Exact adjoint of the QFT. Readout step of phase estimation.
Undo the QFT SWAPs first, then apply inverse controlled phases (negative CP angles) and H from LSB to MSB. QFT then IQFT is identity.
On |000⟩ the inverse QFT is also identity, so this default circuit looks like it “does nothing” in Z. Use it after a QFT, or as the tail of QPE/Shor.
How it works
-
1
Unreverse
SWAP [0,2] undoes the QFT bit reversal.
-
2
Inverse phases + H
For each wire i from 0: CP from earlier wires with angle −1/2^{i−j}, then H i.
Default Qubi (static)
SWAP [0,2] H 0 CP [0,1] -0.5 H 1 CP [0,2] -0.25 CP [1,2] -0.5 H 2
Function form: IQFT(0..2)
Circuit
Expected result
State. IQFT|000⟩ = |000⟩
P(000) = 1 for this input. After QFT, the same circuit restores the original computational state.
| Basis | Amplitude | Probability |
|---|---|---|
|000⟩ |
1 |
Notes
- Counting q0 is the LSB of the recovered integer, same convention as QPE.
- Negative CP angles are π-multiples, e.g. −0.5 is −π/2.
Change parameters
The write-up above is for the default circuit. Use this control to generate other variants and load them in the simulator.