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15 March 2025
 
  » arxiv » quant-ph/0701194

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Computation at a distance
Samuel A. Kutin ; David Petrie Moulton ; Lawren M. Smithline ;
Date 26 Jan 2007
AbstractWe 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.
Source arXiv, quant-ph/0701194
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