The credible quantum-to-robotics path runs through chemistry
Simulating molecules and materials is the application quantum computers are actually suited to. Robots are downstream of materials in a way that is easy to overlook.
Quantum computers are not general accelerators. The application where the case is strongest is simulating quantum systems — which is to say chemistry and materials — because that is a problem whose difficulty comes from exactly the structure the hardware natively represents.
Robotics sits downstream of materials science more than its software-heavy self-image suggests. Actuator performance is a magnetics and alloys problem. Runtime is an electrochemistry problem. Compliant and soft robotics is a polymers problem. Durable joints and skins are a tribology and composites problem. Every one of those is bounded by materials whose behaviour is, at bottom, quantum mechanical.
So the honest causal chain is long and indirect: a quantum computer helps a chemist characterise a catalyst or an electrolyte, that feeds a materials programme, that programme eventually yields a better cell or magnet or elastomer, and years later a robot runs longer or grips more gently. Every arrow in that chain is real. None of them is fast, and the last one is separated from the first by an industrial development cycle.
It is worth stating the timescale explicitly because the alternative — quantum computing as a near-term robotics accelerator — sets expectations that will not be met and then discredits a path that is genuinely sound. Slow and real beats fast and imaginary, provided nobody promised fast.