2007/01/26 by Samuel Kutin, Samuel A. Kutin, Kutin, Samuel A. +5 · 4 citations
Computer Science · Physics and Astronomy · #Coding theory and cryptography #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0701194
19 pages
arxiv created 2007/01/26 · openalex publication_date 2007/01/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 GLn(2) as a circuit of depth 5n. We show that some linear operations require depth at least 2n+1.