Quantum circuit

A quantum circuit is a computational model for quantum computing in which a sequence of quantum gates manipulates a register of qubits to perform a specific computation. Unlike classical circuits, quantum circuits operate on superpositions of states and must respect the unitary constraints of quantum mechanics, meaning every gate is reversible and no information is lost during the computation.

Quantum circuits are typically represented as diagrams where horizontal lines denote qubits and boxes or symbols denote quantum gates — single-qubit rotations, two-qubit entangling gates like the CNOT, and three-qubit gates like the quantum Toffoli gate. The model is the dominant paradigm for programming current quantum computers and for analyzing the complexity of quantum algorithms in computational complexity theory.

The quantum circuit model is often presented as a natural extension of classical circuit design, but this framing understates a profound difference: classical circuits are built from irreversible primitives, while quantum circuits are fundamentally reversible. The transition from classical to quantum computation is not an upgrade — it is a change in physical regime, from thermodynamically lossy to information-preserving dynamics.