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. The creation and manipulation of large quantum states is necessary for quantum information processing tasks. Three-level, four-partite cluster states have now been created in the time and frequency domain of two photons on-chip.