Figure 3
Illustration: Alan Stonebraker

Figure 3: (a) Tripod structure that can be used for holonomic quantum computation. Three degenerate internal states k=1,2,3 of an atom, say, are coupled by three laser fields fk to an excited state e. (b) Two of the resulting energy levels form a degenerate pair of dark states that encodes the states of a single qubit. (c) One-qubit holonomies can be obtained by slowly varying the strengths and phases of the laser fields so that the initial and final field configurations coincide. A possible cyclic variation A→B→C→A in the special case of real-valued fk is shown. The resulting holonomy is fully determined by the solid angle π/2 which yields a holonomic gate that takes the logical states |0〉 and |1〉 into |1〉 and -|0〉, respectively