Quantum computation promises to solve certain problems that are fundamentally out of reach without it. But taking advantage of quantum capability requires a radical change in approach to computation. Quantum computation operates on fundamentally different principles than classical computation. By far the most prevalent model of quantum computation uses quantum circuits. Programming in this low-level and rigid model needs specialist knowledge. Most current quantum programming languages they describe how to construct a circuit, rather than what the circuit should actually do. Universal properties can extract conceptual essence without superfluous mathematical details. A quantum programming language based on them can be used by programmers who understand the concepts but not necessarily the mathematics behind quantum computation. Such a language frees the programmer to express algorithms at a higher level of abstraction. Universal quantum programming is also better at preventing and fixing programming errors. Universal quantum programming has three main advantages. First, programmers can build programs out of smaller components, which can be individually constructed and tested. This is essential for scalability: increasing the size and complexity of programs is only possible if programmers can control this complexity. Second, there are mathematical semantics that abstract from merely implementational details. Programmers can only invent truly new quantum algorithms if the language allows a sufficiently high-level view of computation. Third, the programmer can express their thoughts freely at a natural level of abstraction. This project has two main contributions towards universal quantum programming. First, as a short-term test case, we focus on dynamic quantum measurement. Every step in a quantum circuit is reversible, and only at the end is classical data extracted by an irreversible measurement. There are many advantages to performing measurements dynamically, partway along the quantum circuit, but this breaks many verification tools for quantum programs. Existing languages can express dynamic measurement at a low level of abstraction, but ideally the programmer need not specify when measurements happen and can leave this burden to the compiler. Supporting dynamic measurement through universal properties lets the programmer write bigger and better quantum programs. Second, the project will consider robustness in the face of error-prone quantum hardware. Dynamic quantum programs need to deal with noisy measurements. Relatedly, quantum computation can in theory be more energy-efficient than classical computation, but there is currently a lack of in-depth analysis of the in-principle energy use of quantum computation. This project will quantify the effect of dynamic measurement on the robustness of quantum programs, letting the programmer trade off robustness and energy use against quantum measurements. This project provides Dynamic and Universal Quantum programming, which is more flexible, more scalable, and more verifiable.

Programming classical computers has become a popular practice thanks to high-level programming languages and compilers which enable the running of high-level programs on different computing platforms. For critical applications, we now have verified compilation schemes and certified compilers which ensure the correctness of the compiled executions. This is done by reference to a mathematical model of the high-level code. In this project we will establish such a promising trajectory for quantum computing, taking into account the subtle features of quantum computers. This will be achieved by bringing together expertise in software testing and quantum simulation. The results of this research will lead to verified software for quantum computing applications and consequently, to wide-spread and effective exploitation of quantum computing.

In our everyday life we rarely think about the effects of quantum mechanics, and yet they are constantly around us, determining the properties of every material object in our world. The laws of quantum physics define every property of matter, from the behaviour of individual atoms, to how the atoms bind together to form materials, to the characteristics of these resultant materials. They also determine if and how systems of many interacting particles establish an equilibrium or steady state governed by a handful of statistical laws. Physicists are now able to engineer large, tunable collections of interacting quantum particles, both in quantum computing devices and in ultracold atomic gases and solid-state materials. Often, such systems cannot be described by standard techniques that focus on quantum states that have simple structures. In many cases, the routes by which such systems come to equilibrium involve subtle and surprising features of quantum mechanics, necessitating entirely new ways of thinking, or require substantial extensions of older approaches such as hydrodynamics. Another striking new idea that has emerged recently is that quantum mechanical coherence can be preserved even when many-body systems are far from their lowest-energy state. The word "coherence" here implies that many microscopic objects are acting together in concert. Such behaviour, when it occurs, allows for the effects of quantum physics to be greatly enhanced, but it is usually washed out as systems achieve equilibrium, which can often be described well using classical physics. Finding routes to evade this equilibrium allows for new and unusual physical phenomena with significant potential utility for quantum technology. Yet a third set of new concepts is motivated by the capabilities of the present-day "noisy, intermediate-scale quantum" (NISQ) devices. In contrast to conventional platforms, these offer the possibility of punctuating the time evolution of a many-body system by measurements, and using the results to shape future evolution - a new form of "quantum interactive dynamics", where the scientist is an active participant rather than a passive spectator. Understanding the new states of matter enabled in this setting and the protocols needed to implement them on NISQ processors is an exciting new frontier. We have organised our research into three themes: (1) What are the mechanisms by which quantum systems approach an equilibrium state? We will develop a better understanding of universal aspects of the equilibrium state in quantum many-body systems. We will also seek to understand certain experimental systems, such as cold atomic gases or solid-state materials, that can be studied using hydrodynamic principles and their generalizations. (2) How can quantum many-body systems evade thermalization to access novel non-equilibrium regimes? We will seek to understand how frozen-in randomness and special symmetries can arrest the approach to equilibrium and allow quantum coherence to persist even in highly excited states. (3) What new possibilities are enabled by "quantum interactive dynamics"? We will clarify how the evolution of quantum systems towards or away from equilibrium can be shaped by measurement and feedback. The answers to these questions are likely to be central in harnessing the full power of quantum mechanics to accomplish complex tasks. Understanding the far-from-equilibrium and interactive dynamics of quantum many-particle systems is likely to play a similar role in the development of future quantum computing devices as the quantum theory of solids did in the technological revolutions of the past century. Thus, while our research is mainly academic in nature, we hope that our discoveries will enable technologies needed to address the challenges of the next century.

