# Quantum Computation and Machine Learning

### Home

Our aim is to explore the interplay between quantum computation, quantum information and machine learning. Two main questions drive our research: can we construct better learning algorithms using quantum resources? Can we use the tools of machine learning to better manipulate and investigate quantum states? Some of the topics at the centre of our works are quantum algorithms for machine learning and linear algebra, combinatorial optimisation and quantum learning theory.

For machine learning activities at UCL, see the following links:

- UCL Gatsby Computational Neuroscience Unit
- Centre for for Computational Statistics and Machine Learning
- UCL Intelligent Systems group

For any questions or inquiries related to our research in this area, please contact Andrea Rocchetto or Leonard Wossnig.

### Review Articles

In the following we list our results in various sub-fields of quantum machine learning. Readers who seek a detailed introduction can refer to our recent review articles:

### Learning Theory

Learning theory aims to place the problem of learning from data on a solid mathematical foundation. Typical questions that one asks in this setting are: how much data is required to learn a given function? What computational resources are required to perform a learning task? Through the study of formal models of learning we seek to understand whether quantum resources can be exploited to perform a learning task more efficiently. Known results indicate that depending on the type of learning model considered, it is possible to have a better generalisation error (*i.e.* we can learn with fewer examples) or we can learn functions that would otherwise be hard for classical learners. The framework of learning theory can also be applied to the study of quantum systems. In this case, our research focuses on investigating the relationship between quantum states that can be efficiently learned and the class of circuits that can be efficiently classically simulated.

### Quantum Linear Algebra and Machine Learning

In quantum linear algebra we seek out algorithms that allow us to speed up fundamental tasks like solving systems of linear equations. These are important since many machine learning algorithms rely on such tasks as subroutines. Thus, coming up with genuine ways to improve classical linear algebra methods or developing quantum methods for these tasks is an important part of QML. The practicality of these algorithms remains an open question, due to the underlying assumptions.

### Quantum Sampling

Recently, there has been increasing interest in the potential that quantum computing technologies have for speeding up sampling. This goes beyond the original focus of the quantum annealing computational paradigm, which was solving discrete optimization problems. The focus of our research is the development of hybrid quantum-classical algorithms capable of enhancing and tackling large industrial-scale machine learning data sets.

### Learning for Quantum Hardware

Classical machine learning techniques can be used to help the physical design of quantum hardware for quantum information processing. Indeed, quantum physics is notoriously difficult to understand using our classical intuition, and this limits our ability to engineer physical quantum devices. A possible application is the design of Hamiltonian computers, where machine learning tools are used to reduce the resource overhead for obtaining quantum gates with minimal control.