We propose to create a world-leading programme to search for spatial and temporal variations of fundamental constants of nature, using a network of quantum clocks. Our consortium will build a community that will achieve unprecedented sensitivity in testing variations of the fine structure constant, alpha, and the proton-to-electron mass ratio, mu. This in turn will provide more stringent constraints on a wide range of fundamental and phenomenological theories beyond the Standard Model and on dark matter models. The ambition of the QSNET consortium will be enabled by a unique experimental platform that connects a number of complementary quantum sensors across the UK, namely state-of-the-art atomic clocks, molecular clocks, and a highly-charged ion clock. Key to the proposal is the networked approach in which clocks, with different sensitivities to changes of the fundamental constants, will be linked using optical fibres. The network involves a range of different quantum sensing devices and devices with different technology readiness levels: from the more established microwave atomic clocks on the one end to the highly-charged ion clock on the other. QSNET will be able to deliver important results in the first years, and at the same time develop advanced quantum sensors to provide increasingly impactful results as the project continues and the most sophisticated sensors come on line.

The neutrino is the most abundant matter particle in the universe, and yet we do not know how much it weighs. We know that this particle, which carries 99% of the energy released in supernova explosions and has played an important role in the evolution of the early universe, has an anomalously small mass but we also know that it cannot weigh nothing. It is therefore imperative that we measure this, the last unknown mass in the Standard Model of particle physics. We cannot measure the neutrino mass directly in the laboratory. Rather, we try to constrain as precisely as possible the energy that has gone into creating the neutrino in processes such as nuclear beta-decay. Einstein's famous equation then tells us how to calculate the neutrino mass. Since the neutrino escapes undetected, the experimental task involved in measuring the minimum neutrino energy is actually to measure the maximum energy carried by all of the other particles. The most promising system to use is tritium, in which the proton inside a normal hydrogen nucleus is accompanied by two neutrons. Tritium beta-decays with a half-life of 12.3 years and a very small decay energy of 18.6 kilo-electron-volts; the fact that this decay energy is so small makes it uniquely sensitive to the tiny neutrino mass. We will need to develop techniques for trapping very large populations of tritium and measuring with exquisite sensitivity the energy of beta-decay electrons. As a first step we will use deuterium, which is much easier to handle than radioactive tritium. We will magnetically decelerate beams of deuterium into very well characterised magnetic traps. Electrons generated inside the trap will undergo circular motion and in so doing will emit microwave radiation. We will develop the quantum sensors that are capable of detecting the vanishingly low-power signals that are generated in this way. The ultimate aim of this project is to show that we have, in principle, the technologies required for a much larger experiment that would have sensitivity to all possible values of the neutrino mass. Such an experiment could perhaps be hosted in the UK where, at the Culham Centre for Fusion Energy, world-leading facilities for handling large tritium inventories exist and are being further developed.

