/Open-Quantum-Systems-1

Worksheets for the module Open Quanum Systems, part of the MSc Quantum Science and Technology at Trinity College Dublin.

Primary LanguageJupyter Notebook

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 ($\Delta$)