by Peter Wittek (ICFO-The Institute of Photonic Sciences and University of Borås)
It is not only machine learning that is advancing rapidly: quantum information processing has witnessed several breakthroughs in recent years. In theory, quantum protocols can offer an exponential speedup for certain learning algorithms, but even contemporary implementations show remarkable results – this new field is called quantum machine learning. The benefits work both ways: classical machine learning finds more and more applicability in problems in quantum computing.
After a history spanning over five decades, artificial general intelligence still remains out of reach. Machine learning has common roots with AI research, but focuses on more attainable goals and has achieved tremendous success in many application fields. Similarly, a universal quantum computer is still far ahead in the distant future: the criterion for this machine is to be able to simulate an arbitrary closed quantum system. Nevertheless, uses of quantum information processing are proliferating: two notable examples are quantum key distribution systems and quantum random number generators.
Recently, there has been a surge of interest in the intersection of machine learning and quantum information processing. Combining ideas from these two fields leads to tremendous benefits for both. We are collaborating on several subjects in this domain between ICFO-The Institute of Photonic Sciences, the Autonomous University of Barcelona, the University of the Basque Country, all in Spain, as well as the University of Calgary, Canada.
Figure 1: Overview of the interplay between quantum information processing and machine learning.
At the highest level, abstracting of the actual algorithms and focusing on the foundations of statistical learning theory, we can ask what it means to learn with quantum data and channels, what induction and transduction mean in this setting, how we can define figures of merit to quantify performance, and eventually establish bounds on generalisation performance using sample and model complexity. We studied supervised learning, and proved that in the asymptotic limit and under an assumption of exchangeability, quantum entanglement does not break our traditional notion of induction [L1]. This is an important stepping stone towards understanding generalisation properties of quantum learning protocols.
The next natural question to ask is that given a universal quantum computer, what kind of protocols can we use for learning? Many proposals have been put forward, offering up to an exponential reduction in computational complexity , but it is worth looking at what is attainable with current technology. Quantum adiabatic optimisation leads the way in this regard; it uses quantum annealing – a physical process resembling the widely used global optimisation heuristic simulated annealing that uses both thermal fluctuations and quantum tunnelling to find the global energy minimum of a system. Scalable quantum annealers already exist, but they are not guaranteed to find a global optimum. On the other hand, the local optima retrieved from such machines closely follows a Gibbs distribution. For this reason, they have been used to train various configurations of Boltzmann machines . Gibbs sampling, however, does not only occur in Boltzmann machines: probabilistic inference in Bayesian networks and Markov random fields makes extensive use of it. Since this a #P problem in general, currently we are looking at how one can match these inference methods with existing implementations.
Using quantum resources in learning is only one side of the coin: we can also employ machine learning using classical computers in common problems that arise in quantum information processing, for instance, in quantum control. Quantum control steers quantum dynamics towards realising specific quantum states or operations, and thus it is an important component in constructing a universal quantum computer. We have been working on a reinforcement learning algorithm to control an adaptive quantum metrology scheme , improving noise tolerance and scalability, providing a tool that experimentalists can use [L2, L3].
Our overall vision is that this cross-fertilisation between machine learning and quantum information processing will continue, and that the future of artificial general intelligence and universal quantum computing are intertwined.
 P. Rebentrost, M. Mohseni, S. Lloyd: “Quantum support vector machine for big feature and big data classification”, Physical Review Letters, 2014, 113, 130503.
 S. H. Adachi, M. P. Henderson: “Application of Quantum Annealing to Training of Deep Neural Networks”, arXiv:1510.06356, 2015.
 A. Hentschel, B. C. Sanders: “Machine Learning for Precise Quantum Measurement”, Physical Review Letters, 2010, 104, 063603.
Peter Wittek, ICFO-The Institute of Photonic Sciences, Barcelona, Spain
University of Borås, Borås, Sweden