High-dimensional one-way quantum processing implemented on d-level cluster states

Taking advantage of quantum mechanics for executing computational tasks faster than classical computers ¹ or performing measurements with precision exceeding the classical limit ^2,3 requires the generation of specific large and complex quantum states. In this context, cluster states ⁴ are particularly interesting because they can enable the realization of universal quantum computers by means of a ‘one-way’ scheme ⁵, where processing is performed through measurements ⁶. The generation of cluster states based on sub-systems that have more than two dimensions, d-level cluster states, provides increased quantum resources while keeping the number of parties constant ⁷, and also enables novel algorithms ⁸. Here, we experimentally realize, characterize and test the noise sensitivity of three-level, four-partite cluster states formed by two photons in the time ⁹ and frequency ¹⁰ domain, confirming genuine multi-partite entanglement with higher noise robustness compared to conventional two-level cluster states ^6,11–13. We perform proof-of-concept high-dimensional one-way quantum operations, where the cluster states are transformed into orthogonal, maximally entangled d-level two-partite states by means of projection measurements. Our scalable approach is based on integrated photonic chips ^9,10 and optical fibre communication components, thus achieving new and deterministic functionalities.