Quantum computing has nothing to do with quantum fluctuations.

Where did you get the idea that quantum computers will exist at the Planck scale. That is nonsense.

Quantum computers require multiple quantum states on the macroscopic scale to be effective. They cannot exist on the Planck scale.

Even most quantum fluctuations do not exist on the Planck scale. They are governed by the uncertainty principle expressed as delta distance times delta energy equals a constant times the Planck constant. If the delta distance is on the Planck scale, then the energy delta is large enough to create an electron-positron pair, not at all what a quantum computer needs.

Quantum fluctuations must be eliminated from quantum computers for them to operate. Still not much hope for you.