Abstract
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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Notes
- 1.
In reality, we can simplify experimental setup by using several OPOs.
- 2.
To be precise, the operations we here consider are members of the Symplectic group. Although displacements in phase space are excluded from the Symplectic group, it is known that they can be implemented by using one-step one-mode teleportation circuit (Sect. 5.5).
- 3.
Note again that one might have to remove several modes of a temporal-mode cluster state although the modes to be removed have abilities to implement some operations. See Sect. 10.1.4.
- 4.
Note again that one might have to remove several modes of a temporal-mode cluster state although the modes to be removed have abilities to implement some operations. See Sect. 10.1.4.
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Ukai, R. (2015). Temporal-Mode Cluster States. In: Multi-Step Multi-Input One-Way Quantum Information Processing with Spatial and Temporal Modes of Light. Springer Theses. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55019-8_10
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