Quantum circuits apply reversible operations to qubits. Understanding a circuit means tracking how it steers amplitudes toward a measurable answer.
Learning objectives
Read a circuit diagram as a sequence of unitary operations.
Identify the role of Hadamard, phase, and controlled gates.
Explain circuit depth and why it is limited in practice.
Unitary operations
Every gate except measurement is reversible and preserves total probability. Composing gates multiplies their matrices, so a circuit is one large transformation applied to the initial state.
A minimal toolkit
Single-qubit rotations create and adjust superposition and phase; a two-qubit controlled gate creates entanglement. Together these form a universal set from which any operation can be approximated.
Depth versus coherence
Each gate adds error and consumes coherence time. Useful circuits must finish before noise overwhelms the signal, which is why depth, connectivity, and fidelity are reported together.