  Quantum computers can revolutionize science and technology, but their
realization remains challenging across all platforms. A promising route to
scalability is photonic measurement-based quantum computation, where
single-qubit measurements on large cluster states, together with feedforward,
enable fault-tolerant quantum computation. However, generating large cluster
states at high rates is notoriously difficult, as detection probabilities drop
exponentially with the number of photons comprising the state. We tackle this
challenge by encoding multiple qubits on each photon through high-dimensional
spatial encoding, generating cluster states with over nine qubits at a rate of
100Hz. Additionally, we demonstrate that high-dimensional encoding
substantially reduces the computation duration by enabling instantaneous
feedforward between qubits encoded in the same photon. Our findings pave the
way for resource-efficient measurement-based quantum computation using
high-dimensional entanglement.
