Modern physics explains a stunning variety of phenomena from the smallest of scales to the largest and has already revolutionized the world! Lasers, semi-conductors, and transistors are at the core of our laptops, cellphones, and medical equipment. And every year, new novel quantum technologies are being developed within the National Quantum Technology Programme in the UK and throughout the world that impact our everyday life and the fundamental physics research that leads to new discoveries. Quantum states of light have recently improved the sensitivity of gravitational-wave detectors, whose detections to date have enthralled the public, and superconducting transition-edge-sensors are now used in astronomy experiments that make high-resolution images of the universe. Despite the successes of modern physics, several profound and challenging problems remain. Our consortium will use recent advances in quantum technologies to address two of the most pressing questions: (i) what is the nature of dark matter and (ii) how can quantum mechanics be united with Einstein's theory of relativity? The first research direction is motivated by numerous observations which suggest that a significant fraction of the matter in galaxies is not directly observed by optical telescopes. This mysterious matter interacts gravitationally but does not seem to emit any light. Understanding the nature of dark matter will shed light on the history of the universe and the formation of galaxies and will trigger new areas of research in fundamental and possibly applied physics. Despite its remarkable importance, the nature of dark matter is still a mystery. A number of state-of-the-art experiments world-wide are looking for dark matter candidates with no luck to date. The candidate we propose to search for are axions and axion-like-particles (ALPs). These particles are motivated by outstanding questions in particle physics and may account for a significant part, if not all, of dark matter. First, we propose an experiment which will rely on quantum states of light and will detect a dark matter signal or improve the existing limits on the axion-photon coupling by a few orders of magnitude for a large range of axion masses. Second, we will build a quantum sensor which will improve the sensitivity of the international 100-m long ALPS detector of axion-like-particles by a factor of 3 - 10. Our second line of research is devoted to the nature of space and time. Recent announcements of Google's Sycamore quantum computer and the detection of gravitational waves have provided additional evidence to the long list of successful experimental tests of quantum mechanics and Einstein's theory of relativity. But how can gravity be united with quantum mechanics? To seek answers that inform this question, we propose to study two quantum aspects of space-time. First, we will experimentally investigate the holographic principle, which states that the information content of a volume can be encoded on its boundary. We will exploit quantum states of light and build two ultra-sensitive laser interferometers that will investigate possible correlations between different regions of space with unprecedented sensitivity. Second, we will search for signatures of semiclassical gravity models that approximately solve the quantum gravity problems. We will build two optical interferometers and search for the first time for signatures of semiclassical gravity in the motion of the cryogenic silicon mirrors. Answering these challenging questions of fundamental physics with the aid of modern quantum technologies has the potential to open new horizons for physics research and to reach a new level of understanding of the world we live in. The proposed research directions share the common technological platform of quantum-enhanced interferometry and benefit from the diverse skills of the researchers involved in the programme.