Approaching the Quantum Singleton Bound with Approximate Error Correction

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Abstract

It is well known that no quantum error correcting code of rate R can correct adversarial errors on more than a (1-R)/4 fraction of symbols. But what if we only require our codes to *approximately* recover the message? We construct efficiently-decodable approximate quantum codes against adversarial error rates approaching the quantum Singleton bound of (1-R)/2, for any constant rate R. Moreover, the size of the alphabet is a constant independent of the message length and the recovery error is exponentially small in the message length. Central to our construction is a notion of quantum list decoding and an implementation involving folded quantum Reed-Solomon codes.

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Key words

Quantum Error Correction,Quantum Secret Sharing

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Pretraining has recently greatly promoted the development of natural language processing (NLP)
We show that M6 outperforms the baselines in multimodal downstream tasks, and the large M6 with 10 parameters can reach a better performance
We propose a method called M6 that is able to process information of multiple modalities and perform both single-modal and cross-modal understanding and generation
The model is scaled to large model with 10 billion parameters with sophisticated deployment, and the 10 -parameter M6-large is the largest pretrained model in Chinese
Experimental results show that our proposed M6 outperforms the baseline in a number of downstream tasks concerning both single modality and multiple modalities We will continue the pretraining of extremely large models by increasing data to explore the limit of its performance

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