© 1995 Nature Publishing Group is a male's trait value and G 1 is the trait's genetic variance): the correlation thresh- old then rises to about 0.25, and it rises still further, to about 0.5, if the preference experiences a similar intensity of stabiliz- ing selection as well. No cycling occurs if the correlation is below the threshold value. Instead the population settles into an equilibrium that may or may not fea- ture extreme male displays, depending in part on whether or not exaggerated pref- erences are produced as a side-effect of natural selection on female behaviour. This is an important but unanswered empirical issue. So the possibility of evolutionary cycles hinges on the size of this genetic correla- tion. How large do we expect it to be in nature? So far, theorists have been able to calculate the correlation only under assumptions that are simplified carica- tures of the genetics and behaviours that underlie real traits and preferences. Predictions for the correlation that are robust to these poorly known details and based on measurable quantities would be useful. A second wish is for a theory of how the genetic variation in the preference and trait changes through time - which of course requires that we understand the causes of quantitative genetic variation. Iwasa and Pomiankowski take these vari- ances to be constants, which is reasonable given that the means of the trait and pref- erence make excursions of only about one phenotypic standard deviation in their examples. But that amount of change is trivial compared to the differences we see between, say, the male plumages of differ- ent pheasant specie s. If cycles are involved in generating such diversity, we will ulti- mately need a theory for the dynamics of the variances when means evolve over many phenotypic standard deviations. Whether changing variances will inhibit cycles or amplify them, or perhaps throw evolution into chaos, is anyone's guess. 0 Mark Kirkpatrick is in the Department of Zoology, University of Texas, Austin, Texas 78712, USA. Nick Barton is in the Institute of Cell, Animal, and Population Biology, University of Edinburgh, West Mains Road, Edinburgh EH9 3JT, UK. 1. lwasa. P. & Pomiankowski. A. Nature 377. 420-422 (1995). 2. Joyce. J. Rnnegans Wake (Faber, London, 1939). 3. Pomiankowski, A. J. theor. Bioi. 128, (1987). 4 . Kirkpatri ck, M. in Sexual Selection: Testing the Alternatives (eds Bradbury, J. W. & Andersson. M. B.) 67-82 (W1Iey. Chichester, 1987). 5. Kirkpatrick, M. & Ryan. M. Natur e 350, 33-38 (1991). 6. Fi sher. R. A. The Genetical Theory of Natural Selection (Clarendon, Oxford , 1930). 7. Lande. R. Proc. natn. Acad. Sci. U.S.A. 78, 3721- 3725 (1981). 8. Murray, J. D. Mathemati cal Biology, 161- 166 (Springer. Berl in, 1989). 9 . Ludwig, D., Jones, D. D. & Holling, C. S. J. Anim. Ecol. 47, 315-332 (1978). 10. Turelli, M. Theor. Popular. Bioi. 25, 138-193 (1984). 11. Endler, J. A. Natural Selecti on in the Wild (Princeton Univ. Press, 1986). NATURE · VOL 377 · 5 OCTOBER 1995 NEWS AND VIEWS QUANTUM COMPUTING------------------ Towards an engineering era? Charles H. Bennett and David P. DiVincenzo ONE of the paradoxes of quantum theory is how little its strange foundations obtrude into everyday life, even while sup" porting an edifice of chemistry and physics that explains the existence and properties of ordinary matter in exquisite detail. To marvel at the foundations themselves - in the form, say, of the two-slit experiment or the Einstein-Podolsky-Rosen effect- one must generally visit a textbook or a laboratory. But it is beginning to appear that the foundations of quantum mechan- ics will find a fairly direct and visible application in the new science of informa- tion processing. For about ten years, there have been speculations about the vast and distinctive powers a quantum computer would have if one could ever be built. Now it appears that the subject of quantum computing is emerging from this visionary prehistory into a distinct 'experimental' era. Powerful algorithms exploiting the unique capabili- ties of a quantum computer are now wide- ly understood, and systematic searches for new algorithms are under way. On the hardware side, the implementation of the logic gates of a quantum computer is now, at some rudimentary level, within the purview of well established experimental physics. It is still too early to tell when or whether quantum computing will advance to a third, 'e ngineering' era of routine practical application. At a summer workshop of quantum computation*, the talks, while still includ- ing 'visionary era' discussions of Bell's inequalities, quantum cellular automata and the 'many-worlds' interpretation, had moved on to include concrete discussions of experimental realizations of quantum logic gates - to the extent that the Uni- versity of Innsbruck group unabashedly presented a "realistic model of a quantum computer" (T. Pellizzari; ref. 1). Their scheme for implementing quan- tum logic builds on the details of some of the hottest trends in atomic spectroscopy, in particular a technique called 'dark-state transfer of Zeeman coherence'. A Zee- man-coherent atom is one in which the wavefunction is only non-zero for one of the members of the ground-state multi- plet (containing Zee man fine structure). This wavefunction can be moved to the other member of the multiplet if the atom is exposed to two optical beams which couple these two ground-state levels to an excited state (see figure). Th e rule is first to turn bea m B 2 on, which leaves the sys- tem in state 1, but strongly couples states 2 and 3. When B1 is turned on next, the *Quantum Computation, Institute for Scientific Interchange , Turin, Italy, 25 June-7 July 1995. system is transferred from 1 to the 2-3 complex, but, remarkably, because of quantum interference the amplitude of the wavefunction in the excited state 3 always remains very small. Then if B 2 is turned off, the system wavefunction is entirely in state 2; turning off B 1 com- pletes the process. This kind of spectroscopy has many advantages as a basic step in quantum State 1 State 2 In dark-state spectroscopy, a quantum sys- tem passes from state 1 to state 2 by mixing with an excited state 3 using coherent radia- tion (modes 81 and 8 2 ). computation. The instantaneous state is always 'dark': that is, it cannot suffer spontaneous emission from the excited state, as its probability density for being in this state is vanishingly small (if the beams are turned on and off slowly enough). Thus the system always remains in a pure quantum state. If one of the beams B 2 is a localized cavity mode in a superposition of zero- and one-photon states, then the spectroscopy serves to map that super- position into the same superposition of the two Zeeman sublevels. It is this trans- fer capability which the Innsbruck workers have extended to solve the hardest prob- lem of physical quan tum logic gate design: moving a quantum state undisturbed from one subsystem (atom) to another. Several experiments have proved that different quantum bits (or 'qubits') can be made to interact controllably, in such a way that a rudimentary quantum logic gate is formed. In the work of C. Monroe and collaborators 2 , it has been successfully shown that the low-lying states of beryl- 389