  Before the availability of large scale fault-tolerant quantum devices, 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 where the quantum computation is
supplemented by a classical result. While the presence of the supplementary
classical information helps alone, taking advantage of its anticipation also
leads to a new type of quantum measurements, which we call anticipative.
Anticipative quantum measurements lead to improved success rate over cases
where we would use quantum measurements optimized without assuming the later
arriving supplementing information. Importantly, in an anticipative quantum
measurement the combination of the results from classical and quantum
computations happens only in the end, without the need for feedback from the
one to the other computation, a feature which hence allows for running both
computations in parallel. We demonstrate the method with an experiment using an
IBMQ device and show that it leads to an improved success rate even in a real
noisy setting.
