Estimating decoding graphs and hypergraphs of memory quantum error-correction experiments

Characterizing the error sources of quantum devices is essential for building reliable large-scale quantum architectures and tailoring error correction codes to the noise profile of the devices. Tomography techniques can provide detailed information on the noise or quality of quantum states but are typically both computationally and experimentally intensive with respect to the system’s size. For quantum error correction experiments, however, the information captured by a detector error model is sufficient for extracting the success rate of the experiment, as well as some information about the underlying noise. In this work, we estimate Pauli noise on detector error models, including hypergraphs, using only the syndrome statistics. We apply this method to well-known codes such as the repetition, surface, and two-dimensional color codes. Under bare-ancilla syndrome extraction, twopoint correlations are enough to reconstruct the detector error model for repetition or surface codes. For color codes or repetition codes under Steane-style syndrome extraction, we show how to extend the estimation method to multipoint correlators and extract the error rates of the hypergraphs. Finally, we find an increase in logical error suppression when we calibrate the decoder to noise fluctuations typically present in experiments.

Duke Scholars

Author Kenneth R Brown Electrical and Computer Engineering