Gates & Circuits

Unitary Operators and the Universal Gate Set

Quantum gates are unitary matrices — reversible, norm-preserving operations on state vectors. This tutorial proves why, derives the universal {H, T, CNOT} set, and shows why any quantum computation decomposes into these primitives. With full Qiskit verification.

beginner · ~22 min · prereq: Foundations track (Tutorials 1-3)

Pauli, Phase, and Rotation Gates

Every single-qubit gate is a rotation of the Bloch sphere. This tutorial derives the Pauli matrices, the phase gates (S, T), and the continuous Rx/Ry/Rz rotation family — and shows how to decompose any single-qubit unitary into three Euler-angle rotations. With visualizations and Qiskit verification.

beginner · ~20 min · prereq: Tutorial 4: Unitary Operators

Multi-Qubit Gates: CNOT, CZ, SWAP, Toffoli, and Controlled Everything

CNOT is the workhorse of entanglement, but the two-qubit gate zoo is richer than that. This tutorial walks through CZ, SWAP, iSWAP, Toffoli, and arbitrary controlled unitaries — plus the decomposition theorems that turn them all into CNOT + single-qubit primitives for real hardware.

intermediate · ~23 min · prereq: Tutorial 5: Pauli, Phase, and Rotation Gates

OpenQASM 3 and Your First Real Hardware Run

Qiskit circuits are a convenience. OpenQASM 3 is the portable assembly language underneath — and what you actually send to hardware. This tutorial walks through the OpenQASM 3 syntax that matters, IBM Quantum's free tier, transpilation, and how to interpret noisy results honestly on your first real-hardware run.

intermediate · ~24 min · prereq: Tutorial 6: Multi-Qubit Gates