Measures of quantum computing speedup
Abstract
We introduce the concept of strong quantum speedup. We prove that approximating the groundstate energy of an instance of the timeindependent Schrödinger equation, with d degrees of freedom and large d, enjoys strong exponential quantum speedup. It can be easily solved on a quantum computer. Some researchers in discrete complexity theory believe that quantum computation is not effective for eigenvalue problems. One of our goals in this paper is to explain this dissonance.
 Publication:

Physical Review A
 Pub Date:
 August 2013
 DOI:
 10.1103/PhysRevA.88.022316
 arXiv:
 arXiv:1307.7488
 Bibcode:
 2013PhRvA..88b2316P
 Keywords:

 03.67.Ac;
 02.60.x;
 02.70.c;
 Quantum algorithms protocols and simulations;
 Numerical approximation and analysis;
 Computational techniques;
 simulations;
 Quantum Physics
 EPrint:
 5 pages, to appear in Phys. Rev. A