Quantum template matching

Abstract

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