Generation of large-scale continuous-variable cluster states multiplexed both in time and frequency domains

Large-scale continuous variable (CV) cluster state is necessary in quantum information processing based on measurement-based quantum computing (MBQC). Specially, generating large-scale CV cluster state multiplexed in time domain is easier to implement and has strong scalability in experiment. Here one-dimensional (1D) large-scale dual-rail CV cluster states multiplexed both in time and frequency domains are parallelly generated, which can be further extended to three-dimensional (3D) CV cluster state by combining two time-delay NOPA systems with beamsplitters. It is shown that the number of parallel arrays depends on the corresponding frequency comb lines and the partite number of each array can be very large (million), and scale of the 3D cluster state can be ultra-large. This scheme provides some special-structured CV cluster states, which will be valuable for quantum computing of hybrid domains.