Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking and control of experimental quantum computing systems, including adaptive quantum phase estimation and designing quantum computing gates. On the other hand, quantum mechanics offers tantalizing prospects to enhance machine learning, ranging from reduced computational complexity to improved generalization performance. The most notable examples include quantum enhanced algorithms for principal component analysis, quantum support vector machines, and quantum Boltzmann machines. Progress has been rapid, fostered by demonstrations of midsized quantum optimizers which are predicted to soon outperform their classical counterparts. Further, we are witnessing the emergence of a physical theory pinpointing the fundamental and natural limitations of learning. Here we survey the cutting edge of this merger and list several open problems. Machine learning has fundamentally changed the way humans interact with and relate to data. Applications range from self-driving cars to intelligent agents capable of exceeding the best humans at Jeopardy and Go. These applications exhibit large data sets and push current algorithms and computational resources to their limit. Information is fundamentally governed by the laws of physics. The laws are quantum mechanical at the scales of present day information processing technology, in contrast to the more familiar 'classical' physics at the human scale. The interface of quantum physics and machine learning naturally goes both ways: machine learning algorithms find application in understanding and controlling quantum systems and, on the other hand, quantum computational devices promise enhancement of the performance of machine learning algorithms for problems beyond the reach of classical computing. Machine learning is rapidly being employed for the benchmarking, control, and harnessing of quantum effects [1] [2] [3] [4] [5] [6] [7] [8] [9] . State-of-the art quantum experiments in op- * jacob.biamonte@qubit.org; www.QuamPlexity.org † peterwittek.com ‡ nicola.pancotti@mpq.mpg.de § pr@patrickre.com ¶ nawiebe@microsoft.com * * slloyd@mit.edu tical or solid state systems have recently reached sizes where optimization methods face unprecedented dataintensive landscapes. In addition, machine learning was employed in a variety of related fields, e.g. the discovery of the Higgs Boson [10], molecular energy prediction trained using databases of known energy spectra [11] and gravitational wave detection [12] . In the computing realm, this progress allows experimental breakthroughs which probe the threshold of producing the first practical quantum computer [13] , which in turn enables quantum enhanced versions of these very same learning algorithms. Quantum information has shown promising algorithmic developments leading to quantum speedups of computational problems such as prime number factoring and searching an unstructured database. The underlying algorithmic toolbox allows extensions to problems relevant for machine learning and artificial intelligence. Recently, it was shown that quantum mechanics offers physical resources to enhance machine learning with quantum algorithms [14] [15] [16] [17] [18] [19] [20] [21] . Quantum-enhanced versions of classical machine learning algorithms include least-squares fitting, support vector machines, principal component analysis, and deep learning. Challenges that have to be addressed in this emerging field is the input of classical data into the quantum device, the efficient processing of the data, and subsequent readout of classically relevant information. Beyond quantum algorithms for machine learning, there has been progress in developing a physics based the-2 ory pinpointing the fundamental and natural limitations of learning, quantum enhanced learning algorithms and the employment of learning algorithms to better control and harness these same quantum effects [14] [15] [16] [17] [18] [19] [20] [21] . Quantum information theory sets the stage to understand how fundamental laws of nature impact the ability of physical agents to learn. The cutting edge of the intersection of machine learning and quantum physics is reviewed here. We explain how the above areas interact and we list several open problems that are of contemporary research interest. CONTENTS
Other work at the intersection of machine learning and quantum mechanics includes REF on quantum perceptron models and learning algorithms.
Quantum Machine Learning
Nature 549, 195-202 (2017)
Physics Mathematics Medicine