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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 ($\Delta$)