Here is the latest cutting edge research:
You see, theorists — the potential users of quantum computers — have a dilemma. Quantum computers hold a lot of promise. It is highly likely that a good quantum computer can calculate the properties of things like molecules and atomic nuclei much more efficiently than a classical computer. Unfortunately, the current generation of quantum computers, especially those that the average theorist can get access to, are rather limited. This gives the theorists a challenge: can they make computations less resource-intensive so that they can be performed on the currently available hardware? ...Got that? One or two qubits. You could simulate those qubits on a 1970s era pocket calculator.
They reduced the calculation of nucleon energy levels to mostly single-qubit operations, with just a few two-qubit ones thrown in. From this, they were able to calculate the ground state energy and estimate the binding energy (the energy required to break up the nucleus) for a deuterium nucleus.
As with all quantum computations, the results are statistical in nature, so the researchers have to perform the computation many times and take the average result. In this case, the researchers made use of two quantum computers — the IBM QX5 and the Rigetti 19Q — via their publicly available cloud computing APIs. This limited the number of computations that they could perform. Despite this, they obtained results within a few percent of the experimental values.
The calculation itself is nothing special. This particular nucleus has long been solvable with classical computers.
This is a very very very long way from doing anything worthwhile.
Quantum computers have also claimed to have factored 15 into 3x5, but most of the cleverness went into reducing the work that the quantum computer had to to, so the quantum computer just had to do a couple of steps that any fool could do by hand.