Optical d-Level Frequency-Time-Based Cluster States

Cluster states, a specific class of multi-partite entangled states, are of particular importance for quantum science, as such systems are equivalent to the realization of one-way (or measurement-based) quantum computers [1]. In this scheme, algorithms are implemented through high-fidelity measurements on the parties of the state [2]. While two-level (i.e. qubit) cluster states have been realized so far, increasing the number of particles to boost the computational resource comes at the price of significantly reduced coherence time and detection rates, as well as increased sensitivity to noise, restricting the realization of discrete cluster states to a record of eight qubits. In contrast, the demonstration of d-level (i.e. qudit) cluster states has the potential to i) increase quantum resources without modifying the number of particles; ii) enable the implementation of highly efficient computational protocols; iii) reduce the noise sensitivity of the states. Up till now, the realization of discrete d-level cluster states has not been shown in any quantum platform. We here demonstrate the realization of d-level cluster states, perform d-level one-way quantum processing operations on the states, and show that higher-dimensional forms of cluster states are more noise tolerant than lower dimensional realizations.