Identifying the nature of the dark matter that dominates the mass distribution of galaxies and that plays a key role in our understanding of cosmology is a central unsolved problem of modern physics. Attention over the past 30+ years has focused on weakly interacting dark matter (WIMPs); however, a smaller but active community has been searching instead for 'hidden-sector' particles, including the 'QCD axion', using some of the world's most sensitive electronics. Axions were invoked to solve the so-called strong-CP problem, whereby the theory governing strong interactions is far more symmetric than our current theory, quantum chromodynamics, say it should be. But axions also turn out to be a natural candidate for the mysterious dark matter. Theory suggests that axions should be detectable through the tiny signals they emit, about a millionth of an attowatt, while traversing a microwave cavity in a strong magnetic field. These signals are at the limit of what can be detected using even cryogenically-cooled ultra-low-noise electronics, but in the past few years, rapid progress in developing newer and more sensitive quantum sensors, fueled by parallel research in quantum computing and measurement, has placed the detection of axions within our reach. The UK has considerable expertise in these new quantum devices, and this proposal aims to apply these pivotal new measurement technologies to the search for hidden sector particles. Our proposed search has two main parts. First, we have reached out to the world's most sensitive axion search experiment, ADMX, proposing to form a UK-USA collaboration. ADMX has welcomed this approach, and is keenly encouraging our participation. The UK will design and install a new axion detector inside the magnet and cryostat that ADMX already operate. Using this detector, we will search for axions in our Galaxy's dark matter halo in a previously unexplored mass range between 25 and 40 micro-electron volts. This range is well matched to indications from current theories of what the axion mass might be, although the possible range of masses is far larger, and so there is a great deal of ground to cover. The UK instrument will have at its heart one of our own superconducting quantum measurement technologies - a bolometric detector, a coherent parametric amplifier, a SQUID based amplifier, or a qubit based photon counting device. The technology to be used will be selected after extensive characterisation at participating institutes. The chosen technology will then be integrated into the ADMX instrument module, which will be characterised in a dedicated 10 mK cryostat at the University of Sheffield. This same cryostat will then double as the first target in the UK high-field low-temperature test facility that forms the second part of our proposal. Second, an internationally competitive UK effort in hidden sector physics needs a world class UK facility incorporating an extremely high field magnet: several times larger than those used for MRI imaging in health care. Such a magnet is necessary for axion searches, and axions are arguably the best motivated hidden sector dark matter candidate. The bore of the magnet needs to be very cold for the quantum electronics to work, about 10mK. We will partner with a national laboratory to build and operate a UK facility meeting these specifications. Many hidden sector search experiments could be housed in this facility, but the first one will be our own low-temperature quantum-spectrometer. Finally, to help maintain the UK's international prominence in fundamental physics, we must create a research community. Hidden sector physics is a rapidly growing subject, and the discovery of a whole new class of particles would drive particle physics into a new era, and quantum electronics into new applications and markets. We believe that the technology and techniques developed will have applications in areas as diverse as quantum computing, communications and radar.

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Technologies which operate using quantum superposition and entanglement are set to revolutionise how the world stores, processes, and communicates information. A quantum computer is expected to improve the efficiency of cloud computing by calculating the optimal way to distribute computational tasks amongst classical computers. In materials science, the evolution of chemical reactions is also more efficiently simulated by a quantum computer so they are thus likely to aid developments in synthetic chemistry, where understanding the behaviour of large molecules will lead to smarter power-saving materials. Quantum simulators will also elucidate the role of quantum effects in biological processes related to energy harvesting such as photosynthesis, and inform the design of materials with exotic power-saving capabilities such as a high-temperature superconductivity. The ability for quantum computers to factor in polynomial time could also have an enormous impact on internet security, which currently relies on the near impossibility of factoring large numbers. At the heart of quantum computers are building blocks known as quantum bits, or "qubits", which physically comprise two states that can be manipulated into any quantum superposition. One of the challenges we face with building a quantum computer is preventing the environment from killing these fragile superpositions through intractable and unintentional interactions. Most qubits are based on familiar particles, such as electrons in a quantum dot, ions in an atom trap, or photons in a waveguide, and it is unclear what the ultimate limit will be in the race to optimise their performance. An alternative and elegant approach to this problem is to find a qubit that is intrinsically protected from interacting with the environment. One such qubit employs exotic particles, known as anyons, that can encode the state of a qubit non-locally. Weak interactions with the environment can never collapse its state, making it more robust as a quantum memory. The aim of this research is to pave the way towards quantum control of such qubits by developing devices and techniques for observing anyons that emerge from the collective motion of electrons in a two-dimensional gas in contact with a superconductor. Quite remarkably, particles with very similar properties are already available, though not yet detected, in a material as simple and famous as graphene. My strategy is to expose the presence of these particles by monitoring how single electrons interact with them in nanodevices. In the longer term I anticipate materials with stricter topological protection to be come available, and my aspiration is to use the techniques developed here to store, manipulate, and read out decoherence-free quantum information.