← all environments 11 · Frontier · Quantum · v0.4.0

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 $94\%$ .

11 components · 12 connections · amplitude amplification over 8 states

recommended lab 11 of 11

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

Builds on: Bell-State Entanglement Visualizer

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

structural inventory

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

boundaries

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

diagnosis challenge Fault identity withheld: infer it from the changed outputs first.

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

control console

Mark one of the eight states, then step the register toward it. Each round is an oracle phase-flip, a mean reflection, and a diffuser rebound. The first 2 rounds amplify the target; the final demonstration round deliberately rotates past it.

\lvert q_2q_1q_0\rangle=\lvert\htmlData{math-slot=value}{\mathtt{000}}\rangle

\lvert q_2q_1q_0\rangle=\lvert\htmlData{math-slot=value}{\mathtt{000}}\rangle

switchboard · fault injection

inject hidden fault

test bed · mode=full

Grover 3-Qubit Search

instrumentation rack

Superposition

$\lvert s\rangle=\frac1{\sqrt8}\sum_x\lvert x\rangle\quad a_x=\htmlData{math-slot=amplitude}{\mathtt{+0.000}}$

target others

P=\htmlData{math-slot=value}{\mathtt{00.0}}\%

diagnostic probe