Fast quantum computation at arbitrarily low energy
Abstract
One version of the energytime uncertainty principle states that the minimum time T_{⊥} for a quantum system to evolve from a given state to any orthogonal state is h /(4 ∆ E ) , where ∆ E is the energy uncertainty. A related bound called the MargolusLevitin theorem states that T_{⊥}≥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 timeindependent Hamiltonians in which computational clock speed becomes arbitrarily large relative to <E > and ∆ 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.
 Publication:

Physical Review A
 Pub Date:
 March 2017
 DOI:
 10.1103/PhysRevA.95.032305
 arXiv:
 arXiv:1701.01175
 Bibcode:
 2017PhRvA..95c2305J
 Keywords:

 Quantum Physics
 EPrint:
 Added ref 36. Published version