.ucl.ac.uk/id/eprint/1556721> <http://purl.org/ontology/bibo/abstract> "A central result in the study of quantum Hamiltonian complexity is that the k-local Hamiltonian problem is\r\nquantum-Merlin-Arthur–complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian\r\nis bounded below some value, or above another, promised one of these is true. Given the ground state of the\r\nHamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently\r\nquantum preparable. Kitaev’s proof of QMA-completeness encodes a unitary quantum circuit in QMA into the\r\nground space of a Hamiltonian. However, we now have quantum computing models based on measurement\r\ninstead of unitary evolution; furthermore, we can use postselected measurement as an additional computational\r\ntool. In this work, we generalize Kitaev’s construction to allow for nonunitary evolution including postselection.\r\nFurthermore, we consider a type of postselection under which the construction is consistent, which we call tame\r\npostselection. We consider the computational complexity consequences of this construction and then consider\r\nhow the probability of an event upon which we are postselecting affects the gap between the ground-state energy\r\nand the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the\r\ntwo are not immediately related by giving a family of circuits where the probability of an event upon which we\r\npostselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial."^^<http://www.w3.org/2001/XMLSchema#string> .
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