Models of particles randomly moving through some defined space have been invaluable in studying everything from polymer diffusion to the ups and downs of the stock market. Classically, the simplest random walk is given by a walker (or particle that hops from one site to another) who takes one step either to the right or the left, depending on whether a tossed coin reads heads or tails. In a quantum mechanical setting, the particle can be at more than one site simultaneously. Like Grover’s algorithm for quantum database search, this feature leads to a speedup (here in diffusion) over its classical counterpart.
A quantum walk in a trapped ion system was proposed seven years ago. Now, Hector Schmitz and colleagues at the Max-Planck Institute in Garching, Germany, implement the experiment for a three-step quantum walk. The walker is a single trapped ion in a linear Paul trap. The coin states, which correspond to heads or tails, are two internal (hyperfine) states of the ion. The position of the walker is represented by a phase-space coherent state. The ion is initially prepared in a state of tails and the motional ground state. A radio-frequency pulse acts as the coin flipper, coupling the ion’s internal states, while laser pulses cause the walker to hop by displacing the coherent state. Because the hopping is conditioned on the result of the coin flip, a superposition of entangled coin and position states is created.
The sequence of coin flipping and hopping is done three times and then the state is read out. Three steps are sufficient to observe the differences between the quantum and classical walks, despite the technical limitations that prevented more steps. The authors suggest a different implementation that shows promise for significantly extending the quantum walk to several hundred steps. – Sonja Grondalski