Applied Physics CSIE II: UNIT IV: Quantum Computing

T Gate

Definition, Action, Matrix form, Operation, Bloch Sphere action | Quantum gates

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

Definition

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.

Action

(i) The T gate applies a phase of π/4 (45°) to the |1> state while leaving the |0> state unchanged.

Matrix form

The matrix for the T gate can be defined as


Operation

(i) On |0>

 T|0> = |0>

(i) On |1>

 T|1> = eiπ/4|1>

Bloch Sphere action

The T gate performs a rotation around the Z‒axis by π/4 (45°).

Property

'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


Applied Physics CSIE II: UNIT IV: Quantum Computing



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