Entangling capability of multivalued bipartite gates and optimal preparation of multivalued bipartite quantum states

Abstract

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 gates, uniformly controlled 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 (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 twoqudit state with Schmidt number k can be prepared from a product state by using k − 1 GCX gates, and any two-qudit state can be transformed into any other by using at most 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) 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.

Optimal synthesis of multivalued quantum circuits

“…Most approaches to quantum information processing use twolevel quantum systems (qubits). However there is increasing interest in exploiting protocol with multilevel quantum systems (qudits) [1][2][3][4][5][6][7][8][9]. The simplest multilevel system, the threelevel quantum system, is called a qutrit, the four-level quantum system is called a ququart.…”