Optical systems have been long considered to be appropriate for tasks in quantum communications but not quantum computation. This is because the optical systems are “flying qubits” that need actual physical circuits to implement quantum computation, limiting their scalability. In this chapter, we explain a methodology that does not only overcome this limitation but is also one of the currently most promising methods in terms of scalability: time-domain quantum computation. In this method, quantum states are encoded in a localized temporal wave packet. These wave packets can be multiplexed in time, allowing the generation of large-scale cluster states and multi-step quantum operations using only minimal physical resources. We explain basic ideas of quantum computation in the time domain and show several experimental examples.
Measurement-based quantum computation with continuous variables in an optical setup shows great promise toward implementation of large-scale quantum computation, where the time-domain multiplexing approach enables us to generate the large-scale cluster state used to perform measurement-based quantum computation. To make effective use of the advantage of the time-domain multiplexing approach, in this paper, we propose the method to generate the large-scale three-dimensional cluster state which is a platform for topologically protected measurement-based quantum computation. Our method combines a time-domain multiplexing approach with a divide-and-conquer approach and has two advantages for implementing large-scale quantum computation. First, the squeezing level for verification of the entanglement of the three-dimensional cluster states is experimentally feasible. The second advantage is the robustness against analog errors derived from the finite squeezing of continuous variables during topologically protected measurement-based quantum computation. Therefore, our method is a promising approach to implement large-scale quantum computation with continuous variables.