data_type.md

Data Type Selection

In this computational project, I am doing the Monte Carlo evolution of "a two-level atom coupled to a leaky cavity" with QuTip. Integer and floats are going to be the majority of data types. Simulations of quantum mechanics rely on quantum states. Complex numbers are commonly used to describe quantum states in computational quantum mechanics, and they are frequently stored as arrays or matrices. For instance, a column vector with complex elements could be used to depict a qubit's quantum state. In this regard, I might have to select complex numbers as one of the essential data types. I might be using python's library funtion cmath which has in-built function named complex(a,b).Moreover, Hamiltonian can be represented with either of matrices, operators, or functions. Hamiltonian as fucnction is preferable. In QuTiP, Hamiltonians are often represented using the Qobj data type, which means Quantum Onjects.

Qobj:

It is possible for a Qobj to represent mixed or pure quantum states. It is adaptable for simulating a variety of quantum systems, including time-dependent quantum objects. Here is the reference to QuTip Documentation with Qobj: Qutip Documentation

• To represent the time point, numpy array will be used by utilizing numpy.ndarray and np.linspsce.
• Qobj; quantum onjects will be utilized for quantum state with tensor function and annihilation operators for cavity and atom.
• Within Qobj, Operators and Options classes can be used.
• The expectation values use the list of floating point numbers.

Example Usage: Python annotation:

from typing import List, Union
import numpy as np
import qutip as qt

def evolve_system(time_points: np.ndarray,
                   initial_state: qt.Qobj,
                   hamiltonian: Union[np.ndarray, qt.Qobj, callable]) -> List[float]:
    """
    Evolves the quantum system over time using a given Hamiltonian.

    Parameters:
        time_points (np.ndarray): Array of time points.
        initial_state (qt.Qobj): Initial quantum state of the system.
        hamiltonian (Union[np.ndarray, qt.Qobj, callable]): Hamiltonian of the system,
            represented as a numpy array, Qobj, or a function.

    Returns:
        List[float]: List of expectation values of observables at each time point.
    """