In this repository you can find the worksheets for the module Open Quanum Systems , part of the MSc Quantum Science and Technology at Trinity College Dublin.

• Worksheet 1:
  • simple unitary dynamics of single-qubit systems
  • The simulated hamiltonians include driven systems with time-dependent perturbations
  • A thorough study of the limits of the validity of the rotating wave approximaiton (RWA)
  • The last exercises iclude two-qubit dynamics and a XXY Ising model for an open chain with 5 to 9 spings
• Worksheet 2:
• Dynamics for mixed states ($\hat{\rho}$)
• Properties of thermal states
• Biased multi-sided coin distributions
• Decoherence of a qubit due to transition frequency being a Gaussian random variable
• CPTP map for spontaneous emission using Kraus operators
• Two-qubit dynamics with interaction and purity of reduced density matrix
• Worksheet 3:
• Fluctuations of position and momentum of a simple harmonic hamiltonian
• Driven harmonic oscillator (analytical and numerical approach)
• Two coupled harmonic oscillators
• Husimi-Q functions of cat states (superposition) and mixed states. Both of coherent states
• Husimi-Q function of Fock state and Hilbert space trucation for infinite-dimensional oscillators
• Simulation of quadratic hamiltonians using displacement vector and correlation matrix dynamics. Evolution of bipartite Fock and coherent states
• M-mode quadratic hamiltonian with dynamical simulation of a thermalisation process
• Worksheet 4
• Two-qubit hamiltonian under dephasing. Lindblad equation.
• Master equation with linear dissipation in an M-mode system with quadratic hamiltonian. Finding the steady state of the system
• Use of superoperators for constructing a Liouvillian numerically. Lindblad equation for a thermal bath
• Vectorisation of operators
• Simulation of a driven-dissipative qubit described by an interaction-picture master equation
• Simulation of quantum jump trajectories for the driven-dissipative qubit
• Husimi-Q function of the steady state of a cavity mode interacting with a non-linear medium (anharmonic oscillator) for different values of the detunning ($\Delta$)