  Domain walls (DWs) on magnetic racetracks are at the core of the field of
spintronics, providing a basic element for classical information processing.
Here, we show that mobile DWs also provide a blueprint for large-scale quantum
computers. Remarkably, these DW qubits showcase exceptional versatility,
serving not only as stationary qubits, but also performing the role of
solid-state flying qubits that can be shuttled in an ultrafast way. We estimate
that the DW qubits are long-lived because they can be operated at sweet spots
to reduce potential noise sources. Single-qubit gates are implemented by moving
the DW, and two-qubit entangling gates exploit naturally emerging interactions
between different DWs. These gates, sufficient for universal quantum computing,
are fully compatible with current state-of-the-art experiments on racetrack
memories. Further, we discuss possible strategies for qubit readout and
initialization, paving the way toward future quantum computers based on mobile
topological textures on magnetic racetracks.
