10 - Clustering Structure and Quantum Computing

Abstract

Unsupervised learning finds a natural fit with quantum computing. Quantum states are capable of self-analysis—that is, they can reveal their own eigenstructure. This leads to efficient quantum principal component analysis and quantum manifold learning. Moving beyond low-dimensional embedding, if we use quantum random access memory, we are able to calculate dot products and the Euclidean distance in a high-dimensional space. This enables us to use efficient clustering methods, such as quantum $K$-means and $K$-medians, and quantum hierarchical clustering. We can use adiabatic quantum computing or Grover's search to find optima. If the input and output states are allowed to be quantum, then an exponential speedup is feasible over classical algorithms.