**A simple nearest-neighbour two-body Hamiltonian system for which the ground state is a universal resource for quantum computation** - Steve Bartlett

We present a simple quantum many-body system - a two-dimensional lattice of
qubits with a Hamiltonian composed of nearest-neighbour two-body
interactions - such that the ground state is a universal resource for
quantum computation using single-qubit measurements. This ground state
approximates a cluster state that is encoded into a larger number of
physical qubits. The Hamiltonian we use is motivated by the projected
entangled pair states, which provide a transparent mechanism to produce such
approximate encoded cluster states on square or other lattice structures (as
well as a variety of other quantum states) as the ground state. We show that
the error in this approximation takes the form of independent errors on
bonds occurring with a fixed probability. The energy gap of such a system,
which in part determines its usefulness for quantum computation, is shown to
be independent of the size of the lattice. In addition, we show that the
scaling of this energy gap in terms of the coupling constants of the
Hamiltonian is directly determined by the lattice geometry. As a result, the
approximate encoded cluster state obtained on a hexagonal lattice (a
resource that is also universal for quantum computation) can be shown to
have a larger energy gap than one on a square lattice with an equivalent
Hamiltonian.