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arXiv:1504.08054 · New Journal of Physics

Overcoming erasure errors with multilevel systems

Sreraman Muralidharan, Chang‐Ling Zou, Linshu Li, Jianming Wen, Liang Jiang

Published Jan 20, 2017• 63 citations
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Abstract

We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum polynomial codes to encode quantum information and generalizes teleportation based error correction for multilevel systems to correct photon losses and operation errors in a fault-tolerant manner. We discuss the application of quantum polynomial codes to one-way quantum repeaters. For various types of operation errors, we identify different parameter regions where quantum polynomial codes can achieve a superior performance compared to qubit based quantum parity codes.

DOI
10.1088/1367-2630/aa573a

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We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum polynomial codes to encode quantum information and generalizes teleportation based error correction for multilevel systems to correct photon losses and operation errors in a fault-tolerant manner. We discuss the application of quantum polynomial codes to one-way quantum repeaters. For various types of operation errors, we identify different parameter regions where quantum polynomial codes can achieve a superior performance compared to qubit based quantum parity codes.
We show that quantum Reed-Solomon codes constructed from classical Reed-Solomon codes can approach the capacity on the quantum erasure channel of ddd-level systems for large dimension ddd. We study the performance of one-way quantum repeaters with these codes and obtain a significant improvement in key generation rate compared to previously investigated encoding schemes with quantum parity codes and quantum polynomial codes. We also compare the three generations of quantum repeaters using quantum Reed-Solomon codes and identify parameter regimes where each generation performs the best.
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.
One-way quantum repeaters where loss and operational errors are counteracted by quantum error-correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum error-correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimized resource overhead by interspersing repeater nodes that each specialize in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication.
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. The present code has a high encoding efficiency, since only one auxiliary qubit is needed for one message qubit on average. In addition, we note that the code can also work even in a worse case that the interaction with the environment causes a leakage out of the qubit space. The code may have some applications in the storage of quantum information for small-scale quantum computing, quantum information processing, and quantum communication.
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