rwa-tools 0.1.1

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RWA-Tools

A Python package for working with quantum Hamiltonians in the Rotating Wave Approximation (RWA) frame.

Overview

RWA-Tools provides a set of utilities for symbolic manipulation of quantum Hamiltonians, particularly focusing on applying the Rotating Wave Approximation to simplify time-dependent quantum systems. This package leverages SymPy for symbolic mathematics to represent and transform Hamiltonians.

Installation

pip install rwa-tools

For development installation:

git clone https://github.com/ograsdijk/rwa-tools.git
cd rwa-tools
pip install -e .

Features

• Symbolic representation of quantum Hamiltonians
• Application of the Rotating Wave Approximation (RWA)
• Unitary transformations to rotating frames
• Handling of multi-level quantum systems
• Simplification of time-dependent Hamiltonians

Usage Examples

Creating a Symbolic Hamiltonian

import matplotlib.pyplot as plt
import networkx as nx
import sympy as smp

from rwa_tools import (
    create_coupling_graph,
    create_hamiltonian_symbolic,
    create_hamiltonian_rwa,
)
from rwa_tools.graph_transform import create_transform_matrix

# Define your quantum system
nstates = 5
couplings = [[(0, 4), (1, 4)], [(2, 4), (3, 4)], [(1, 3)], [(0, 4), (1, 4)]]

# Create the Hamiltonian and coupling graph
hamiltonian = create_hamiltonian_symbolic(couplings, nstates)
coupling_graph = create_coupling_graph(couplings, nstates=nstates)

# Visualize the coupling graph
fig, ax = plt.subplots()
nx.draw(coupling_graph)

Applying RWA Transformation

from rwa_tools import (
    create_coupling_graph,
    create_hamiltonian_symbolic,
    create_hamiltonian_rwa,
)
from rwa_tools.graph_transform import create_transform_matrix

# Define your quantum system
nstates = 5
couplings = [[(0, 4), (1, 4)], [(2, 4), (3, 4)], [(1, 3)], [(0, 4), (1, 4)]]
hamiltonian = create_hamiltonian_symbolic(couplings, nstates)
coupling_graph = create_coupling_graph(couplings, nstates=nstates)

# Create transformation matrix from coupling graph
T = create_transform_matrix(coupling_graph, hamiltonian.coupling_symbol_paths)

# Apply RWA transformation
hamiltonian_rwa = create_hamiltonian_rwa(hamiltonian, T)

# Print the resulting RWA Hamiltonian
print(hamiltonian_rwa.hamiltonian)

Working with Independent Subsystems

from rwa_tools import (
    create_coupling_graph,
    split_into_independent_components,
    create_hamiltonian_symbolic,
    split_hamiltonian_by_components,
)

# Define a system with independent components
nstates = 7
couplings = [[(0, 2), (1, 2)], [(3, 5), (4, 5)]]
hamiltonian = create_hamiltonian_symbolic(couplings, nstates)
coupling_graph = create_coupling_graph(couplings, nstates=nstates)

# Split into independent components
independent_graphs = split_into_independent_components(coupling_graph)

# Split the Hamiltonian by components
independent_hamiltonians = split_hamiltonian_by_components(
    hamiltonian, independent_graphs
)

# Access individual subsystem Hamiltonians
print(independent_hamiltonians[0].total)
print(independent_hamiltonians[1].total)

API Documentation

Core Classes

• HamiltonianSymbolic: Represents a symbolic quantum Hamiltonian in the lab frame
• HamiltonianRWA: Represents a quantum Hamiltonian in the rotating wave approximation frame

Key Functions

• create_hamiltonian_symbolic: Create a symbolic representation of a quantum Hamiltonian
• create_coupling_graph: Create a graph representing couplings between quantum states
• create_hamiltonian_rwa: Generate a Hamiltonian in the RWA frame from a lab-frame Hamiltonian and unitary transformation
• create_transform_matrix: Create a transformation matrix based on the coupling graph
• split_into_independent_components: Split a graph into independent connected components
• split_hamiltonian_by_components: Split a Hamiltonian into independent subsystems

Mathematical Background

The Rotating Wave Approximation is a technique used in quantum optics and quantum mechanics to simplify the treatment of time-dependent systems. The transformed Hamiltonian is calculated using:

$H_{RWA} = U^{\dagger}HU - i\hbar U^{\dagger}(\partial U/\partial t)$

Where $U$ is the unitary transformation matrix and $H$ is the original Hamiltonian.

License

This project is licensed under the MIT License - see the LICENSE file for details.