Pauli, Hadamard, CNOT gates

Quantum Gates

Learn quantum gates and build quantum circuits interactively

What are Quantum Gates?

Quantum gates are the building blocks of quantum circuits. They are unitary operations that manipulate qubits, similar to how logic gates manipulate classical bits.

Key Properties:
  • Unitary: All quantum gates are reversible
  • Linear: They preserve quantum superposition
  • Probabilistic: Operations affect measurement probabilities

Single-Qubit Gates

Interactive Gate simulator
Available Gates:
X
Y
Z
H
S
T
|0⟩
Current State: |0⟩

Two-Qubit Gates

Two-qubit gates operate on pairs of qubits and can create entanglement.

CNOT Gate Demonstration
Control |0⟩
Target |0⟩
+
Input: |00⟩
Output: |00⟩

Gate Matrices

Each quantum gate can be represented as a unitary matrix:

Pauli-X Gate (NOT Gate)
X = [0  1]
    [1  0]
X
Y
Z
H

Common Gates

  • X (NOT): Bit flip
  • Y: Bit and phase flip
  • Z: Phase flip
  • H (Hadamard): Creates superposition
  • S: Phase gate (π/2)
  • T: π/8 gate
  • CNOT: Controlled NOT

universal Gate Sets

Any quantum computation can be performed using:

  • H, S, T, CNOT gates
  • Rotation gates + CNOT
  • Toffoli + Hadamard

Next Topics

Quantum Algorithms Quantum Entanglement Quantum Cryptography