Stabiliser sets and physical ancillas for the Lechner-Hauke-Zoller Annealer
Andrea Rocchetto, Simon C. Benjamin, Ying Li · arXiv (Cornell University) · 2016
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 of this approach, which permits some generalisation to the parity constraints proposed by LHZ. One variant we obtain may simplify the physical realisation since the required ancillas are only spin-$\frac{1}{2}$ systems (i.e.~qubits, rather than qutrits) and moreover the interactions {are} very simple. We make a preliminary assessment of the impact of different design choices by simulating small (few-qubit) systems; we find some indications that the new variant may maintain a larger minimum energy gap during the annealing process.