Performance tradeoffs in quantum machine learning

Machine learning, a branch of artificial intelligence, is concerned with automating the construction of models and drawing of inference from data. Applications abound, from data retrieval to image recognition, and such techniques are now ubiquitous in branches of science or industry dealing with large datasets. In particular, they are finding increasing use in image processing and recognition, and computational imaging techniques employing machine learning are an active field of research. These techniques, while powerful, can be computationally intensive: for a large dataset, training a model can take days or weeks of CPU time.



Quantum machine learning is an emerging and rapidly developing inter-disciplinary field, exploring the potential of devices operating under the laws of quantum physics to speed-up machine learning algorithms, as well as to perform new algorithms for equivalent uniquely quantum problems. Some of these involve plugging in known quantum algorithms to classical machine learning protocols, while others are fundamentally new. A fundamental difference in the quantum case however is that measurement inevitably causes disturbance, and thus if the algorithm provides output at some point, any data received and fed into the algorithm up to that point is disturbed.



The question therefore naturally arises to what extent a quantum machine learning algorithm can incorporate further data provided at a later time to e.g. classify new samples, or improve the learned model. In the case of truly quantum input data, e.g. the quantum state of light which has interacted with an object, or polarisation states following transmission through an unknown channel, the problem of classification and incorporation of subsequent data instances is particularly pertinent, and remains unexplored.



The project will thus consider in particular quantum classification tasks, by which we mean those in which data is encoded in properties of quantum systems and we wish to search for patterns within the data. The student will apply tools from quantum measurement theory to analyse proposed algorithms, in particular by varying the strength of measurements performed on the data. The stronger the measurement the greater the information gain but the more severe the disturbance - a realisation that goes back to Heisenberg and the very foundations of the theory. There is thus a tension between optimising the information extracted and thereby the performance of the classifier, and minimising measurement back-action, and it is this tradeoff which will be explored in the project.



This is a theoretical project, which may however be expected to shed light on the performance of techniques in current use or feasible with current technology, compared to the theoretically optimal performance. It sits within the EPSRC research area "Quantum Optics and Information", as well as being of relevance to "Quantum Technologies", "Information Systems", and "Artificial Intelligence". It is a collaboration with QuantIC, the quantum imaging hub.



In the long term there are numerous potential applications relevant to EPSRC research themes - fundamentally all information extracted about the world is in the form of quantum states, as nature is ultimately quantum mechanical. In scenarios as diverse as gravitational wave detection and in image recognition the signal of interest is encoded in the quantum state of light exiting an interferometer or reaching a camera, and one can imagine it may become desirable to directly classify the quantum states of light, rather than convert via measurement to a classical signal. Understanding the theoretical limits to quantum machine learning can allow benchmarking of existing techniques, as well as paving the way, in the longer run, for the processing of quantum big data.