Quantum mechanics has been known for weird nature it predicts: It allows several distinct states to exist simultaneously (quantum superposition) and super-strong correlations (quantum entanglement) between particles. Quantum computing (QC) makes use of this weird nature for faster and more accurate data processing and secure data protection than any conventional computers can offer. Five use cases for QC identified by the UK National Quantum Computing Centre are optimisation, quantum chemistry, fluid dynamics, machine learning and small molecule simulation. The UK government has long recognised the future potential of QC, having established in 2014 a national network of Quantum Technology Hubs. Now, QC appears as one of three "foundational technologies" for the digital sector in the UK National Plan for Growth. International development in quantum technology is proceeding rapidly, with a recent, early academic demonstration of digital quantum advantage by the US technology monolith Google. Besides established companies, QC development has spawned many start-up companies worldwide with UK representations including Cambridge Quantum Computing, ORCA Quantum Computing, Oxford Ionics, Oxford Quantum Computing, Phasecraft, Quantum Motion, Rahko and Riverlane. The increasing scale of QC raises several key technological challenges: (1) Isolated control and inter-system crosstalk, (2) Efficient classical monitoring and feedback, and (3) Efficient quantum access to large amounts of relevant problem data. Indeed, facing similar problems in conventional computing, researchers in information and communication technology (ICT) have been working on 'distributed computing', including cloud computing and optimal processing of distributed data. With ICT and QC researchers working together, this multi-disciplinary team will tackle the timely challenge of the design and efficient use of networked clusters of quantum devices for distributed quantum information processing (DQIP). While complementing the on-going efforts on scalable quantum computing, this project aims to develop a clear and feasible roadmap to practical DQIP and to introduce lynchpin design principles to enable cohesive efforts across each of the complex and strongly inter-related aspects of DQIP development. This project will therefore also contribute to showing significant quantum advantages as quantum systems grow toward the industrial scale, increasing certainty in the timeline and practical industrial evaluation of QC, laying a foundation for increased investment and growth in this area for the UK economy moving forward. Specifically, this project will explore four key aspects of the design problem: (1) At the application layer, we set concrete structures and requirements for the algorithm and architecture; (2) At the algorithm layer, we define communication requirements in a hybrid environment of quantum and conventional processing nodes; (3) At the network layer, the required quantum processes will be optimised for the maximum connectivity; and (4) At the optical interconnect layer, the encoding and efficient transmission of quantum information in photonic systems will be studied. Our goal is to bridge the gap between QC and the established tools and methods in ICT, and to focus in on the strong network of inter-related constraints between these different aspects of the design problem to enable the development of practical DQIP. To achieve this goal, the project brings together an investigative team with strong track records for prior research in diverse and complementary fields, including computational finance and fluid dynamics, optimised networked systems and distributed computing, and quantum information and optics.

For many years, quantum mechanics has been a curiosity at the heart of physics. Its development was essential to many of the key breakthroughs of 20th century science, but it is famous for counter-intuitive features; the superposition illustrated by Schrödinger's cat; and the quantum entanglement responsible for Einstein's "spooky action at a distance". Quantum Technologies are based on the idea that the "weirdness" of quantum mechanics also presents a technological opportunity. Since quantum mechanical systems behave in a fundamentally different way to large-scale systems, if this behaviour could be controlled and exploited it could be utilised for fundamentally new technologies. Ideas for using quantum effects to enhancing computation, cryptography and sensing emerged in the 1980s, but the level of technology required to exploit them was out of reach. Quantum effects were only observed in systems at either very tiny scales (at the level of atoms and molecules) or very cold temperatures (a fraction of a degree above absolute zero). Many of the key quantum mechanical effects predicted many years ago were only confirmed in the laboratory in the 21st century. For example, a decisive demonstration of Einstein's spooky action at a distance was first achieved in 2015. With such rapid experimental progress in the last decade, we have reached a turning point, and quantum effects previously confined to university laboratories are now being demonstrated in commercially fabricated chips and devices. Quantum Technologies could have a profound impact on our economy and society; Quantum computers that can perform computations beyond the capabilities of the most powerful supercomputer; microscopic sensing devices with unprecedented sensitivity; communications whose security is guaranteed by the laws of physics. These technologies could be hugely transformative, with potential impacts in health-care, finance, defence, aerospace, energy and transport. While the past 30 years of quantum technology research have been largely confined to universities, the delivery of practical quantum technologies over the next 5-10 years will be defined by achievements in industrial labs and industry-academic partnerships. For this industry to develop, it will be essential that there is a workforce who can lead it. This workforce requires skills that no previous industry has utilised, combining a deep understanding of the quantum physics underlying the technologies as well as the engineering, computer science and transferrable skills to exploit them. The aim of our Centre for Doctoral Training is to train the leaders of this new industry. They will be taught advanced technical topics in physics, engineering, and computer science, alongside essential broader skills in communication and entrepreneurship. They will undertake world-class original research leading to a PhD. Throughout their studies they will be trained by, and collaborate with a network of partner organisations including world-leading companies and important national government laboratories. The graduates of our Centre for Doctoral Training will be quantum technologists, helping to create and develop this potentially revolutionary 21st-century industry in the UK.