We investigate the entangling capability of various types of two-qudit gates in both the no-ancilla case and the ancilla-assisted case. The investigation involves controlled $$U$$ U gates, uniformly controlled $$U$$ U gates and some high-rank two-qudit gates. The optimal input states for these gates to generate entanglement are also given. By comparison of some important two-qudit gates, the generalized controlled $$X$$ X (GCX) gate shows the excellent properties. Based on the GCX gate, we study the preparation of arbitrary two-qudit quantum states and the transformation of such states. Any two-qudit state with Schmidt number $$k$$ k can be prepared from a product state by using $$k-1$$ k - 1 GCX gates, and any two-qudit state can be transformed into any other by using at most $$d-1$$ d - 1 GCX gates. The result reveals that using multivalued quantum systems has obviously advantages over the binary systems in these respects. The best known result for a four-qubit state preparation is that it needs at most nine CNOT gates. A two-ququart state ( $$d=4$$ d = 4 ) corresponds to a four-qubit state; its preparation and transformation only need at most three GCX gates. Using other gates as the two-qudit elementary gate of multivalued quantum computing, the advantages no longer hold. This once again illustrates that it is reasonable to choose the GCX gate as the two-qudit elementary gate of multivalued quantum computing.
Quantum Information Processing – Springer Journals
Published: Feb 27, 2015
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