A quantum circuit is the standard model for describing quantum computations. It consists of a set of qubits (represented as horizontal lines), quantum gates (represented as symbols on those lines), and measurements (typically at the end). The circuit is read from left to right, with gates applied in temporal order. This circuit model is analogous to classical circuit diagrams but operates on quantum states instead of classical bits.
A typical quantum circuit begins by initializing all qubits to the |0⟩ state, applies a sequence of single-qubit and two-qubit gates to perform the desired computation, and ends with measurements that extract classical results. The design of the gate sequence determines what computation is performed — different arrangements of the same gates produce different algorithms. Quantum circuits can also include mid-circuit measurements with classical feed-forward, where measurement results during the circuit determine subsequent gate operations.
Quantum circuits are compiled from high-level algorithm descriptions into hardware-native gate sequences through a process called transpilation. This involves decomposing arbitrary gates into the processor's native gate set, routing operations to respect the hardware's qubit connectivity constraints, and optimizing the resulting circuit for minimal depth and gate count. Tools like IBM's Qiskit, Google's Cirq, and Quantinuum's TKET handle this compilation. The efficiency of transpilation significantly impacts the practical performance of quantum algorithms, as unnecessary gates add noise and increase the chance of computational errors.