January 1, 1998
      
                  
        
  Author(s)
  C  Monroe,   Wayne M. Itano,   D  Kielpinski,   B E. King,   Dietrich  Leibfried,   C J. Myatt,   Q A. Turchette,   David J. Wineland,   Chris S. Wood
 
       
            
    
    
        Small laser-cooled crystals of atomic ions have attracted considerable interest in the last several years for their possible application toward quantum computation. This paper considers quantum logic schemes for small numbers of ions in the context of