Gravitational waves are tiny perturbations of the space-time structure, which propagate at the speed of light and are searched using large interferometric detectors. Gravitational waves are typically buried in the instrumental noise, so proper data analysis algorithms are necessary to extract these signals from the detector data stream. Some searches need to cover a huge parameter space, and are computationally bounded. This means that optimal analysis methods, based on matched filtering, which would provide the best sensitivity, cannot be used. An example is represented by all-sky searches for long duration signals emitted by spinning neutron stars. In this presentation I will discuss these issues and describe how
quantum computing may provide the needed speed-up to make, in principle, optimal wide parameter space searches computationally tractable.