# TdgGate¶

class TdgGate(label=None)[source]

It induces a $$-\pi/4$$ phase.

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

Matrix Representation:

$\begin{split}Tdg = \begin{pmatrix} 1 & 0 \\ 0 & 1-i \end{pmatrix}\end{split}$

Circuit symbol:

     ┌─────┐
q_0: ┤ Tdg ├
└─────┘


Equivalent to a $$\pi/2$$ radian rotation about the Z axis.

Create new Tdg gate.

Attributes

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

Methods

 TdgGate.add_decomposition(decomposition) Add a decomposition of the instruction to the SessionEquivalenceLibrary. Assemble a QasmQobjInstruction TdgGate.broadcast_arguments(qargs, cargs) Validation and handling of the arguments and its relationship. TdgGate.c_if(classical, val) Add classical condition on register classical and value val. TdgGate.control([num_ctrl_qubits, label, …]) Return controlled version of gate. TdgGate.copy([name]) Copy of the instruction. Return inverse Tdg gate (i.e. Return True .IFF. For a composite instruction, reverse the order of sub-gates. TdgGate.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. Return a numpy.array for the inverse T gate.