The T gate is a single‒qubit quantum gate that applies a phase of π/4 (45°) to the |1> state while leaving the |0> state unchanged.
T GATE
The
T gate is a single‒qubit quantum gate that applies a phase of π/4 (45°) to the |1>
state while leaving the |0> state unchanged.
(or)
The
T‒gate is also called a π/8 gate is a single‒qubit phase gate that leaves |0>
unchanged and multiplies |1> by a phase eiπ/4.
(i)
The T gate applies a phase of π/4 (45°) to the |1> state while leaving the |0>
state unchanged.
The
matrix for the T gate can be defined as

(i)
On |0>
T|0> = |0>
(i)
On |1>
T|1> = eiπ/4|1>
The
T gate performs a rotation around the Z‒axis by π/4 (45°).
'S'
gate can be obtained by connecting two T gates in series, i.e.,

Applied Physics CSIE II: UNIT IV: Quantum Computing : Tag: Applied Physics : Definition, Action, Matrix form, Operation, Bloch Sphere action | Quantum gates - T Gate
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