Scalable graph states are essential for measurement-based quantum computation
and many entanglement-assisted applications in quantum technologies. Generation
of these multipartite entangled states requires a controllable and efficient
quantum device with delicate design of generation protocol. Here we propose to
prepare high-fidelity and scalable graph states in one and two dimensions,
which can be tailored in an atom-nanophotonic cavity via state carving
technique. We propose a systematic protocol to carve out unwanted state
components, which facilitates scalable graph states generations via adiabatic
transport of a definite number of atoms in optical tweezers. An analysis of
state fidelity is also presented, and the state preparation probability can be
optimized via multiqubit state carvings and sequential single-photon probes.
Our results showcase the capability of an atom-nanophotonic interface for
creating graph states and pave the way toward novel problem-specific
applications using scalable high-dimensional graph states with stationary
qubits.Comment: 5 figures with supplemental materia