T†¶
T† ("T-dagger") is the inverse of the T gate: a \( -\pi/4 \) phase shift instead of \( +\pi/4 \).
| Qubits | 1 |
| Parameters | None |
| Inverse | T |
| Also called | T-dagger, adjoint of T; equal to P(−π/4) |
What it does¶
T† rotates the relative phase between \( |1\rangle \) and \( |0\rangle \) by \( -\pi/4 \), undoing a T gate.
Matrix¶
\[
T^\dagger = \begin{pmatrix} 1 & 0 \\ 0 & e^{-i\pi/4} \end{pmatrix}
\]
Action on basis states¶
- \( |0\rangle \rightarrow |0\rangle \)
- \( |1\rangle \rightarrow e^{-i\pi/4}\,|1\rangle \)
Example¶
Two T† gates in a row are the same as one S† gate; four are the same as one Z gate.
Other notations¶
Naming conventions across ecosystems; exact syntax can vary by library version, and this does not claim to be Qompile's generated output unless otherwise noted.
| Language | Typical form |
|---|---|
| OpenQASM 2.0 | tdg q[0]; |
| Qiskit | circuit.tdg[q[0]] |
| Cirq | cirq.T(q[0])**-1 |
| Q# | Adjoint T(q[0]); |