Two-level quantum walkers on directed graphs. I. Universal quantum computing

In the present paper, first in a series of two, we propose model universal quantum computation using fermionic or bosonic multiparticle continuous-time walk with two internal states (e.g., spin-up and -down an electron). A dual-rail encoding is adopted to convert information: single qubit represented by presence walker either parallel paths. We develop roundabout gate that moves from one path next, clockwise counterclockwise, depending on its state. It can be realized single-particle scattering directed weighted graph edge weights 1 $\ifmmode\pm\else\textpm\fi{}i$. The also allows spatial information temporarily encoded states. gates are constructed appropriately combining several gates, some unitary act states, two-particle scatterings straight No ancilla qubits required our model. done just passing walkers through properly designed Namely, there no need for any time-dependent control. physical implementation random access memory compatible will considered second paper [R. Asaka et al., following Phys. Rev. 107, 022416 (2023)].