Quantum Simulation Repository: Jaynes–Cummings & Transmon Qubits

This repository contains two Python projects for simulating quantum two-level systems and qubits coupled to resonators, including visualization of the dynamics. The primary goal is to demonstrate understanding of quantum physics and qubit-resonator dynamics.

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Repository Contents

1. Jaynes–Cummings Model with Dissipation

• Main file: jaynes_cummings.py

• Description:
  Simulates the Jaynes–Cummings model: a single qubit coupled to a quantum resonator. Features include:

  • Hamiltonian under the Rotating Wave Approximation (RWA)
  • Optional dissipation:
    • Resonator decay
    • Qubit relaxation
    • Qubit dephasing
  • Time evolution solved via the Lindblad master equation using QuTiP
  • Expectation values computed:
    • Qubit excitation probability
    • Average photon number in the resonator
    • Total system energy
  • Visualization:
    • Rabi oscillations
    • Energy decay over time

• Code structure:

  • JaynesCummings: defines the physical model and Hamiltonian
  • Simulation: handles time evolution
  • Plotter: generates visualizations

• Dependencies: qutip, numpy, matplotlib

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2. Transmon Qubit Simulation with Control Pulses

• Main file: transmon_qubit.py

• Description:
  Simulates a two-level transmon qubit controlled by a microwave pulse. Features include:

  • Pulse definition (Pulse) with Gaussian or rectangular envelopes
  • Numerical calibration of the pulse to achieve a target rotation angle (e.g., π for an X-gate)
  • Qubit Hamiltonian and dynamics (TransmonQubit), with the option to use:
    • Rotating Wave Approximation (RWA)
    • Full lab-frame Hamiltonian (non-RWA)
  • Time evolution via numerical integration of the Schrödinger equation (Heun method)
  • Analysis and visualization of results:
    • Populations of |0⟩ and |1⟩ states
    • Bloch sphere trajectory

• Code structure:

  • Pulse: defines and calibrates control pulses
  • TransmonQubit: defines the qubit system
  • Simulator: handles time evolution
  • SimulationResult: stores and visualizes results

• Dependencies: numpy, scipy, matplotlib

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Usage Examples

After cloning the repository, ensure all dependencies are installed.

Jaynes–Cummings

python jaynes_cummings.py

Outputs

• Rabi oscillations of the qubit
• Average photon number
• Total system energy over time

Transmon Qubit

python transmon_simulator.py

Outputs

• Qubit-resonator interactions
• Quantum dissipation
• Dynamics of pulse-controlled qubits

Repository Goals

• Demonstrate understanding of quantum physics concepts, including:
  • Qubit-resonator interactions
  • Quantum dissipation
  • Dynamics of pulse-controlled qubits
• Provide tools for visualizing and interpreting quantum dynamics

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Author / Contribution

Fabio Calabrese

Primary contributions: understanding, analysis, and application of physical models; guided code development with AI assistance

Screenshots

Simulation with the default parameters