quantum gate directory
T
Symbol
$T$
Description:
A $\pi/8$ phase gate which is a non-Clifford rotation about $Z$.
Alternate notations:
- $\pi/8$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.TGate
|
| PennyLane |
pennylane.T
|
| Cirq |
cirq.T
|
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
Groups
This gate is contained in the following groups:
The $T$ gate applies a phase of $\mathrm{e}^{i\pi/4}$ to $|1\rangle$.
$$ T = \begin{bmatrix} 1 & 0 \\ 0 & \mathrm{e}^{i\frac{\pi}{4}} \end{bmatrix} $$
Properties
- Non-Clifford; together with Clifford gates yields universal quantum computation.
- $T^2 = S$, $T^4 = Z$, and $T^8 = I$.
- $P(\pi/4) = T$.
- Often referred to as the $\pi/8$ gate because when viewed as a rotation around the $Z$-axis of the Bloch sphere, it can be written as $T = \mathrm{e}^{i\pi/8}R_z(\pi/4)$.
Usage
- Resource gate in fault-tolerant protocols (magic state distillation).
- Phase rotations and compiling arbitrary single-qubit unitaries.
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