Quantum computer succeeds where a classical algorithm fails
People have performed many mathematical proofs to show that a quantum computer will vastly outperform traditional computers on a number of algorithms. But the quantum computers we have now are error-prone and don't have enough qubits to allow for error correction. The only demonstrations we've had involve quantum computing hardware evolving out of a random configuration and traditional computers failing to simulate their normal behavior. Useful calculations are an exercise for the future.
But a new paper from Google's quantum computing group has now moved beyond these sorts of demonstrations and used a quantum computer as part of a system that can help us understand quantum systems in general, rather than the quantum computer. And they show that, even on today's error-prone hardware, the system can outperform classical computers on the same problem.
To understand what the new work involves, it helps to step back and think about how we typically understand quantum systems. Since the behavior of these systems is probabilistic, we typically need to measure them repeatedly. The results of these measurements are then imported into a classical computer, which processes them to generate a statistical understanding of the system's behavior. With a quantum computer, by contrast, it can be possible to mirror a quantum state using the qubits themselves, reproduce it as often as needed, and manipulate it as necessary. This method has the potential to provide a route to a more direct understanding of the quantum system at issue.