Stabilisers as a design tool for new forms of Lechner-Hauke-Zoller Annealer

Understand

In a recent paper Lechner, Hauke and Zoller (LHZ) described a means to translate a Hamiltonian of $N$ spin-$\frac{1}{2}$ particles with 'all-to-all' interactions into a larger physical lattice with only on-site energies and local parity constraints.

• LHZ used this mapping to propose a novel form of quantum annealing.
• Here we provide a stabiliser-based formulation within which we can describe both this prior approach and a wide variety of variants.
• Examples include a triangular array supporting all-to-all connectivity, and moreover arrangements requiring only $2N$ or $N\log N$ spins but providing interesting bespoke connectivities.