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IEEE Globecom Workshops (GC Wkshps)

Recovery of Distributed Quantum Information Using Graph States from a Node Failure

Priya J. Nadkarni, Ankur Raina, Shayan Garani Srinivasa

Published Dec 1, 2017• 5 citations
Publisher

Abstract

Quantum graph states are highly entangled quantum states known to exhibit properties useful in applications such as quantum error correction, quantum computation, etc. We distribute quantum information across nodes, each having a qubit at its location, by using encoding techniques. We call it a quantum graph state code. By modeling the loss of a qubit due to failure of a node as a quantum erasure, we present a recovery mechanism for distributed quantum information using purification followed by an error correction procedure.

DOI
10.1109/glocomw.2017.8269075

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Quantum graph states are highly entangled quantum states known to exhibit properties useful in applications such as quantum error correction, quantum computation, etc. We distribute quantum information across nodes, each having a qubit at its location, by using encoding techniques. We call it a quantum graph state code. By modeling the loss of a qubit due to failure of a node as a quantum erasure, we present a recovery mechanism for distributed quantum information using purification followed by an error correction procedure.
Distributed quantum information stored over nodes within a quantum network are prone to node failures, motivating the need for coded quantum networks. We encode kkk qubits of quantum information over an nnn-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 nnn, we design the network links to obtain an $(n\ensuremath{-}3)/n$ rate-optimal modified graph state code.
Many protocols of quantum information processing, like quantum key distribution or measurement-based quantum computation, 'consume' entangled quantum states during their execution. When participants are located at distant sites, these resource states need to be distributed. Due to transmission losses quantum repeater become necessary for large distances (e.g. ). Here we generalize the concept of the graph state repeater to D -dimensional graph states and to repeaters that can perform basic measurement-based quantum computations, which we call quantum routers. This processing of data at intermediate network nodes is called quantum network coding. We describe how a scheme to distribute general two-colourable graph states via quantum routers with network coding can be constructed from classical linear network codes. The robustness of the distribution of graph states against outages of network nodes is analysed by establishing a link to stabilizer error correction codes. Furthermore we show, that for any stabilizer error correction code there exists a corresponding quantum network code with similar error correcting capabilities.
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by distributing quantum information over six qubits which is the minimal number for the present task (see reference [1]). The encoding and error recovery operations for such a code are presented. It is noted that the present code is also a three-qubit quantum hidded information code over each qubit. In addition, an encoding scheme for hiding nnn-qubit quantum information over each qubit is proposed.
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by distributing quantum information over six qubits. The encoding and error recovery operations for such a code are presented. We also show that the present code is a three-qubit quantum hidded information code over each qubit. In addition, hiding nnn-qubit quantum information over each qubit is considered.
Quantum error correction (QEC) is crucial for reliable quantum computation, but traditional approaches often suffer from scalability issues. This work introduces a novel distributed information theory protocol for QEC, departing from classical distributed coding paradigms. The core idea is to utilize correlated information sharing across a network of nodes, exploiting quantum entanglement to achieve greater efficiency and resilience to errors. We present a framework where the redundancy is distributed intelligently, minimizing the required resources per qubit while maintaining high correction capabilities. The protocol's performance is analyzed theoretically, demonstrating its potential to significantly improve the practicality of QEC in large-scale quantum systems. We explore the key mathematical concepts underpinning this approach, including the distribution of quantum states, the quantification of information, and the analysis of error propagation within the distributed network. The theoretical analysis focuses on characterizing the rate of information transfer and the fidelity of the corrected state, providing a framework for optimizing the protocol's parameters.
We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known that the three codes always allow error recovery if only one among the sent qubits is disturbed in the transmitting channel. However, if two qubits and more are disturbed, then the correction will depend on the used code. We compare in this paper the three codes by computing the average fidelity between the sent secret and that measured by the receivers. We will treat the case where, at most, two qubits are affected in each one of five depolarizing channels.