Recent progress in quantum technologies is underpinning significant advances across many sectors including defence, healthcare, and communication. At the same time, several challenges emerge as scientists strive to manipulate quantum states for signal enhancement, noise reduction, and ultimately quantum computing. A paradigmatic example is the recent demonstration of noise mitigation on a 127-qubit chip, but this has highlighted the limitations of coherence time, gate fidelity, and error suppression, as well as the challenge of connecting large numbers of physically separate qubits. Therefore, whilst improvements on established technologies remain crucial for scaling them up, the search for alternative routes towards quantum computing remains a most promising pathway towards useful quantum supremacy. Quantum Information with Mechanical Systems (QuIMS) explores the potential of mechanical resonators as a novel computing platform, both in support of existing qubit technologies (e.g., for quantum memories) and as a stand-alone qubit technology. To this end, we will build mechanical resonators with ultra-high coherence times that are manipulated with extreme precision by means of light fields. In this opto-mechanical system, we will attempt for the first time to embed several qubits in a single mechanical resonator, removing the need for cumbersome connecting wires that impedes, for instance, spin qubit devices. These mechanical qubits are expected to offer exciting opportunities to implement multi-qubit gates directly on a single resonator, which can greatly suppress the main sources of errors encountered in current platforms. The core novelty on which QuIMS leverages is the quadratic opto-mechanical coupling, which is needed for mechanical quantum computing but has so far been out of reach. We will design new devices that exploit symmetry and phononic crystals to suppress detrimental contributions such as heating of the mechanical resonators. We will work with graphene and carbon nanotubes that are uniquely suited to achieve the quadratic regime owing to their extremely low mass and strong interaction with radio-frequency light. The synergy of our complementary state-of-the-art facilities and of experimental and theoretical expertise at the Universities of Exeter and Lancaster are ideally suited to nurture the ambitious aims of this proposal. Upon demonstrating the quadratic opto-mechanical interaction, in collaboration with project partners including the National Quantum Computing Centre, we will explore the potential of our devices for applications such as signal enhancement, noise reduction, mechanical signal processing, filtering, and transduction. Hence, we will benchmark the performance of our opto-mechanical quantum systems against that of other known platforms such as superconducting, photonic, Rydberg and ion devices. Finally, we will investigate how our platforms can be combined with existing technologies, to be employed, e.g., as highly coherent memories (due to the extreme quality factors attainable by mechanical resonators).

The project Software Enabling Early Quantum Advantage (SEEQA, pronounced 'seeker') is a joint effort by Oxford, UCL, and Bristol, supported by multiple UK quantum startup companies and NQCC. The aim is to make the era of "quantum advantage" arrive sooner! "Advantage" means having real working quantum computers that can perform tasks that are either impossible, or prohibitively slow or expensive, by any conventional means. We'll know this era has arrived when we can solve otherwise-infeasible tasks in areas such as chemistry and materials discovery or in solving complicated resource allocation problems with near-zero waste. Although quantum computers have long promised this kind of advantage, it has not yet been realised. There are many reasons -- partly it is just that the prototype hardware needs more time to mature. But progress needs to be made in the practical theory to support quantum computing, to 'lower the bar' that the hardware needs to be able to reach. This is what SEEQA will do, in three main themes: 1. Figuring out how best to use state-of-the-art conventional computing power to help early quantum computers. There are two main ways: First, the conventional computers can actually help run the task that the quantum computer is performing. The task gets broken up into lots of small quantum computations, and the conventional computer gets all the results and puts them together to decide what to do next. The other way a conventional computer can help is by monitoring the quantum processor for errors: there is some detective work to do in order to infer the nature of the errors from the evidence that comes from monitoring, and a conventional computer needs to do this -- it's called decoding. 2. Coming up with new ways in which to handle or suppress errors. As mentioned, quantum computers (especially the early ones) suffer from 'noise' which means little imperfections in everything that is done. If not handled, the resulting errors will lead to useless outputs. There are many ideas for fighting errors, but SEEQA will address new possibilities. In particular, SEEQA will investigate the interface between two major approaches to find new solutions: The approaches are called Quantum Error Mitigation (QEM), which suppresses error damage, and Quantum Error Correction (QEC) which can totally fix errors but is currently very expensive in terms of number of components needed. Also, SEEQA will explore and advance some of the more recent and sophisticated ideas for handling measurement errors -- if you can't trust the output of the quantum computer you are very limited! 3. Finally, SEEQA will focus on the interrelationship between the architecture or protocol we would like to perform, and the available hardware architecture (including noise sources and other imperfections, the 'topology' which means the question of which qubits can directly 'see' other qubits, and so on). Although quite a bit is known about this, there remain a great many questions within the two themes (a) "what algorithms can run well on my architecture?", and (b) "what architectures can my algorithm run on?" Underpinning all this theoretical research, it will be vital to be able to test things out. The SEEQA project will have two kinds of provision: First, very efficient software that runs on conventional computers to 'pretend' to be quantum computers - exactly simulating them using the well-known laws of quantum physics. However it will only ever be possible to work with small emulated quantum computers because the quantum state is so complex. So it is vital that SEEQA also has access to real prototype quantum processors -- and as many as possible because they are various types. Fortunately SEEQA has multiple letters of support, offering resources approaching £500k, from pioneering UK hardware companies that have working quantum prototypes right now. They will make available their experts and their devices to SEEQA in order to help us to succeed.

