Environment¶
The references that inspired this chapter are all mentioned in the References section.
Quantum channels¶
Quantum channels, also known as quantum maps [B2] or quantum operations [B3], are a mean to describe the three different kinds of evolution that may affect an open quantum system:
Unitary evolution obeying the dynamics prescribed by the closed system’s Hamiltonian
Measurement
Erratic interaction with the environment (noise)
Keywords:
Density operator, the key representation of the state of open systems
- Quantum maps, Kraus sum representation /Quantum operations, operator-sum representation
More to investigate:
- Tensor networks and graphical calculus for open quantum systems [136],in relation with the Pauli Transfer Matrix (PTM) representation of a Quantum Channel (see PTM on qiskit), and completely positive trace preserving (CPTP) maps
Master equation¶
The Lindblad master equation.
A differential equation that formalizes the evolution of the system under the action of its environment. The involved \(L_\mu\) operators describe the relaxation events which affect the system, and can be, in many cases, guessed from a careful analysis of the system.
The evolution according to the master equation can be numerically evaluated by Monte Carlo simulations.