Quantum computers can be seen as "quantum accelerators" attached to a classical computer.

The application of quantum gates is a problem of sending signals to the quantum device/accelerator.

The classical aspect of signal sending is clocked by the classical computer. The speed of the quantum machine is determined:

relatively: to the worst case complexity of executing the algorithm on the classical machine instead of the quantum one (imagine using a CPU instead of the quantum accelerator)

exactly: time needed to run the algorithm on the quantum accelerator

The latter depends on the "gate times" of the accelerator.

Therefore, a quantum computer is clocked in multiple ways:

However, the clock speed does not play a significant role to why quantum machines seem for particular algorithms more powerful.

3Classical computers can work without a clock. Early designs were clocked because it's simpler, and current designs are clocked because that's what everyone has experience designing. – Mark – 2019-10-10T00:58:17.487