Fermionic Linear Optics Revisited
David P. Divincenzo, Barbara M. Terhal · 2004
We provide an alternative view of the efficient classical simulatibility of fermionic linear optics in terms of Slater determinants. We investigate the generic effects of two-mode measurements on the Slater number of fermionic states. We argue that most such measurements are not capable (in conjunction with fermion linear optics) of an efficient exact implementation of universal quantum computation. Our arguments do not apply to the two-mode parity measurement, for which exact quantum computation becomes possible, see [1]. Dedication to Asher Peres It is a pleasure to contribute to the Festschrift for Asher Peres ’ 70th birthday. To characterize Asher’s achievements in physics and quantum information theory, we would like to quote from a novel by the Austrian writer Robert Musil (1880-1942) The man without qualities written in 1930 [2]. The protagonist of the novel, Ulrich, is full of praise about science: But one thing, on the other hand, could safely be said about Ulrich: he loved mathematics because of the kind of people who could not endure it. He was in love with science not so much on scientific as on human grounds. He saw that in all the problems that come within its orbit, science thinks differently from the laity. If we translate “scientific outlook ” into “view of life,” “hypothesis ” into “attempt, ” and “truth ” into “action, ” then there would be no notable scientist or mathematician whose life’s work, in courage and revolutionary impact, did not far outmatch the greatest deeds of history. The man has not yet been born who could say to his followers: ”You may steal, kill, fornicate- our teaching is so strong that it will transform the cesspool of your sins into clear, sparkling mountain streams. ” But in science it happens every few years