Open quantum systems are quantum systems coupled to an environment (a reservoir or bath). Unlike isolated systems (unitary evolution), open systems evolve non-unitarily: they lose information to the environment through decoherence and dissipation.

The environment is typically very large (infinitely many degrees of freedom) and unobserved. It induces irreversible processes: energy loss (T1 decay), dephasing (T2 decay), and spontaneous emission. QuTiP models these effects via the master equation.

Real quantum hardware is always open: superconducting qubits couple to electromagnetic noise, trapped ions couple to thermal vibrations, photonic systems couple to material absorption. Understanding and modeling open system dynamics is essential for designing robust quantum algorithms and error mitigation strategies.

Markovian (memoryless) systems: the environment forgets interactions fast—the master equation is local in time. This is the typical regime for QuTiP's default solvers.

Non-Markovian systems: the environment has memory—past interactions affect the future. These are harder to simulate but important for strong coupling regimes.

Most QuTiP applications assume the Markovian limit, which holds when the environment's correlation time is much shorter than the system's timescale.

The master equation is derived under the Born-Markov approximation: (1) the system and environment are initially uncorrelated, (2) the system-environment coupling is weak, (3) the environment is in equilibrium. These assumptions are excellent for typical quantum systems but break down for strong coupling or structured reservoirs.