Quantum Arcade

A hidden state is drawn. Steer yours (blue) onto the ghost (dim), fidelity ≥ 99% wins.

Set the odds with θ, then call the collapse. Long streaks get exponentially unlikely, that is the Born rule doing its job.

Drive the qubit with a rotation pulse. A perfect π pulse lands the whole amplitude on |1⟩, this is exactly how real qubits get flipped.

Split one qubit onto two paths (H), twist the phase between them, recombine (H). The output probability swings from certain to impossible, with nothing removed, only phase.

One fixed state, two questions. Ask in Z: pure coin flip. Ask in X: dead certain. The state didn't change, your question did.

Before and after. Which gate did it?

Turn one knob from “two separate qubits” to “one inseparable pair.” Watch qubit A's purity drop to ½, alone, it becomes a pure coin flip, because the information lives in the pair.

Two dice, one wavefunction. Each roll is individually 50/50 random, and they always agree. Randomness and perfect correlation, at the same time.

Classical physics caps |S| at 2. A Bell pair reaches 2√2 ≈ 2.83. Collect rounds and watch your sampled S climb past what any local hidden variable story allows.

A message qubit, an entangled pair, and two classical bits, the state moves without any qubit traveling. Step through the actual amplitudes.

Share a Bell pair in advance, and one qubit can carry two classical bits. Pick the bits; the decoder lands on the matching basis state with certainty.

CNOT is supposed to change the target. Put the target in |−⟩ and fire: the target shrugs, the control flips from |+⟩ to |−⟩. This backwards kick powers Deutsch, Grover, and phase estimation.

One button. It copies an unknown qubit. Try it.

Eight drawers, one prize. Classically you open ~4. Grover finds it in 2 iterations, and if you keep going past the sweet spot, the amplitude rotates away again. Try over searching.

A mystery coin function: constant (same answer always) or balanced (half and half). Classically you must ask twice. The Deutsch circuit asks once, and is never wrong.

Hardware quantum RNGs sell exactly this: prepare |+⟩, measure, repeat. Sample away, entropy should hug 1 bit/bit.

This is the enemy every quantum computer fights. Turn up the noise on a crisp |+⟩ and watch its off diagonal coherence, the part that interferes, bleed away into a classical coin.

Encode one bit into three qubits; majority vote fixes any single flip. Below ~50% noise the code beats the bare qubit, the same idea, scaled up, is how Willow class processors reach below threshold error correction.

Alice sends key bits in random bases; Bob measures in his own. Toggle an eavesdropper: her measurements must disturb the states (no cloning, two cards up), and the error rate betrays her at ~25%.

Classically, a ball below the wall's height never crosses. Quantum mechanically the odds are small, but never zero. Thinner or lower walls help exponentially.

Cut a 4-node ring into two colors with as many crossing edges as possible (max = 4). QAOA doesn't search, it sculpts a superposition so the good cuts get more amplitude. Find the γ, β sweet spot.

edges: 0, 1, 1, 2, 2, 3, 3, 0 · random guess averages 2.0

Same coin, same line. The classical walker wanders ~√t from home. The quantum walker interferes with itself and races out ~t, with two peaks and almost nothing in the middle. This ballistic spread is the engine behind quantum search speedups.

The oracle hides a 5 bit string s and will only answer dot products s·x. Classically you need 5 questions, one per bit. The quantum circuit asks one question in superposition and the interference writes the whole secret into the output register.

every run reads the secret perfectly; that certainty is interference, not luck

Three players share an entangled triple and cannot communicate. The referee hands out bits r, s, t and the answers must XOR to r OR s OR t. The best any classical team can do is win 3 of 4 cases (75%). The quantum team wins every round.

Shor's algorithm never sees the factors directly. It hides a period r in a register, applies the quantum Fourier transform, and reads the period off the interference peaks, spaced 2ⁿ/r apart. Slide r and watch the spectrum answer.

when r divides 64 the peaks are exact; other r values smear, which is why Shor finishes with continued fractions