The move to electric vehicles (EVs) and fuel cell powertrains promises to eliminate tailpipe emissions but introduces fresh challenges further up the value chain with the use of rare earth elements (REEs). Permanent magnets found in EV electric motors can contain large amounts of metals such as neodymium, praseodymium and dysprosium, while fuel cells rely on platinum and ruthenium. The International Energy Agency estimates that production of REEs will need to grow by a factor of ten by 2030 in order to meet global net zero carbon targets. The problem is these elements are not only in scarce supply and expensive, but their extraction and processing are often linked to inhumane labour and harmful environmental practices. The shift to zero-emission mobility cannot be averted, but there could be a solution to reducing or eliminating these REEs, and quantum computing promises to help find it.