A quantum logic gate is a device which performs a fixed unitary operation on selected qubits in a fixed period of time. The gates listed below are common enough to have their own names. The matrices describing n qubit gates are written in the computational basis {|x⟩}, where x is a binary string of length n. The diagrams provide schematic representation of the gates.

Hadamard gate

The Hadamard gate is a common single qubit gate H defined as

Image:Img44.png

The matrix is written in the computational basis {|0⟩,|1⟩} and the diagram on the right provides a schematic representation of the gate H acting on a qubit in state |x⟩, with x = 0, 1.

Phase gate

The phase shift gate ϕ defined as | 0⟩ ↦ | 0⟩ and | 1⟩ ↦ e^iϕ| 1⟩, or, in matrix notation,

Image:Img59.png

Controlled NOT gate

The controlled-NOT (C-NOT) gate, also known as the XOR or the measurement gate is one of the most popular two-qubit gate. It flips the second (target) qubit if the first (control) qubit is | 1⟩ and does nothing if the control qubit is | 0⟩. The gate is represented by the unitary matrix

Image:Img76.png

where x, y = 0 or 1 and ⊕ denotes XOR or addition modulo 2. If we apply the C-NOT to Boolean data in which the target qubit is |0⟩ and the control is either |0⟩ or |1⟩ then the effect is to leave the control unchanged while the target becomes a copy of the control, i.e.

|x⟩|0⟩ ↦ |x⟩|x⟩   x = 0, 1.

Category:Evolutions and Operations Category:Quantum Computation Category:Handbook of Quantum Information