Summary The "Atomic Quantum Clock" is a milestone of the European Quantum Technologies Timeline. Q-Clocks seeks to establish a new frontier in the quantum measurement of time by joining state-of-the-art optical lattice clocks and the quantized electromagnetic field provided by an optical cavity. The goal of the project is to apply advanced quantum techniques to state-of-the-art optical lattice clocks, demonstrating enhanced sensitivity while preserving long coherence times and the highest accuracy. A three-fold atom-cavity system approach will be employed: the dispersive quantum non-demolition (QND) system in the weak coupling regime, the QND system in the strong collective coupling regime, and the quantum enhancement of narrow-linewidth laser light generation towards a continuous active optical frequency standard. Cross-fertilization of such approaches will be granted by parallel theoretical investigations on the available and brand-new quantum protocols, providing cavity-assisted readout phase amplification, adaptive entanglement and squeezed state preparation protocols. Novel ideas on quantum state engineering of the clock states inside the optical lattice will be exploited to test possible quantum information and communication applications. By pushing the performance of optical atomic clocks toward the Heisenberg limit, Q-Clocks is expected to substantially enhance all utilizations of high precision atomic clocks, including tests of fundamental physics (test of the theory of relativity, physics beyond the standard model, variation of fundamental constants, search for dark matter) and applied physics (relativistic geophysics, chrono geodetic leveling, precision geodesy and time tagging in coherent high speed optical communication). Finally, active optical atomic clocks would have a potential to join large scale laser interferometers in gravitational waves detection. Relevance Q-Clocks will provide a major advance in the area of "Quantum metrology sensing and imaging", in particular by “the use of quantum properties”, such as multi-particle entanglement, quantum state engineering and quantum non-demolition measurement, “to enhance the precision and sensitivity of time and frequency standards”. In atomic clocks, like all atom sensors, the information is encoded in the quantum wave function of atoms: the quantum protocols developed and experimented in this project aim at “developing detection schemes that are optimised with respect to extracting relevant information from physical systems” in order to reduce the inherent quantum noise associated with this extraction. With Q-clocks we pursue an important technological development that will extend sensing to new targets and applications, including Earth mass flow (better weather forecast), underground composition (mineral survey), surveying the Earth’s interior (models for earthquakes), chrono geodetic leveling (better models of the geoid) and time tagging in coherent high speed optical communication, with important spin-offs such as generation of ultra-stable microwave sources with numerous applications in advanced electronics.

The quantum internet will drastically change the way we process information, communicate and compute. The last decade saw the development of the first small-medium size quantum networks, prototypes of this ambitious long-term goal. These already existing real-world quantum networks open new possibilities for quantum information processing. New recent protocols show that they offer a radically new range of application of quantum technologies, e.g., for certification tasks based on Bell nonlocality of quantum correlations, cryptography, or fault-tolerant quantum computation. However, the potentialities they offer are primarily ignored: in nowadays experiments, quantum networks are mainly used to simulate single quantum states, e.g., the standard Alice and Bob scenario. Genuine quantum network protocols remain mostly experimentally infeasible due to their unrealistic theoretical requirements, e.g., in terms of noise. With COMPUTE, we will drive the future development of quantum networks by (1) providing a coherent framework to guide the theoretical study and real-world development of quantum networks, (2) making possible the implementation of real-world quantum network protocols and (3) developing a framework for distributed quantum computing running on the quantum network architecture to outperform noisy intermediate-scale (single processor) quantum computers. From a methods perspective, COMPUTE will meet these objectives by dramatically improving existing noncommutative polynomial optimisation methods central to tackling quantum information problems. COMPUTE will (4) cross the traditional boundaries between the polynomial optimisation and quantum information communities by making the former's tools accessible to the latter and the latter's challenges available to the former.