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