Quantum Technologies promise to harness the power of quantum mechanics to deliver a new generation of devices whose performance surpasses what is possible with conventional technology. We can expect Quantum Technologies to deliver more powerful methods of computation, completely secure communication, enhanced metrology and sensors with unparalleled sensitivity. Accordingly, the development of Quantum Technologies has attracted substantial investments from national funding agencies worldwide, including in the UK and USA, as well as significant private investment in numerous start-up companies. Many Quantum Technology platforms are being developed, including trapped ions, ultracold atoms, superconducting devices and photons, each with their own strengths and weaknesses. Compared to these more established technologies, ultracold molecules are new to the arena. And yet molecules have many advantages stemming from their rich internal structure of vibration and rotation, long-range dipole-dipole interactions and strong coupling to applied electric and microwave fields. The goal of this proposal is to establish an international collaboration focused on overcoming the scientific and technical challenges that lie between our current experimental platforms and the realisation of molecular Quantum Technologies. Our collaboration involves researchers from Durham University, Imperial College, Oxford University, Harvard University and JILA at the University of Colorado. Our team consists of 10 world-leading investigators, all of whom are embedded in internationally recognised centres of excellence for atomic, molecular and optical physics research. Each investigator brings complementary expertise spanning the experimental and theoretical methods needed to realise our vision. Over the last decade, we have all individually contributed to the transformation of the field of ultracold molecules. We have learned how to produce a wide range of molecular species at ultracold temperatures - the key first step necessary to reveal and access the quantum behaviour of molecules. Subsequently, we have learned to trap, manipulate and control individual molecules at the quantum level. With our molecules now under control and a wave of second-generation experimental platforms coming online, we are on the cusp of a new era for ultracold molecule research. Now is therefore the perfect time for us to join forces and coordinate our research effort in this flourishing field towards Quantum Technology. Our specific research programme is organised around three major, inter-related goals. Firstly, we will learn to control molecule-molecule and atom-molecule collisions and interactions, enabling us to further cool our molecules deep into the quantum regime. Secondly, with our control of molecule-molecule interactions, we will create many-body quantum states of molecules in optical lattices suitable for quantum simulation of systems that are difficult to model on a classical device. Finally, we will learn how to engineer high-fidelity quantum gates between molecules held in optical tweezers - the essential building block of a molecule-based quantum computer. Successful delivery of these ambitious research goals will establish ultracold molecules as a competitive Quantum Technology and will enhance the UK's leadership in this strategically important area.

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.

Two-dimensional materials (2DM), derived from bulk layered crystals with covalent intra-layer bonding and weak van der Waals (vdW) interlayer coupling, offer a versatile playground for creating quantum materials with properties tailored for particular applications. This is achieved by combining different atomically thin 2DM crystals into heterostructures layer-by-layer in a chosen sequence. Unlike conventional crystal growth, this technique is not limited by lattice matching or interface chemistry, hence, it enables us to build heterostructures from several dozens of readily available vdW crystals with diverse physical properties (electronic, optical or magnetic). This platform offers broadly acknowledged potential for the realisation of nano-devices and designer meta-materials with new properties and functionalities determined by the coupling of adjacent layers, including interlayer band hybridisation and strong proximity effects. A new degree of freedom for controlling the properties of vdW heterostructures is the mutual crystal rotation - twist - of the constituent 2D crystals. Together with the lattice mismatch of the adjacent 2D crystals it gives rise to the moiré superlattice (mSL): a periodic variation of the local atomic registry, with the period controlled by the twist angle. Even a small twist can lead to remarkable changes in the properties of heterostructures - for instance, in homobilayers of 2DM it leads to strong spectrum reconstruction and formation of electron and hole minibands. So far, the breakthrough studies of moiré superlattices have been focused on graphene heterostructures with hexagonal boron nitride and on twisted graphene bilayers. Recently, initial exploration of twisted layers of transition metal dichalcogenides have begun, featuring four letters in a single issue of Nature in March 2019 (in one of those the members of this consortium have reported moire minibands for excitons). Not surprisingly, these recent developments have fuelled a world-wide race to develop this new field of materials science and solid state physics, branded as 'twistronics'. This project will pioneer the new scientific area of twistronics in novel types of 2DM heterostructures, mapping out the limits to which one can control their properties through the interlayer proximity and moiré superlattice effects. Using this approach, we aim to engineer flat electronic bands in semiconducting 2DM heterostructures, promoting quantum many-body effects, which we will explore through quantum transport and optical studies. Furthermore, we will realise the world-first twisted bilayers of new emerging 2DMs that exhibit strongly correlated states in their natural form ((anti)ferromagnetic, charge-density waves, or superconductivity) and explore novel physics in those system with an outlook for practical applications. In all material combinations, we will look into two distinct cases of (1) intermediate twist angles, where lattices are expected to behave as rigid solids, producing smooth variation in interlayer registry and (2) small twist angles where we have recently found that twisted 2D materials reconstruct to form extended commensurate domains separated by stacking faults. To achieve the ambitious and game-changing goals of this proposal, the consortium will employ a recently commissioned world-first nanofabrication facility, which allows assembly of van der Waals heterostructures in ultra-high vacuum. This unique instrument will provide the game-changing quality materials necessary for this project. Funding of this proposal will allow us to fully employ the potential of this new instrument and deliver ground-breaking new research and disruptive technologies.