RC3X¶
RC3X extends RCCX to three controls: a cheaper, relative-phase version of a triply-controlled X gate (C3X) on four qubits.
| Qubits | 4 (three controls, one target) |
| Parameters | None |
| Inverse | Itself, on computational basis inputs |
| Also called | Simplified 3-controlled Toffoli |
What it does¶
On computational basis states, RC3X flips the target exactly when all three controls are \( |1\rangle \), matching a true C3X (triply-controlled X) gate. Like RCCX, it achieves this more cheaply by allowing relative phases on non-basis-state inputs.
Action on basis states¶
(three controls first, target last - identical to C3X on computational basis states)
- \( |1110\rangle \rightarrow |1111\rangle \)
- \( |1111\rangle \rightarrow |1110\rangle \)
- every other computational basis state is left unchanged
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 | rc3x q[0], q[1], q[2], q[3]; |
| Qiskit | circuit.rc3x[q[0], q[1], q[2], q[3]] |
| Cirq | - |
| Q# | - |
Notes¶
Because RC3X needs four qubits, it appears greyed out in the Operations catalog until your circuit has at least four quantum registers - see the note on the Operations page.