Redundant string symmetry-based error correction: Demonstrations on quantum devices

Abstract: Computational power in measurement-based quantum computing stems from the symmetry-protected topological (SPT) order of entangled resource states. However, resource states are prone to preparation errors. We introduce a quantum error correction approach using redundant nonlocal symmetry of the resource state. We demonstrate it within a teleportation protocol based on extending the $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry of one-dimensional cluster states to other graph states. Qubit ZZ-crosstalk errors, which are prominent in quantum devices, degrade the teleportation fidelity of the usual cluster state. However, as we demonstrate on quantum hardware, once we grow graph states with redundant symmetry, perfect teleportation fidelity is restored. We identify the underlying redundant-SPT order as error-protected degeneracies in the entanglement spectrum.