In-situ Adaptive Encoding for Asymmetric Quantum Error Correcting Codes

We present techniques that improve the performance of asymmetric stabilizer codes in the presence of unital channels with unknown parameters. Our method estimates the channel parameters using information recovered from syndrome measurements during standard stabilizer quantum error correction and adaptively realigns the codespace to minimize the uncorrectable error rate. We find that for dephasing channels parametrized by a single angle our scheme yields lifetimes dominated by the bit-flip error rate for which the asymmetric code has an improved distance. In the case of general unital channels we are able to learn and exploit orientations of the channel that yield a constant improvement to the code lifetime. In both cases, since our method is adaptive and online, we are able to model the effect of drift in the channel parameters.