Fidelity estimator, randomized benchmarking and ZNE for quantum pulses

Most previous research focused on designing pulse programs without considering the performance of individual elements or the final fidelity. To evaluate the performance of quantum pulses, it is required to know the noiseless results of the pulses. However, quantum pulses can implement unitary matrices that are not analytically known to the user, and pulse simulator usually comes with significant computational overhead. Consequently, determining fidelity of a pulse program is challenging without the knowledge of the ideal results. In this paper, we propose to use reversed pulses to evaluate the performance of quantum pulses, which can provide guidance to design pulse programs. By employing reversed pulses, we can ensure that, in the noiseless situation, the final quantum states are the same as the initial states. This method enables us to evaluate the fidelity of pulse programs by measuring the difference between the final states and the initial states. Such fidelity estimator can tell whether the results are meaningful for quantum pulses on real quantum machines. There are various quantum error correction (QEC) methods available for gate circuits; however, few studies have demonstrated QEC on pulse-level programs. In this paper, we use reversed pulses to implement zero noise extrapolation (ZNE) on pulse programs and demonstrate results for variational quantum eigensolver (VQE) tasks. The deviation from the idea energy value is reduced by an average of 54.1\% with our techniques.