There has been rapid progress in recent years in exploring the possibility to use microscopic systems as quantum computers, to process information and solve computational challenges that are intractable even on the largest conventional supercomputers. While there has been a lot of progress in developing quantum computing, and even demonstrations claiming quantum primacy (where quantum systems outperform conventional computers on problems designed to test the specific quantum hardware), there are major open questions as to when we will first achieve a practical quantum advantage. This would mean obtaining solutions faster or that are novel compared to what is possible with a conventional computer, for problems of interest to science or industry (beyond simply testing the quantum hardware). While many systems under development are digital quantum computing devices, there is a growing class of analogue quantum simulators, which are highly controlled devices that can be used to implement and study models of other quantum systems. These are somewhat more analogous to analogue computers, or to devices in which we build scale models of dynamics such as wind and water tunnels. Like their analogue classical computing predecessors, these are likely to have impact for a restricted class of problems before we have large-scale digital quantum computers - and like wind and water tunnels they are likely to outperform digital quantum computers for specific tasks. In this Programme Grant, we aim to make a major step-change in the development of these devices, by demonstrating and then using a verified quantum advantage over any known classical device for specific classes of quantum dynamics. Our experimental programme is based on the most advanced platforms for analogue quantum simulation, specifically over 150 neutral atoms controlled by configurable arrays of laser light. We have three distinct platforms across our experimental teams, in which we will first demonstrate and verify operation in regimes of practical quantum advantage. In a close collaboration between experimental and theoretical researchers who set a roadmap for development of these platforms, we will explore and expand potential application areas. These will range from solid-state physics and material science, to using analogue quantum simulators as a testbed to develop next generations of quantum technologies, especially for measurement and sensing. Our overall vision is to make a transformative contribution to making these quantum simulation platforms useful beyond basic science, through development of the technologies and identification and prototyping of new application areas.

The primary objective of the QC2 CDT is to train the upcoming generation of pioneering researchers, entrepreneurs, and business leaders who will contribute to positioning the UK as a global leader in the quantum-enabled economy by 2033. The UK government and industry have demonstrated their commitment by investing £1 billion in the National Quantum Technologies Programme (NQTP) since 2014. In its March 2023 National Quantum Strategy document, the UK government reaffirmed its dedication to quantum technologies, pledging £2.5 billion in funding over the next decade. This commitment includes the establishment of the UKRI National Quantum Computing Centre (NQCC). The fields of quantum computation and quantum communications are at a pivotal juncture, as the next decade will determine whether the long-anticipated technological advancements can be realized in practical, commercially-viable applications. With a wide-ranging spectrum of research group activities at UCL, the QC2 CDT is uniquely situated to offer comprehensive training across all levels of the quantum computation and quantum communications system stacks. This encompasses advanced algorithms and quantum error-correcting codes, the full range of qubit hardware platforms, quantum communications, quantum network architectures, and quantum simulation. The QC2 CDT has been co-developed through a partnership between UCL and a network of UK and international partners. This network encompasses major global technology giants such as IBM, Amazon Web Services and Toshiba, as well as leading suppliers of quantum engineering systems like Keysight, Bluefors, Oxford Instruments and Zurich Instruments. We also have end-users of quantum technologies, including BT, Thales, NPL, and NQCC, in addition to a diverse group of UK and international SMEs operating in both quantum hardware (IQM, NuQuantum, Quantum Motion, SeeQC, Pasqal, Oxford Ionics, Universal Quantum, Oxford Quantum Circuits and Quandela) and quantum software (Quantinuum, Phase Craft and River Lane). Our partners will deliver key components of the training programme. Notably, BT will deliver training in quantum comms theory and experiments, IBM will teach quantum programming, and Quantum Motion will lead a training experiment on semiconductor qubits. Furthermore, 17 of our partners will co-sponsor and co-supervise PhD projects in collaboration with UCL academics, ensuring a strong