Temporal-Mode Cluster States

The temporal-mode Gaussian cluster state [1] is a promising resource for large-scale one-way quantum computation. We show that quantum computations using a temporal-mode cluster state for one-mode operations are equivalent to a concatenation of quantum teleportations. In this process, we can utilize all the degrees of freedom of cluster modes for one-mode Gaussian operations without wasting resource modes by cluster mode erasing. In addition to this, we show that one-mode non-Gaussian operations and multi-mode Gaussian operations can also be achieved without eliminating resource modes of temporal-mode cluster states. These findings show that the same operation can be achieved by using less resource cluster modes than the original proposal in Ref. [1], leading to less error obtained from imperfect resources in quantum computation.

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