Grover 3-Qubit Search

Quantum

Grover’s algorithm searching an $8$ -item space with $3$ qubits. Uniform superposition, then repeated rounds of oracle (phase-flip the target) and diffusion (invert about the mean) rotate the state vector toward the marked item. Real $8$ -amplitude linear algebra drives a live bar chart; after the optimal $\lfloor\pi\sqrt{8}/4\rfloor=2$ rounds the target probability peaks near $94\%$ .

Live circuit Superposition, P(target) = 12 %

Toggle the qubits to choose the marked item; step the timeline to watch amplitudes rotate. Click a gate to read it.

Causal signal trace paused

Uniform superposition Three Hadamards spread one unit of probability evenly across all eight basis states.

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

Step 1 / 11 Uniform superposition

Notebook: 11 parts and 12 wires, modelled as amplitude amplification over 8 states

Recommended lab 12 of 18

Explain Grover search as amplitude rotation and identify over-rotation.

Builds on: Phase Kickback

Predict, then test

For $N=8$ , apply a third Grover round after the optimal two. What happens to target probability?

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

Governing model

|s\rangle \to (D\,U_f)^k|s\rangle,\quad k \approx \dfrac{\pi}{4}\sqrt{N} \;\cdot\; N = 8

Parts

$3$ -qubit uniform superposition
oracle $U_f$ (phase flip)
diffusion $2|s\rangle\langle s|-I$
$8$ -state amplitude readout

Limits of the model

$N=8$ search space
optimal $k=2$ rounds
peak $P(\mathrm{target})\approx0.945$

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

Notebook: 11 parts and 12 wires, modelled as amplitude amplification over 8 states

For N=8N=8N=8, apply a third Grover round after the optimal two. What happens to target probability?

For $N=8$ , apply a third Grover round after the optimal two. What happens to target probability?