by Brian Patterson
(translated from my final paper in Quantum Information Theory,Fall 2000)
As quantum computers move closer to being a reality, the various theoretical parts of the computer are being examined ever more closely. A crucial part of quantum computing is the manipulation of the relevant qubits by what are called quantum gates. A quantum gate is formally defined as a device which performs a fixed unitary operation on selected qubits in a fixed period of time and a quantum network is a device consisting of quantum logic gates whose computational steps are synchronized in time [2]. Mathematically, a qubit is represented as a vector with two dimensions, a and b, and a quantum gate on k qubits is a unitary matrix U of dimensions 2k x 2k [3]. An in-depth understanding of theoretical quantum gates is crucial both to initially constructing the gates and understanding possible applications. I will look at how basic gates work, how those basic gates form more advanced gates, and how these gates are being investigated in experimental physics.