Two-level Quantum Walkers on Directed Graphs I: Universal Quantum Computing

Abstract

We propose a universal quantum computation via a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states. A dual-rail encoding is adopted to convert the information: a single-qubit is represented by the presence of a single quantum walker in either of the two parallel paths. We develop a roundabout-like gate that moves a walker from one path to the other, either clockwise or counterclockwise, depending on its internal state. The roundabout gate can be concretely realized by a single-particle scattering on a directed weighted graph with the edge weights $1$ and $\pm i$. The universal gates are constructed by appropriately combining two-particle scatterings on straight paths, several roundabout gates, and some unitary gates that act on the internal states of quantum walkers. Any ancilla qubit is not required in our model, and hence the architecture can be simplified. The computation is done by just passing quantum walkers through properly designed paths. Namely, there is no need for any time-dependent control. The implementation of quantum memory is also presented.Comment: 20 pages, 16 figure