Quantum technology is an exciting field where new scientific discoveries have great potential to be used in practical applications such as in quantum computing. Although quantum supremacy has been recently demonstrated in fully superconducting qubits, there is a major challenge in promoting these many-qubit processors feasible for technological applications and advanced science experiments: higher fidelity in a power-efficient control and readout architecture is required. This action ConceptQ aims to demonstrate a new superconducting-qubit concept that has a surprisingly simple structure consisting only of standard materials and a single Josephson junction while providing insensitivity to charge and flux noise, and most importantly large anharmonicity. We combine these properties with new ideas in the pursuit of record-breaking fidelities in quantum-logic gates, in initialization, and in readout. Importantly, we introduce cryogenic active components to implement elementary qubit operations at millikelvin temperatures thus paving the way for a power-efficient integrated quantum-classical control system. Finally, we aim to combine the best new methods and designs for a multi-qubit processors and for a demonstration of a set of algorithms at unprecedent fidelity. With these breakthroughs, we aim to contest the transmon, the standard high-fidelity superconducting qubit, thus boosting quantum-technology research and methodology not only in computing but also in sensing and simulation. This potentially opens horizons for novel scientific discoveries in classical cryoelectronics, quantum calorimetry, open quantum systems, and quantum thermodynamics. ConceptQ is a science project, but thanks the quantum industry, it holds great potential for advancement of global wellbeing, e.g. through envisioned long-term applications in security, quantum chemistry, and artificial intelligence.