Proof of the usefulness of a quantum computer. Quantum supremacy means that a quantum computer is capable of solving a problem that would take many years with a classical computer.
A First Claim
In 2019, Google claimed its Sycamore quantum computer solved a mathematical problem in three minutes that would take a supercomputer 10,000 years. However, this has been refuted by IBM and others, stating that it would only take a few weeks of classical computation. In addition, the problem that was solved was considered irrelevant for all practical purposes.
In Roger Grimes' book "Cryptography Apocalypse," an alternative type of quantum supremacy was proposed. Grimes said that a quantum computer may achieve supremacy when it is able to solve a problem that a classical computer cannot solve at all no matter how much time it takes. See
quantum computing and
quantum secure.