Anticipative measurements in hybrid quantum-classical computation

Until large-scale fault-tolerant quantum devices become available, one has to find ways to make the most of current noisy intermediate-scale quantum devices. One possibility is to seek smaller repetitive hybrid quantum -classical tasks with higher fidelity, rather than directly pursuing large complex tasks. We present an approach in this direction in which quantum computation is supplemented by a classical result. While the presence of the supplementary classical information is helpful in and of itself, taking advantage of its anticipation also leads to a distinct type of quantum measurement, which we call anticipative. Anticipative quantum measurements lead to an improved success rate compared with cases in which quantum measurements are optimized without assuming the subsequent arrival of supplementary information. Importantly, in an anticipative quantum measurement, we do not combine the results from classical and quantum computations until the end of the process, and there is no need for feedback from one computation to the other, thus both computations can be run in parallel. We demonstrate the method using an IBMQ device, and we show that it leads to an improved success rate even in a noisy setting.