中央研究院 資訊科學研究所

Quantum information needs to be protected by quantum error-correcting codes due to imperfect quantum devices and operations. One would like to have an efficient and high-performance decoding procedure for quantum codes. A potential candidate is Pearl's belief propagation (BP), but its performance suffers from the many short cycles inherent in quantum codes. Many attempts to improve BP decoding of quantum codes have been made in the literature; however,  there is a general impression that BP cannot work for topological codes, such as the surface and toric codes. In this paper, we propose a decoding algorithm (called MBP)  for quantum codes based on  BP  but with a memory effect without any additional overhead. MBP exploits the degeneracy of quantum codes so that it has a better chance to find the most probable error or its degenerate errors. Moreover, the memory effect helps BP converge. MBP significantly improves the decoding performance of usual BP  for various quantum codes, especially highly-degenerate codes (that is, codes with many low-weight stabilizers). For the surface or toric codes, our MBP decoder achieves a threshold of ~16% or  ~17.5%, respectively, over the depolarizing channel.

【Reference】

Quantum information needs to be protected by quantum error-correcting codes due to imperfect quantum devices and operations. One would like to have an efficient and high-performance decoding procedure for quantum codes. A potential candidate is Pearl's belief propagation (BP), but its performance suffers from the many short cycles inherent in quantum codes. Many attempts to improve BP decoding of quantum codes have been made in the literature; however,  there is a general impression that BP cannot work for topological codes, such as the surface and toric codes. In this paper, we propose a decoding algorithm (called MBP)  for quantum codes based on  BP  but with a memory effect without any additional overhead. MBP exploits the degeneracy of quantum codes so that it has a better chance to find the most probable error or its degenerate errors. Moreover, the memory effect helps BP converge. MBP significantly improves the decoding performance of usual BP  for various quantum codes, especially highly-degenerate codes (that is, codes with many low-weight stabilizers). For the surface or toric codes, our MBP decoder achieves a threshold of ~16% or  ~17.5%, respectively, over the depolarizing channel.

【Reference】