Benchmarking the performance of a high-Q cavity qudit using random unitaries

High-coherence cavity resonators are excellent resources for encoding quantum information in higher-dimensional Hilbert spaces, moving beyond traditional qubit-based platforms. A natural strategy is to use the Fock basis to encode information in qudits. One can perform quantum operations on the cavity mode qudit by coupling the system to a non-linear ancillary transmon qubit. However, the performance of the cavity-transmon device is limited by the noisy transmons. It is, therefore, important to develop practical benchmarking tools for these qudit systems in an algorithm-agnostic manner. We gauge the performance of these qudit platforms using sampling tests such as the Heavy Output Generation (HOG) test as well as the linear Cross-Entropy Benchmark (XEB), by way of simulations of such a system subject to realistic dominant noise channels. We use selective number-dependent arbitrary phase and unconditional displacement gates as our universal gateset. Our results show that contemporary transmons comfortably enable controlling a few tens of Fock levels of a cavity mode. This framework allows benchmarking even higher dimensional qudits as those become accessible with improved transmons.