Back to search

IKTPLUSS-IKT og digital innovasjon

Quantum Machine Learning

Alternative title: Quantum Maskin Læring

Awarded: NOK 7.2 mill.

The usual setting for quantum computing in general is that the quantum computer operates at near zero degrees Kelvin, which is a big disadvantage in practice. Topological quantum computation (TQC) is an established method that aims to use the topology of the computer structure to propose quantum computational structures that operate at room temperature. However, TQC poses a large number of challenges that need to be overcome. The focus of this project has been to consider quantum machine learning as a tool to overcome the difficulties related to TQC. Some examples of the achieved outcomes are extracting information from fusion rules using skein-theoretic methods and a rotation operator, patching the gap between the fundamental principle of exchange symmetry and the categorical framework, and a generalization of Catalan numbers by considering the number of ways to parenthesize some discrete configuration of objects. Based on the theoretical structures that have been proposed in this project, we believe that we have provided new tools for the experimentalists to be able to develop appropriate structures upon which TQC could be implemented.

We believe that the project results will have impact on quantum machine learning.

Machine learning on graphs induces correlations between unconnected nodes. How can non-local quantum resources enhance performance? We shall develop strategies for distributed measurement and (neural) message-passing for quantum machine learning, based on quantum random walks on graphs, where `creative' learning scenarios are developed and assessed. Shannon capacity is a graph-theoretic method to assess the ability of a channel to transmit messages. It is a celebrated problem to determine the Shannon capacity of a graph - the Shannon capacity of the simple 7-cycle remains open for 56 years now, reflecting the importance of the problem. Recent results identify that the Lovasz number, an upper bound on Shannon capacity, evaluates the quantum advantage of performing quantum measurements on a system as opposed to classical measurements and is central to the notion of quantum contextuality. Our project proposes to investigate generalisations of Shannon capacity and Lovasz - the edge of a graph usually connects mutually exclusive propositions, and we generalise so that connected propositions are exclusive to within some probability. We also associate to each edge a probabilistic message allowing us to consider generalised Shannon capacities and Lovasz numbers of graph and hypergraph-based message-passing algorithms. A further generalisation is to replace with generalised measurement strategies based on, say, tight frames or other non-orthogonal sequence sets. Moreover we shall classify graphs according to generalisations and variations of their Shannon capacity, Lovasz number, and fractional packing number. We plan to consider message-passing algorithms on non-bipartite, mixed, and dynamic graph and hypergraph scenarios, both in classical and quantum contexts. The project team comprises 2 international partners - see: http://personal.us.es/adan/home.htm and http://www.ucl.ac.uk/~ucapsse/ and 1 national expert and the project leader, and we apply for 1 postdoc and 1 PhD.

Funding scheme:

IKTPLUSS-IKT og digital innovasjon