# TGate¶

class TGate(label=None)[source]

Single qubit T gate (Z**0.25).

It induces a $$\pi/4$$ phase, and is sometimes called the pi/8 gate (because of how the RZ(pi/4) matrix looks like).

This is a non-Clifford gate and a fourth-root of Pauli-Z.

Matrix Representation:

$\begin{split}T = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix}\end{split}$

Circuit symbol:

     ┌───┐
q_0: ┤ T ├
└───┘


Equivalent to a $$\pi/4$$ radian rotation about the Z axis.

Create new T gate.

Attributes

 TGate.decompositions Get the decompositions of the instruction from the SessionEquivalenceLibrary. TGate.definition Return definition in terms of other basic gates. TGate.label Return gate label TGate.params return instruction params.

Methods

 TGate.add_decomposition(decomposition) Add a decomposition of the instruction to the SessionEquivalenceLibrary. Assemble a QasmQobjInstruction TGate.broadcast_arguments(qargs, cargs) Validation and handling of the arguments and its relationship. TGate.c_if(classical, val) Add classical condition on register classical and value val. TGate.control([num_ctrl_qubits, label, …]) Return controlled version of gate. TGate.copy([name]) Copy of the instruction. Return inverse T gate (i.e. Return True .IFF. DEPRECATED: use instruction.reverse_ops(). TGate.power(exponent) Creates a unitary gate as gate^exponent. Return a default OpenQASM string for the instruction. Creates an instruction with gate repeated n amount of times. For a composite instruction, reverse the order of sub-instructions. Return a numpy.array for the T gate.