Phase Kickback

Quantum

$H$ puts the control in $|+\rangle$ , $CP(\varphi)$ acts on the target, and a second $H$ reads the control. For an eigenstate target the eigenphase moves onto the control and $P(1)=\sin^2(\varphi/2)$ ; any other target entangles with the control and shortens its Bloch vector. Exact $4$ -amplitude linear algebra drives the Bloch view and the histogram.

Live circuit clean kickback, P(1) = 0.500

Phase Kickback

Drag φ on the controlled-phase gate and choose the target state. Step the timeline to follow the control; click a gate to read it.

Causal signal trace paused

Prepare control and target The control starts in $\lvert 0\rangle$ and the target in the chosen state; an eigenstate of the phase gate is what makes kickback clean.

t_{\mathrm{stage}}=\htmlData{math-slot=value}{\mathtt{0.00}}\,\mathrm{s}

Step 1 / 5 Prepare control and target

Notebook: 7 parts and 6 wires, modelled as two-qubit state vector + reduced Bloch vector

Recommended lab 11 of 18

Show that an eigenstate target moves a controlled phase onto the control.

Builds on: Bell-State Entanglement Visualizer

Predict, then test

The target is $|1\rangle$ and $\varphi = \pi$ . After the final Hadamard, what does measuring the control give?

Commit before the explanation appears. This is a prediction, not a quiz score.

Governing model

\tfrac{1}{\sqrt2}(|0\rangle + |1\rangle)|1\rangle \xrightarrow{CP(\varphi)} \tfrac{1}{\sqrt2}(|0\rangle + e^{i\varphi}|1\rangle)|1\rangle \;\cdot\; P(1) = \sin^2\tfrac{\varphi}{2}

Parts

control + target qubits
$2\times$ Hadamard on the control
controlled phase $CP(\varphi)$
control measurement

Limits of the model

$\varphi\in[0,2\pi]$
targets $|0\rangle,|1\rangle,|+\rangle,|-\rangle$
purity $|\vec r|\in[0,1]$

Diagnosis challenge The fault is hidden. Work it out from the changed outputs first.

Notebook: 7 parts and 6 wires, modelled as two-qubit state vector + reduced Bloch vector

The target is ∣1⟩|1\rangle∣1⟩ and φ=π\varphi = \piφ=π. After the final Hadamard, what does measuring the control give?

The target is $|1\rangle$ and $\varphi = \pi$ . After the final Hadamard, what does measuring the control give?