There's a lot of mystifying jargon in the field of quantum computation, so I would like to pose a question from elementary physics to maybe help clarify things. Is it not true that the speed of a real-world reversible computer scales linearly with applied force and entropy? The Heisenberg energy-time bound shows that energy release per time step is greater than Planck's constant over the step time. Also, the bound on total entropy over a complete computation is O(Boltzmann's constant) to avoid decoherence. By Boltzmann law, if the entropy release per step is much greater than Boltzmann's constant, then the quantum computer decoheres, and noise will be read out. So the runtime of a general quantum computer seems to be lower bounded by $(h*S^2)/(k*T)$, where $S$ is the number of steps, $h$ is Planck’s constant, $k$ is Boltzmann’s constant and $T$ is the ambient temperature. The runtime bounds on Grover’s and Shor’s algorithms don’t look too impressive under this basic analysis. It seems that MT and ML bounds dramatically overestimate the speed of quantum evolution. What is a straightforward answer to this objection?
Update: I additionally found this article by John D. Norton. Abstract: "The thermodynamics of computation assumes that computational processes at the molecular level can be brought arbitrarily close to thermodynamic reversibility and that thermodynamic entropy creation is unavoidable only in data erasure or the merging of computational paths, in accord with Landauer’s principle. The no-go result shows that fluctuations preclude completion of thermodynamically reversible processes. Completion can be achieved only by irreversible processes that create thermodynamic entropy in excess of the Landauer limit."
1.64 E-4nano seconds. What is there not so impressive ? $\endgroup$