Modified graph-state codes for single-node recovery in quantum distributed storage
Priya J. Nadkarni, Ankur Raina, Shayan Srinivasa Garani · Physical Review A · 2020
Distributed quantum information stored over nodes within a quantum network are prone to node failures, motivating the need for coded quantum networks. We encode $k$ qubits of quantum information over an $n$-node network in a distributed fashion, with one qubit per node, using modified graph-state codes. We devise a procedure to recover the encoded quantum information in any given arbitrary network after a detected node fails. The recovery procedure is locally within four edges of the failed node. For a network with even number of nodes, we provide a class of scalable modified graph-state codes with rate $(n\ensuremath{-}2)/n$, saturating the quantum Singleton bound. This yields higher coding rates than Grassl et al.'s well-known erasure codes and has asymptotic rate 1. For odd node size $n$, we design the network links to obtain an $(n\ensuremath{-}3)/n$ rate-optimal modified graph state code.