Reliable classical computation requires energy dissipation. Landauer's principle sets the floor: erasing one bit costs at least kT ln 2. But achieving high reliability costs more — the dissipation increases as the error rate decreases. A classical memory that flips between 0 and 1 must dissipate energy proportional to the logarithm of its reliability. High-fidelity computation is thermodynamically expensive.
Quantum systems offer a continuous family of time-reversal symmetries that classical systems lack. A classical two-state memory has one natural symmetry: swap 0 and 1. A quantum two-state memory has a continuum of reversal operations parametrized by the Bloch sphere. This is not an exotic feature of quantum mechanics but a consequence of the geometry of Hilbert space — the state space has continuous symmetry where the classical state space has only discrete symmetry.
The thermodynamic advantage follows from the symmetry. The dissipation cost of reliable computation depends on how far the dynamics deviates from time-reversal. With more reversal symmetries to choose from, quantum systems can find reversals that are closer to the actual dynamics, reducing the deviation and thus the dissipation. The advantage is not marginal — it can be orders of magnitude in energy cost for the same reliability.
The structural point: the thermodynamic cost of computation is controlled by symmetry, not by the physics of the computing substrate. Classical systems are expensive because their symmetry group is small. Quantum systems are cheap because their symmetry group is large. The advantage of quantum computing, in this context, is not speed but efficiency — the same computation performed with less waste heat, enabled by a richer geometry of reversals.