@article{discovery1556721,
           title = {Nonunitary quantum computation in the ground space of local Hamiltonians},
            year = {2017},
       publisher = {AMER PHYSICAL SOC},
         journal = {Physical Review A},
           month = {September},
          number = {3},
          volume = {96},
            note = {{\copyright}2017 American Physical Society. This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.},
             url = {http://doi.org/10.1103/PhysRevA.96.032321},
            issn = {2469-9934},
          author = {Usher, N and Hoban, MJ and Browne, DE},
        abstract = {A central result in the study of quantum Hamiltonian complexity is that the k-local Hamiltonian problem is
quantum-Merlin-Arthur-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian
is bounded below some value, or above another, promised one of these is true. Given the ground state of the
Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently
quantum preparable. Kitaev's proof of QMA-completeness encodes a unitary quantum circuit in QMA into the
ground space of a Hamiltonian. However, we now have quantum computing models based on measurement
instead of unitary evolution; furthermore, we can use postselected measurement as an additional computational
tool. In this work, we generalize Kitaev's construction to allow for nonunitary evolution including postselection.
Furthermore, we consider a type of postselection under which the construction is consistent, which we call tame
postselection. We consider the computational complexity consequences of this construction and then consider
how the probability of an event upon which we are postselecting affects the gap between the ground-state energy
and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the
two are not immediately related by giving a family of circuits where the probability of an event upon which we
postselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial.},
        keywords = {Science \& Technology, Physical Sciences, Optics, Physics, Atomic, Molecular \& Chemical, Physics, LINEAR OPTICS, COMPLEXITY}
}