The last years have seen significant advances in the field of quantum technologies, consolidating the development of basic requirements for quantum computation. Protecting the quantum computation from noise and decoherence has become more topical than ever, challenging and bringing quantum error correction fairly close to the integration into practical quantum computers. To make such an integration viable, the EQUIP project aims at (1) providing radically new solutions to fault tolerant quantum computation, covering both intermediate and large-scale quantum systems, and (2) bridging the critical gap between algorithmic solutions and latency-power-scalability constrained hardware designs. To achieve these goals, the project brings together interdisciplinary expertise, extending from the computer science foundations of quantum error correction and fault-tolerant computation, to algorithmic aspects, computer architectures, and hardware designs. The main contributions of the proposed research are as follows. First, the project will develop optimised low-qubit overhead solutions, suited but not restricted to intermediate scale quantum systems, including application-aware and software-based error mitigation techniques, and flag error correction protocols. Second, for large-scale systems, the project will develop thoroughly new approaches to accurate and hardware friendly decoding of quantum low-density parity-check codes, and will explore pioneering approaches relying on quantum polar codes. Third, the effectiveness of the proposed solutions will be demonstrated through either their implementation into real intermediate-scale quantum devices and quantum simulators, or the hardware prototyping of the most promising decoding solutions for large-scale devices. The ambition of the proposed research is to cover the essential prerequisites for preparing the European industry for the forthcoming challenge of quantum technologies.