As the year-to-year gains in speeds of classical computers continue to taper off, computational chemists are increasingly examining quantum computing as a possible route to achieve greater computational performance. Quantum computers, built upon the properties of superposition, interference, and entanglement of quantum bits, offer, in principle, the possibility to outperform classical computers for solving many important classes of problems. In the field of chemistry, quantum algorithm development offers promising propositions for solving classically intractable problems in areas such as electronic structure, chemical quantum dynamics, spectroscopy, and cheminformatics. However, physical implementations of quantum computers are still in their infancy and have yet to outperform classical computers for useful computations. Still, quantum software development for chemistry is a highly active area of research. In this perspective, we summarize recent progress in the areas of quantum computing algorithms, hardware, and software, and we describe the challenges that remain for useful implementations of quantum computing for chemical applications.
Machine learning and quantum computing are both areas with considerable progress in recent years. The combination of these disciplines holds great promise for both research and practical applications. Recently there have also been many theoretical contributions of quantum machine learning algorithms with experiments performed on quantum simulators. However, most questions concerning the potential of machine learning on quantum computers are still unanswered such as How well do current quantum machine learning algorithms work in practice? How do they compare with classical approaches? Moreover, most experiments use different datasets and hence it is currently not possible to systematically compare different approaches. In this paper we analyze how quantum machine learning can be used for solving small, yet practical problems. In particular, we perform an experimental analysis of kernel-based quantum support vector machines and quantum neural networks. We evaluate these algorithm on 5 different datasets using different combinations of quantum feature maps. Our experimental results show that quantum support vector machines outperform their classical counterparts on average by 3 to 4% in accuracy both on a quantum simulator as well as on a real quantum computer. Moreover, quantum neural networks executed on a quantum computer further outperform quantum support vector machines on average by up to 5% and classical neural networks by 7%.