2 research outputs found
Performance Analysis of Quantum Error-Correcting Codes via MacWilliams Identities
One of the main challenges for an efficient implementation of quantum
information technologies is how to counteract quantum noise. Quantum error
correcting codes are therefore of primary interest for the evolution towards
quantum computing and quantum Internet. We analyze the performance of
stabilizer codes, one of the most important classes for practical
implementations, on both symmetric and asymmetric quantum channels. To this
aim, we first derive the weight enumerator (WE) for the undetectable errors of
stabilizer codes based on the quantum MacWilliams identities. The WE is then
used to evaluate the error rate of quantum codes under maximum likelihood
decoding or, in the case of surface codes, under minimum weight perfect
matching (MWPM) decoding. Our findings lead to analytical formulas for the
performance of generic stabilizer codes, including the Shor code, the Steane
code, as well as surface codes. For example, on a depolarizing channel with
physical error rate it is found that the logical error rate
is asymptotically for the
Shor code, for the
Steane code, for the surface
code, and for the surface
code.Comment: 25 pages, 5 figures, submitted to an IEEE journal. arXiv admin note:
substantial text overlap with arXiv:2302.1301