alignment between the research outcomes of the CDT and the critical research objectives of the UK quantum economy. In total the cash and in-kind contributions from our partners exceed £9.1 million, including £2.944 million cash contribution to support 46 co-sponsored PhD studentships. QC2 will provide an extensive cohort-based training programme. Our students will specialize in advanced research topics while maintaining awareness of the overarching system requirements for these technologies. Central to this programme is its commitment to interdisciplinary collaboration, which is evident in the composition of the leadership and supervisory team. This team draws expertise from various UCL departments, including Chemistry, Electronics and Electrical Engineering, Computer Science, and Physics, as well as the London Centre for Nanotechnology (LCN). QC2 will deliver transferable skills training to its students, including written and oral presentation skills, fostering an entrepreneurial mindset, and imparting techniques to maximize the impact of research outcomes. Additionally, the programme is committed to taking into consideration the broader societal implications of the research. This is achieved by promoting best practices in responsible innovation, diversity and inclusion, and environmental impact.

Quantum information science and technologies (QIST) are uniquely placed to disrupt and transform sectors across the board. Quantum technologies, by exploiting the distinctive phenomena of quantum physics, can perform functions fundamentally unachievable by technologies based solely upon classical physics. For example, when applied to computing, calculations and operations that would take the best supercomputers hundreds of years to complete could be resolved within seconds using quantum computers; as another example, QIST can also be used in sensing and imaging to obtain enhanced precision in a variety of measurements ranging from gas concentrations to gravitational waves, supporting established industries in sectors like manufacturing, energy and healthcare. Furthermore, the application of quantum technologies will have significant implications within communications and security given their ability to break traditional encryption methods used to protect data within financial transactions or military communications while at the same time offering a range of novel, secure solutions largely compatible with the existing infrastructures. The potential of quantum technologies is well demonstrated through its significant financial and strategic backing globally. Restricted to academic environments up until the start of the last decade, the worldwide investment into quantum initiatives has now reached $33 billion, with significant contributions made across China, the US, and Europe. In the UK, the strategic importance of quantum technologies is clear: with a strategic commitment of £2.5 billion over the next decade, EPSRC has listed Quantum Technologies a mission-inspired research priority and the Department for Science Innovation and Technology have named quantum technologies as one of their seven technology families within the UK's Innovation Strategy. It is clear that, around the world, quantum technologies are flourishing. While the technological potential and national importance of QIST to the UK is undeniable, a key challenge to realising our ambitions in this area is the ability to develop a quantum workforce of capable physicists, engineers, computer scientists, and mathematicians with both the requisite expertise in quantum information science and expertise in the technologies that will realise it. In addition, the leaders of the UK's quantum future must possess critical professional skills: they must be excellent communicators, leaders, entrepreneurs, and project managers. To meet this key ambition and its resultant needs, the programme offered by the Quantum Information Science and Technologies Centre for Doctoral Training (QIST CDT) is uniquely positioned to deliver the diversity of skills and experience needed to supply the UK with internationally renowned QIST leaders across policy, innovation, research, entrepreneurship, and science communication. QIST CDT students will receive academic training delivered by world-recognised top educators and researchers; undertake industrially-relevant training modules co-delivered with industry partners; gain hands-on experience within world-leading quantum research laboratories; receive one-to-one entrepreneurial mentorship; undergo intellectual property and science policy training; undertake on-site industry placements; and complete multi-faceted cohort projects designed to develop multidisciplinary teamwork. This combination of world-class academic research training, which can be undertaken in a vast array of quantum-technology-relevant sectors, with bespoke instruction in professional skills driven by the needs of current and future quantum industry, will produce graduates with a drive to make a difference in Quantum Technologies and the skills to make that happen.