Replies to some questions that I am frequently asked.

The short answer is yes. Quantum computers have performed meaningful computations, but not yet ones that give useful advantage, i.e. ones where using classical computation is outperformed. Some examples are calculating the ground state energy of molecules [1] [2] [3], MAXCUT optimization [4], or classification tasks [5] [6]. While these do give accurate answers for non-trival problems by running on real quantum hardware, the instances sizes are still very small.

When asking about milestones for quantum computer performance, clear terminology is important. I wrote a short, useful taxonomy in this post. Recently, an example of quantum supremacy was demonstrated, which means that some computation was performed that would be intractable to perform classically and that - in the computational complexity sense - we believe it to be hard for a classical computer and easy for a quantum one. I'd hesitate to say that this was a useful calcuation, though it may have application to generating certifiable random numbers. I co-wrote a short blog post about what the supremacy calculation does that covers the main idea using some short Python snippets.

When it comes to performing a valuable computation, we recently released some work on the required resources for derivative pricing [7] and there are there are other examples in chemistry [8] [9] and prime factorization [10]. Note that there is much left to discover in applying quantum computers.

There's been more then a few surprising creative uses already. There are folks looking at generating music [1] [2] [3]. There is also a growing field of quantum gaming. James Wooten has an excellent summary history of quantum computer games (with mention of a mobile game that Jo and I made at the one of the worlds first quantum computer hackathons). There's also a board game, mobile game, and quantum chess.