  In his famous 1981 talk, Feynman proposed that unlike classical computers,
which would presumably experience an exponential slowdown when simulating
quantum phenomena, a universal quantum simulator would not. An ideal quantum
simulator would be controllable, and built using existing technology. In some
cases, moving away from gate-model-based implementations of quantum computing
may offer a more feasible solution for particular experimental implementations.
Here we consider an adiabatic quantum simulator which simulates the ground
state properties of sparse Hamiltonians consisting of one- and two-local
interaction terms, using sparse Hamiltonians with at most three-local
interactions. Properties of such Hamiltonians can be well approximated with
Hamiltonians containing only two-local terms. The register holding the
simulated ground state is brought adiabatically into interaction with a probe
qubit, followed by a single diabatic gate operation on the probe which then
undergoes free evolution until measured. This allows one to recover e.g. the
ground state energy of the Hamiltonian being simulated. Given a ground state,
this scheme can be used to verify the QMA-complete problem LOCAL HAMILTONIAN,
and is therefore likely more powerful than classical computing.
