The random walk is a useful model in fields from biology to computer science to math (see Physics Today, September 2019, page 18). For a horizontal one-dimensional walker, each step has some probability of going right or left. With the appropriate parameters, that simple picture turns out to be an accurate description of, for example, the paths that particles take during diffusion. The quantum analogue of the random walk replaces stochastic steps with superpositions: The walker steps left and right. With each step, the wavepacket spreads and eventually interferes with itself.
Quantum walks, like their classical counterparts, are versatile. They have applications in fields such as quantum optics, condensed-matter physics, and quantum information. Experimentally, they are typically realized and performed by photons in waveguides. Kenji Toyoda of Osaka University and his colleagues have now for the first time demonstrated quantum walks with phonons, the quanta of vibration. The phonons, which are exchanged between ultracold ions, have the advantage of being easily generated at a desired location and conveniently measured through fluorescence.
Toyoda and his team optically trap a row of four calcium ions close to their ground state energy and about 20 µm apart. A laser then excites one ion into its first vibrational state in the trap—that is, it introduces a phonon at one site (ion 2 in the image). That phonon jumps to neighboring ions through the particles’ Coulomb interactions. With each step, the phonon wavepacket either splits into a superposition or reflects at the edge. For example, a phonon starting on ion 2 steps to both ion 1 and ion 3. The resulting phonon at ion 3 steps to ions 2 and 4, while the phonon at ion 1 reflects at the boundary back to ion 2, where it interferes with the other wavepacket. The researchers tracked the phonon’s journey with single-site resolution for up to 10 ms—any longer than that and heating would likely introduce another phonon, which would sully the results. The experimental interference pattern matched the numerical results for a quantum walk.
The group’s technique can extend to a longer chain of ions or to two dimensions, for which numerical calculations fall short. With the introduction of additional phonons, the system could also realize a simplified demonstration of quantum computing known as boson sampling. Its goal is to predict the output distribution of bosons sent through an interferometer—a problem that can, with enough bosons, stump a classical computer. The experiment by Toyoda and his colleagues is well-matched for the problem’s first step: physically sampling all the interferometer’s possible outcomes. (M. Tamura, T. Mukaiyama, K. Toyoda, Phys. Rev. Lett. 124, 200501, 2020.)