Recovery of quantum information from a node failure in a graph

Quantum entanglement is a well-known quantum way of introducing redundancy in quantum error correcting codes. The unitary interactions when modeled using edges of a graph with qubits as nodes give rise to a quantum graph state. Quantum graph states are highly entangled quantum states created using specific unitary interactions between qubits. We consider the problem of failure of a node of the graph. The node failure leads to the loss of one of the qubits of the graph state, resulting in a mixed state. In order to restore the quantum information originally stored in the graph state, we devise a mechanism to purify the mixed state via a unitary operation, followed by measurement. We propose a modification to the existing graph state and call it a modified graph state. This improves the error correction ability of the graph state, and it is able to correct single bit flip errors ensuing after the measurement stage. Using this modified graph state code, our procedure recovers the quantum information in the graph in the event of one node failure.