10120959QUantum Algorithms to SImulate MAny-body Physics (QuASi-MaP)ActiveCollaborative R&DInnovate UKQuantum computing holds great promise for simulating complex quantum many-body systems. This was identified already by Feynman in his 1982 speech at the very beginning of quantum computing as a research field. It remains the most promising application of quantum computing, both near-term and longer-term. The huge potential for large-scale quantum computers to address concrete problems in materials modelling, condensed matter physics and quantum chemistry that are beyond the reach of accurate simulation on classical computers has been mapped out in the decades since. Sophisticated quantum algorithms -- both rigorous and heuristic -- have been developed over the past two decades to address many of the most important fundamental quantum simulation tasks: time-dynamics simulation, ground state problems, spectral estimation and sampling from thermal states. However, there is a very large gap between the resources required to apply these algorithms to real simulation tasks of interest in research and in industry, and the resources available on current or foreseeable quantum computing hardware. For example, recent estimates of the resources required to simulate Strontium Vanadate (an important electron-transfer material used for a range of applications including battery technology and next generation solar cells) using the standard state-of-the-art algorithms require in excess of 800 qubits and circuit depths on the order of 10^8\. Whereas the largest quantum hardware platforms currently available have on the order of 100 qubits and are limited by noise to circuit depths on the order of 1000\. The overarching goal of this project is to bridge this gap and make the next significant advance in quantum simulation of many-body systems by combining the development of new theory approaches for the description and representation of said systems with new application-specific and hardware-specific algorithm design and optimisation techniques. With this project, we bring together 5 of the leading teams in Europe from industry and academia to deliver this: with expertise spanning from underpinning theory, through quantum algorithm and software, to quantum hardware design we are uniquely positioned to advance all three of these pathways in a coordinated way, which will enable us to make the most of the synergies between the three approaches.