# QuTiP

**QuTiP** (Quantum Toolbox in Python) is an open-source Python library for simulating the dynamics of open quantum systems. Model decoherence, dissipation, and environmental effects via the master equation; evolve quantum states in time; compute entanglement and correlations. Used in cavity QED, superconducting qubits, trapped ions, and quantum optics.

A **quantum object** (`Qobj`) represents operators and states; the **master equation** describes how open systems evolve under dissipation. Use **collapse operators** (Lindblad operators) to model energy loss, dephasing, and spontaneous emission. Evolve systems forward in time, then measure expectation values of observables.

```python
from qutip import *
import numpy as np

# Damped two-level system
H = 2 * np.pi * 0.5 * sigmaz()
gamma = 0.1
c_ops = [np.sqrt(gamma) * sigmam()]

# Time evolution under master equation
times = np.linspace(0, 10, 100)
psi0 = basis(2, 0)
result = mesolve(H, psi0, times, c_ops, [sigmaz()])
print(result.expect[0])
```

QuTiP doesn't execute quantum circuits—it solves differential equations. Useful for modeling hardware noise, designing robust pulses, and studying open system dynamics that quantum circuit simulators don't capture.

## Concepts

 1. [[qutip-quantum-objects|Quantum objects (Qobj)]]
 2. [[qutip-open-systems|Open quantum systems]]
 3. [[qutip-master-equation|Master equation]]
 4. [[qutip-lindblad-operators|Lindblad operators]]
 5. [[qutip-collapse-operators|Collapse operators]]
 6. [[qutip-time-evolution|Time evolution]]
 7. [[qutip-mesolve|Mesolve (master equation solver)]]
 8. [[qutip-mcsolve|Mcsolve (Monte Carlo trajectories)]]
 9. [[qutip-expectation-values|Expectation values]]
 10. [[qutip-steady-states|Steady states]]
 11. [[qutip-partial-trace|Partial trace]]
 12. [[qutip-entanglement|Entanglement measures]]
 13. [[qutip-correlations|Quantum correlations]]
 14. [[qutip-decoherence|Decoherence and dissipation]]
 15. [[qutip-optimal-control|Optimal control]]
 16. [[qutip-pulses|Pulse shaping]]
 17. [[qutip-superoperators|Superoperators]]
 18. [[qutip-quantum-gates|Quantum gates in QuTiP]]
 19. [[qutip-fidelity|Fidelity and metrics]]
 20. [[qutip-visualization|State visualization]]