  Quantum computation promises applications that are thought to be impossible
with classical computation. To realize practical quantum computation, the
following three properties will be necessary: universality, scalability, and
fault-tolerance. Universality is the ability to execute arbitrary multi-input
quantum algorithms. Scalability means that computational resources such as
logical qubits can be increased without requiring exponential increase in
physical resources. Lastly, fault-tolerance is the ability to perform quantum
algorithms in presence of imperfections and noise. A promising approach to
scalability was demonstrated with the generation of one-million-mode
1-dimensional cluster state, a resource for one-input computation in
measurement-based quantum computation (MBQC). The demonstration was based on
time-domain multiplexing (TDM) approach using continuous-variable (CV) optical
flying qumodes (CV analogue of qubit). Demonstrating universality, however, has
been a challenging task for any physical system and approach. Here, we present,
for the first time among any physical system, experimental realization of a
scalable resource state for universal MBQC: a 2-dimensional cluster state. We
also prove the universality and give the methodology for utilizing this state
in MBQC. Our state is based on TDM approach that allows unlimited resource
generation regardless of the coherence time of the system. As a demonstration
of our method, we generate and verify a 2-dimensional cluster state capable of
about 5,000 operation steps on 5 inputs.
