  One version of the energy-time uncertainty principle states that the minimum
time $T_{\perp}$ for a quantum system to evolve from a given state to any
orthogonal state is $h/(4 \Delta E)$ where $\Delta E$ is the energy
uncertainty. A related bound called the Margolus-Levitin theorem states that
$T_{\perp} \geq h/(2 E)$ where E is the expectation value of energy and the
ground energy is taken to be zero. Many subsequent works have interpreted
$T_{\perp}$ as defining a minimal time for an elementary computational
operation and correspondingly a fundamental limit on clock speed determined by
a system's energy. Here we present local time-independent Hamiltonians in which
computational clock speed becomes arbitrarily large relative to E and $\Delta
E$ as the number of computational steps goes to infinity. We argue that energy
considerations alone are not sufficient to obtain an upper bound on
computational speed, and that additional physical assumptions such as limits to
information density and information transmission speed are necessary to obtain
such a bound.
