NISQ-friendly measurement-based quantum clustering algorithms

Two novel measurement-based, quantum clustering algorithms are proposed based on quantum parallelism and entanglement. The first algorithm follows a divisive approach. The second algorithm is based on unsharp measurements, where we construct an effect operator with a Gaussian probability distribution to cluster similar data points. A major advantage of both algorithms is that they are simplistic in nature, easy to implement, and well suited for noisy intermediate scale quantum computers. We have successfully applied the first algorithm on a concentric circle data set, where the classical clustering approach fails, as well as on the Churritz data set of 130 cities, where we show that the algorithm succeeds with very low quantum resources. We applied the second algorithm on the labeled Wisconsin breast cancer dataset, and found that it is able to classify the dataset with high accuracy using only O(log(D)) qubits and polynomial measurements, where D is the maximal distance within any two points in the dataset. We also show that this algorithm works better with an assumed measurement error in the quantum system, making it extremely well suited for NISQ devices.