A system configured for generating a ground state having non-Abelian topological order, the system comprising:
- a confinement apparatus configured to confine a plurality of physical qubits;
- one or more manipulation sources configured to generate respective manipulation signals for interaction with respective physical qubits of the plurality of physical qubits;
- and
- a controller configured to control operation of the confinement apparatus and the one or more manipulation sources, the controller configured to perform:
- causing the plurality of physical qubits to be confined by the confinement apparatus, the plurality of physical qubits being logically organized onto a lattice comprising a plurality of vertices connected by edges and a plurality of plaquettes, wherein the lattice is formed of a plurality of sublattices, wherein each sublattice comprises a respective three or more vertices of the plurality of vertices and a respective one or more plaquettes of the plurality of plaquettes, the respective three or more vertices and the respective one or more plaquettes of a sublattice of the plurality of sublattices are connected by edges to form the sublattice;
- causing entanglement of vertex qubits of the plurality of physical qubits assigned to the respective three or more vertices of a respective sublattice in a first subset of sublattices with one or more plaquette qubits of the plurality of physical qubits assigned to the respective one or more plaquettes of the respective sublattice in the first subset of sublattices;
- causing measurement of the one or more plaquette qubits assigned to the respective one or more plaquettes of the respective sublattice in the first subset of sublattices;
- causing entanglement of physical qubits of the plurality of physical qubits assigned to the respective three or more vertices of a respective sublattice in a second subset of sublattices with one or more plaquette qubits of the plurality of physical qubits assigned to the respective one or more plaquettes of the respective sublattice in the second subset of sublattices;
- causing measurement of the one or more plaquette qubits of the respective sublattice in the second subset of sublattices;
- determining, based on the measurement of the one or more plaquette qubits of the respective sublattice in the first subset and the measurement of the one or more plaquette qubits of the respective sublattice in the second subset, whether any plaquettes of the plurality of sublattices are hosting an Abelian topological order;
- and
- responsive to determining that at least a pair of plaquettes of the plurality of sublattices is hosting an Abelian topological order, causing performance of a feed-forward action to be performed on the pair of plaquettes to generate the ground state having non-Abelian topological order.