Abstract
The emerging and innovative field of quantum computation and quantum information could bring new insight to our understanding of nature with many applications such as quantum cryptography, quantum secret sharing, quantum teleportation, and quantum computer. In conventional scheme, a quantum computer could be design by quantum gates and circuits. In this paper, we construct geometrical controlled phase quantum gate entanglers for multi-qubit states based on the complex projective Grassmann variety which is defined by the Plucker embedding of Grassmann space. We explicitly give an expression for a geometrical three-qubit quantum gate entangler. We also discuss in detail the construction of the gate entangler for four-qubit states. Moreover, We give illustrative examples of physical implementations of our quantum gate entangler for two- and multi-qubit systems.
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