In most practical quantum mechanical systems,quantum noise due to decoherence is highly biased towards dephasing.The quantum state suffers from phase flip noise much more seriously than from the bit flip noise.In this...In most practical quantum mechanical systems,quantum noise due to decoherence is highly biased towards dephasing.The quantum state suffers from phase flip noise much more seriously than from the bit flip noise.In this work,we construct new families of asymmetric quantum concatenated codes(AQCCs)to deal with such biased quantum noise.Our construction is based on a novel concatenation scheme for constructing AQCCs with large asymmetries,in which classical tensor product codes and concatenated codes are utilized to correct phase flip noise and bit flip noise,respectively.We generalize the original concatenation scheme to a more general case for better correcting degenerate errors.Moreover,we focus on constructing nonbinary AQCCs that are highly degenerate.Compared to previous literatures,AQCCs constructed in this paper show much better parameter performance than existed ones.Furthermore,we design the specific encoding circuit of the AQCCs.It is shown that our codes can be encoded more efficiently than standard quantum codes.展开更多
Quantum degenerate code may improve the hashing bound of quantum capacity. We propose a family of quantum degenerate codes derived from two-colorable graphs. The coherent information of the codes is analyticaJly obtai...Quantum degenerate code may improve the hashing bound of quantum capacity. We propose a family of quantum degenerate codes derived from two-colorable graphs. The coherent information of the codes is analyticaJly obtained as a function of the channd noise for the depolarizing channel. We find a new code which has a higher noise threshold than that of the repetition code.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61802175,61871120,61872184,and 62071240)the Fundamental Research Funds for the Central Universities,China(Grant No.NZ2020021)。
文摘In most practical quantum mechanical systems,quantum noise due to decoherence is highly biased towards dephasing.The quantum state suffers from phase flip noise much more seriously than from the bit flip noise.In this work,we construct new families of asymmetric quantum concatenated codes(AQCCs)to deal with such biased quantum noise.Our construction is based on a novel concatenation scheme for constructing AQCCs with large asymmetries,in which classical tensor product codes and concatenated codes are utilized to correct phase flip noise and bit flip noise,respectively.We generalize the original concatenation scheme to a more general case for better correcting degenerate errors.Moreover,we focus on constructing nonbinary AQCCs that are highly degenerate.Compared to previous literatures,AQCCs constructed in this paper show much better parameter performance than existed ones.Furthermore,we design the specific encoding circuit of the AQCCs.It is shown that our codes can be encoded more efficiently than standard quantum codes.
基金Supported by the National Natural Science Foundation of China under Grant Nos.60972071 and 11375152
文摘Quantum degenerate code may improve the hashing bound of quantum capacity. We propose a family of quantum degenerate codes derived from two-colorable graphs. The coherent information of the codes is analyticaJly obtained as a function of the channd noise for the depolarizing channel. We find a new code which has a higher noise threshold than that of the repetition code.
