# Quantum Gates in QuTiP

**Quantum gates** in QuTiP are unitary operators (or approximately unitary after time evolution). QuTiP provides built-in gates and methods to construct custom gates.

## Built-in Single-Qubit Gates

```python
from qutip import *

# Pauli gates
X = sigmax()
Y = sigmay()
Z = sigmaz()

# Hadamard
H = hadamard_transform()

# Phase gates
S = phasegate(np.pi/2)
T = phasegate(np.pi/4)

# Rotations
Rx = rx(np.pi/4)   # Rotate π/4 around x
Ry = ry(np.pi/2)   # Rotate π/2 around y
Rz = rz(np.pi/3)   # Rotate π/3 around z
```

## Two-Qubit Gates

```python
# CNOT (control on qubit 0, target on qubit 1)
CNOT = cnot(2, 0, 1)  # 2 total qubits

# Swap
SWAP = swap(2, 0, 1)

# Controlled Z
CZ = cz(2, 0, 1)

# iSWAP
iSWAP = iswap(2, 0, 1)
```

## Custom Gates from Evolution

Construct unitary gates by time-evolving under a Hamiltonian:

```python
H = 0.5 * sigmaz() + 0.1 * sigmax()
U = (-1j * H * t).expm()  # Matrix exponential: e^{-iHt}

# Verify unitarity
print((U.dag() * U).full())  # Should be identity
```

QuTiP's gate library covers standard quantum computing. Use `tensor()` to build multi-qubit unitaries.