Notes: qubits and gates — Quantum 3D Lab

Experiments in the Quantum 3D Lab

• QVL-01 Introduction Lab: meet the qubit — Eight short stations on one qubit: measure, flip, superpose, phase, rotate, interfere, other bases, and a challenge.
• QVL-02 Two qubits side by side — Two independent qubits: four outcomes, and probabilities that multiply.
• QVL-03 The quantum "if": CNOT and the Bell pair — CNOT's truth table, then a Hadamard before it: the Bell pair, where neither qubit has a state of its own.
• QVL-04 Is it really spooky? The CHSH game — A game no classical team wins more than 75 % of the time. Entangled players win 85 %.
• QVL-05 Phase kickback — The control of a controlled gate changes, while the target does not: the trick behind every algorithm.
• QVL-06 Superdense coding — Two classical bits sent with one qubit, thanks to a shared Bell pair.
• QVL-07 Quantum teleportation — A qubit's state moved to another qubit with one Bell pair and two classical bits.
• QVL-08 BB84: a secret key — Two bases, random choices, and an eavesdropper who cannot hide.
• QVL-09 Oracles and reversible logic: a quantum adder — XOR from CNOT, AND from Toffoli, and a half adder that adds every input at once.
• QVL-10 Deutsch–Jozsa: constant or balanced? — One question to the oracle instead of five: the first algorithm faster than any classical one.
• QVL-11 Bernstein–Vazirani: a secret in one look — A hidden bit string read in a single query.
• QVL-12 Grover's search — One marked number in 32, found with 99.9 % certainty after 4 rounds: 109 gates on 5 qubits.
• QVL-13 The quantum Fourier transform — Numbers turned into phases, and patterns into peaks.
• QVL-14 Phase estimation — Reading the phase of a gate to three binary places.
• QVL-15 Shor's algorithm: factoring 15 — The period of 7ˣ mod 15 found on 7 qubits, and from it 15 = 3 × 5.
• QVL-16 Noise and error correction — A bit-flip code on 5 qubits: find the error without looking at the data, and undo it.
• QVL-17 A spin in a magnetic field — Larmor precession, Rabi oscillation and Ramsey fringes: NMR and MRI on one qubit.
• QVL-18 The energy of H₂ (VQE) — A variational quantum eigensolver finds the ground-state energy of the hydrogen molecule.
• QVL-19 Optimisation with QAOA — The best cut of a 4-node network, found by tuning two angles.

• Build your own circuit
• Notes: qubits and gates