At the beginning of the last century the discovery of the laws of quantum mechanics shocked the entire scientific community. Theorizing and subsequent observation of highly counterintuitive phenomena, such as superposition (i.e., the ability of a quantum particle to take more than one state at a time) or entanglement (a connection between particles without direct physical interaction) have encountered skepticism of many important minds, such as Professor Albert Einstein. Nevertheless, the evidence of quantum behaviours did not take long to arrive. Today we are all in agreement that the microscopic world follows physical laws different from those of the macroscopic world. Thanks to the continuous work of the scientific community, today we are able to understand the deeper aspects of quantum mechanics much better. Over the years many technologies based on quantum mechanics have emerged, such as lasers or transistors. Our ever deeper knowledge of the laws of quantum mechanics is bringing us ever closer to the realization of revolutionary quantum computers, able to perform complex calculations in minimal time. When these computers will reach their peak of functionality, they will be so powerful that no classic supercomputer will be able to match its performance. In this paper we present how it is possible to exploit the rising Quantum Computer hardware to efficiently implement a optimization algorithm known as Nonnegative Matrix Factorization, a well-known method that is useful to solve many problems in chemometrics, image analysis, text mining, etc.

Given a matrix V, the NMF problem consists in finding two matrices with non-negative components, W and H, such that their product is as close as possible to the starting matrix V. Thanks to the technology provided by the Canadian company D-Wave, we were able to solve for the first time with this type of technology the NMF problem with matrices composed by real numbers. Despite the current level of technology, the results obtained have proved to be very promising and ready to be applied to large scale optimization problems.

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