Computation at a distance
Quantum Physics
2007-05-23 v1
Abstract
We consider a model of computation motivated by possible limitations on quantum computers. We have a linear array of n wires, and we may perform operations only on pairs of adjacent wires. Our goal is to build a circuits that perform specified operations spanning all n wires. We show that the natural lower bound of n-1 on circuit depth is nearly tight for a variety of problems, and we prove linear upper bounds for additional problems. In particular, using only gates adding a wire (mod 2) into an adjacent wire, we can realize any linear operation in GL_n(2) as a circuit of depth 5n. We show that some linear operations require depth at least 2n+1.
Cite
@article{arxiv.quant-ph/0701194,
title = {Computation at a distance},
author = {Samuel A. Kutin and David Petrie Moulton and Lawren M. Smithline},
journal= {arXiv preprint arXiv:quant-ph/0701194},
year = {2007}
}
Comments
19 pages