Gates & Circuits
Quantum Gate
A basic operation applied to qubits that transforms their quantum state — the quantum equivalent of a classical logic gate.
Definition
A quantum gate is a mathematical operation — represented as a unitary matrix — that transforms the state of one or more qubits. Quantum gates are the building blocks of quantum circuits and quantum algorithms, analogous to logic gates (AND, OR, NOT) in classical computing. Unlike most classical gates, all quantum gates are reversible.
Technical Definition
A single-qubit gate is a 2×2 unitary matrix U applied to a qubit's state vector. A two-qubit gate is a 4×4 unitary matrix. The Hadamard gate H = (1/√2)[[1,1],[1,-1]] puts a qubit into equal superposition. The CNOT gate flips a target qubit if and only if the control qubit is |1⟩, and is the primary way entanglement is created in quantum circuits.
Visual Explanation: An Analogy
Think of a quantum gate like a precise physical transformation — similar to how rotating a compass needle by exactly 90 degrees changes where it points. The gate specifies exactly how the qubit's 'direction' in an abstract mathematical space changes.
Real-World Use Cases
- Creating superposition with the Hadamard gate
- Creating entanglement with the CNOT gate
- Building quantum circuits and algorithms from sequences of gates
Common Misconceptions
- Quantum gates are not like classical logic gates in one key way: all quantum gates are reversible — you can always 'undo' a gate by applying its inverse.