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 steps, 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 100 Hz. We also 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.

量子计算机可以彻底改变科学和技术，但其在所有平台上的实现仍然具有挑战性。实现可扩展性的一个有前途的途径是基于光子测量的量子计算，其中对大簇状态的单量子位测量与前馈步骤一起，实现了容错量子计算；然而，众所周知，以高速率生成大型簇态是非常困难的，因为检测概率随着构成该态的光子数量呈指数下降。我们通过高维空间编码对每个光子上的多个量子位进行编码来应对这一挑战，以 100 Hz 的速率生成具有超过 9 个量子位的簇状态。我们还证明，高维编码通过在同一光子中编码的量子位之间实现瞬时前馈，大大减少了计算持续时间。我们的研究结果为使用高维纠缠的资源高效、基于测量的量子计算铺平了道路。