Quantum Template Matching

We consider the quantum analogue of the pattern matching problem, which consists of classifying a given unknown system according to certain predefined pattern classes. We address the problem of quantum template matching in which each pattern class ${\cal C}_i$ is represented by a known quantum state $\hat g_i$ called a template state, and our task is to find a template which optimally matches a given unknown quantum state $\hat f$. We set up a precise formulation of this problem in terms of the optimal strategy for an associated quantum Bayesian inference problem. We then investigate various examples of quantum template matching for qubit systems, considering the effect of allowing a finite number of copies of the input state $\hat f$. We compare quantum optimal matching strategies and semiclassical strategies and demonstrate an entanglement assisted enhancement of performance in the general quantum optimal strategy.