Solving Materials Science Problems with Quantum Computers*

It has been twenty years of quantum computing research, and it is still not clear whether quantum computers can solve important problems in materials science. There are many obstacles that current quantum algorithms are facing. In particular, they only apply to a limited number of simulation problems and they assume properties of models that are not met in real-life scenarios. Furthermore, their complexities have been derived in the limit of infinite system size, which can be substantially different in practical situations. As a consequence, current requirements to achieve quantum advantage for problems in material science (where a quantum computer surpasses its classical counterpart) are not realistic. I will be discussing practical methods and techniques for solving materials science problems by current noisy and future fault-tolerant quantum computers. Those problems include the study of superconductivity and magnetism in strongly-correlated materials. I will be focusing on problems that appear to be best candidates for achieving quantum advantage, which naturally fit on existing and future quantum-computer hardware but are simultaneously intractable for classical computers.