Fast quantum computation at arbitrarily low energy

One version of the energy- time uncertainty principle states that the minimum time T-perpendicular to 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. Arelated bound called the Margolus-Levitin theorem states that T-perpendicular to >= 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. 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.