While our *bread and butter* is theory, our research also spans foundational issues, and sometimes leads to applications.

## Applied

### Hidden structure in complex time series

### Noise in quantum technologies

Many physical systems, both in nature and in the laboratory, exhibit highly complex behaviour as they evolve. However, this behaviour is often the result of underlying patterns that reveal themselves through temporal correlations in time series data. We have been applying methods from computational mechanics to extract the hidden structure from processes ranging from the intricate firing patterns of neurons in the fly brain and the unusual blinking statistics of quantum dots.

Current generation quantum technologies are typically noisy and prone to rapid decoherence due to their interactions with the wider environment. This is usually thought to be detrimental to their operation, but theoretical treatments often neglect correlations in the noise, since they are difficult to treat using conventional approaches. We have been using our framework to characterise the significant correlations in existing quantum devices, and are working to show how they could be exploited to perform classically hard tasks and achieve quantum supremacy.

A central obstacle in predicting the future behaviour of a dynamical process is to understand how much of the system's past affects its future. This topic is crucial for understanding the necessary resources to model the dynamics of an arbitrary system. We have developed a framework for operationally characterising memory effects in quantum dynamics, and are applying it to explore the structure of stochastic processes in the quantum domain. The methods we are developing will be used to battle non-Markovian noise via new error correction methods.

Time-energy uncertainty relations can be operationally interpreted as bounds on the minimal time required to achieve a measurable transition of the state of a system, and are thus known as quantum speed limits. In this picture, finding the fastest transition between two states is equivalent to finding the shortest path that connects them in the space of states. With our research we are working to exploit the geometry of quantum state space to improve the performance of these bounds and develop methods to better control quantum systems to perform useful tasks.

A primary goal of classical thermodynamics has always been to understand transformations of physical resources which enable useful tasks to be performed. The anticipated rise of quantum computing has catalysed a renewed interest in this question from the perspective of quantum information theory. The existing literature has explored how certain classes of quantum states can be useful in tasks such as information processing or communication. Our ongoing contribution to this field is to uncover how quantum processes can play the role of resources in the same way that quantum states do. In connection with our work on quantum dynamics, we have constructed an operational framework where non-Markovianity in a noisy background process can be useful.

Many-body quantum systems or those that interact with a complicated environment are notoriously hard to simulate, but predicting their properties and behaviour is crucial to the development of novel drugs, materials and nano-scale devices. We are using our understanding of the structure of memory in quantum processes to construct new theoretical tools and numerical methods to efficiently model technologically important chemical and solid-state dynamics.

The emergence of statistical mechanics from quantum mechanical laws is a topic of interest that dates back to the foundations of quantum theory itself. In particular, several questions remain concerning the emergence and robustness of quantum evolution towards equilibrium, now commonly known as equilibration. Our research focuses on the interplay between the general dynamics of open systems, equilibration and the statistical properties of complex systems.

We have been examining temporal correlations in classical and quantum mechanics to understand how they differ from their spatial counterparts. We have found connections between entanglement breaking channels, Markov processes and the CHSH inequality. We have also found that entanglement is often necessary to simulate exotic quantum causal structures. Our framework for describing quantum processes gives us a window into the structure of correlations and causality in space-time, which is far richer than that in space alone.