Quantum circuit is a model of quantum computation in which a sequence of quantum gates is applied to a quantum register. Quantum circuits are the quantum analogue of classical digital circuits, but instead of Boolean logic gates acting on bits they use unitary matrices acting on qubits.

A quantum circuit consists of qubits (horizontal wires), quantum gates (boxes or symbols on the wires), and measurements at the end. Circuits are read from left to right in the direction of time. The initial state of the register (usually $\lvert 0\rangle^{\otimes n}$) is prepared on the left, gates are applied in sequence, and measurements are performed at the end to extract a classical outcome.

The width of a quantum circuit is the number of qubits it acts on. The depth of a circuit is the number of layers of gates when all gates that can be applied simultaneously are grouped into a single layer. A circuit of depth $d$ and width $n$ uses at most $nd$ gate operations. Minimizing circuit depth is critical in practice because qubits decohere over time — shallower circuits are more noise-resilient and more feasible on NISQ hardware.

Any quantum computation can be expressed as a quantum circuit using a universal gate set such as $\{H, T, \text{CX}\}$. The Solovay-Kitaev theorem guarantees that any single-qubit gate can be approximated to accuracy $\varepsilon$ using $O(\text{polylog}(1/\varepsilon))$ gates from a finite universal gate set.

Measuring a qubit in the circuit collapses its state irreversibly to either $\lvert 0\rangle$ or $\lvert 1\rangle$ with probabilities given by the Born rule. The classical outcome is stored in a classical bit. When measurement results are used to condition subsequent gate operations (mid-circuit measurement), the circuit is called adaptive or dynamic.