Chicago Journal of Theoretical Computer Science

Volume 2007

Article 1

Published by Dept. CS U. Chicago. Copyright 2007 CJTCS

Computation at a Distance

Samuel Kutin, Center for Communications Research
David Petrie Moulton, Center for Communications Research
Lawren Smithline, Center for Communications Research
25 September 2007
(Submitted May 4, 2007)

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.

DOI: 10.4086/cjtcs.2007.001
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