Calibration of syndrome measurements in a single experiment

Abstract: Quantum error correction can reduce the effects of noise in quantum systems, e.g. in metrology or most notably in quantum computing. Typically, this requires making measurements that provide information about the errors that have occurred in the system. However, these syndrome measurements themselves introduce noise into the system, for example by using noisy gates. A complete characterization of the measurements is very costly. Here we describe a calibration method to obtain the syndrome statistics taking into account the additional noise sources. All calibration data are extracted from a single experiment in which the syndrome measurement is performed twice in a row. Thus, our method allows an accurate evaluation of syndrome measurements with significantly less effort than existing methods. We give examples of the application of this method to noise estimation and error correction. Finally, we discuss the results of experiments performed on an IBM quantum computer.