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Quantum computers can revolutionize science and technology, but theirrealization remains challenging across all platforms. A promising route toscalability is photonic measurement-based quantum computation, wheresingle-qubit measurements on large cluster states, together with feedforward,enable fault-tolerant quantum computation. However, generating large clusterstates at high rates is notoriously difficult, as detection probabilities dropexponentially with the number of photons comprising the state. We tackle thischallenge by encoding multiple qubits on each photon through high-dimensionalspatial encoding, generating cluster states with over nine qubits at a rate of100Hz. Additionally, we demonstrate that high-dimensional encodingsubstantially reduces the computation duration by enabling instantaneousfeedforward between qubits encoded in the same photon. Our findings pave theway for resource-efficient measurement-based quantum computation usinghigh-dimensional entanglement.

Resource-efficient photonic quantum computation with high-dimensional cluster states