Estimation of Error Probabilities for the Quantum Repetition Code

Abstract

In this thesis, the repetition code for bit flip errors is examined. Based the stabilizer measurements outcome of a run of the repetition code, one does not know exactly which errors have occurred. Statistics can be used to estimate the probability of all possible error events. This probability estimation is investigated for simulated data assuming phenomenological and circuit level noise. Experiments on the repetition code are performed by the DiCarlo group at the Delft University of Technology on a superconducting quantum computer. For this data, some error probabilities are estimated to be nonphysical. The goal of this thesis is to investigate these nonphysical probabilities and to determine whether they result from sampling noise or a problem with the assumed error model that determines the estimation of the probabilities. By estimating the standard deviation using the bootstrap method it is shown that the nonphysical probabilities are not due to sampling noise. Therefore, it is possible that non-conventional errors, such as leakage or crosstalk, are affecting these estimates.

In a further analysis on the error probabilities and their standard deviation, it is shown that the standard error for space and time edges in the experiment is consistent with the standard error from phenomenological noise initialised with the average error data and ancilla error probabilities, even when
these may be affected by non-conventional errors.