@article {1396,
title = {QMA-complete problems for stoquastic Hamiltonians and Markov matrices},
journal = {Physical Review A},
volume = {81},
year = {2010},
month = {2010/3/29},
abstract = { We show that finding the lowest eigenvalue of a 3-local symmetric stochastic
matrix is QMA-complete. We also show that finding the highest energy of a
stoquastic Hamiltonian is QMA-complete and that adiabatic quantum computation
using certain excited states of a stoquastic Hamiltonian is universal. We also
show that adiabatic evolution in the ground state of a stochastic frustration
free Hamiltonian is universal. Our results give a new QMA-complete problem
arising in the classical setting of Markov chains, and new adiabatically
universal Hamiltonians that arise in many physical systems.
},
doi = {10.1103/PhysRevA.81.032331},
url = {http://arxiv.org/abs/0905.4755v2},
author = {Stephen P. Jordan and David Gosset and Peter J. Love}
}
@article {1399,
title = {Polynomial-time quantum algorithm for the simulation of chemical dynamics
},
journal = {Proceedings of the National Academy of Sciences},
volume = {105},
year = {2008},
month = {2008/11/24},
pages = {18681 - 18686},
abstract = { The computational cost of exact methods for quantum simulation using
classical computers grows exponentially with system size. As a consequence,
these techniques can only be applied to small systems. By contrast, we
demonstrate that quantum computers could exactly simulate chemical reactions in
polynomial time. Our algorithm uses the split-operator approach and explicitly
simulates all electron-nuclear and inter-electronic interactions in quadratic
time. Surprisingly, this treatment is not only more accurate than the
Born-Oppenheimer approximation, but faster and more efficient as well, for all
reactions with more than about four atoms. This is the case even though the
entire electronic wavefunction is propagated on a grid with appropriately short
timesteps. Although the preparation and measurement of arbitrary states on a
quantum computer is inefficient, here we demonstrate how to prepare states of
chemical interest efficiently. We also show how to efficiently obtain
chemically relevant observables, such as state-to-state transition
probabilities and thermal reaction rates. Quantum computers using these
techniques could outperform current classical computers with one hundred
qubits.
},
doi = {10.1073/pnas.0808245105},
url = {http://arxiv.org/abs/0801.2986v3},
author = {Ivan Kassal and Stephen P. Jordan and Peter J. Love and Masoud Mohseni and Al{\'a}n Aspuru-Guzik}
}