Generalization of common gates for quantum computation

As problems in computer science become increasingly more computationally intense, researchers have begun to examine other methods of computation. One of the largest new models of computation is the quantum computer. Based on the concepts of quantum mechanics, quantum computers process bits of quantum information, or qubits, using quantum gates. So far some impressive results have been obtained using quantum computers on current problems (e.g. search problems). Many quantum algorithms make use of the Hadamard Gate, and a few use a more general form of that gate. In this paper we present a generalized quantum gate that can be shown to encapsulate the standard gates used in quantum algorithms and quantum information processing: Pauli X, Y, and Z, Hadamard, T Phase Shift, S Phase Shift, and Identity. This generalized gate may also lead to new, interesting, and useful gates for quantum computation.