second_quantization 0.1.0

Converting second quantized operators to matrix form and back

Second Quantization

A Python package for seamless conversion between symbolic second-quantized operators and their numerical matrix representations.

Features

• Symbolic to Matrix: Convert fermionic operators (creation/annihilation) to matrix form using Jordan-Wigner transformation
• Matrix to Symbolic: Decompose matrices back into fermionic operator expressions
• Efficient: Supports both dense and sparse matrix representations for large Hilbert spaces
• Flexible: Handle parameterized Hamiltonians with symbolic coefficients
• Fast Parameter Sweeps: Reuse basis operators for different parameter values

Installation

pip install second-quantization

Quick Start

import sympy
from sympy.physics.quantum.fermion import FermionOp
from sympy.physics.quantum import Dagger
from second_quantization import hilbert_space

# Define fermionic operators
c, d = [FermionOp(name) for name in "cd"]

# Create a simple Hamiltonian: t(c†d + d†c) + U c†c d†d
t, U = sympy.symbols("t U", real=True)
H = t * (Dagger(c) * d + Dagger(d) * c) + U * Dagger(c) * c * Dagger(d) * d

# Convert to matrix representation
matrix_dict = hilbert_space.to_matrix(H, operators=[c, d], sparse=False)

# Create a callable function for parameter sweeps
hamiltonian_func = hilbert_space.make_dict_callable(matrix_dict)

# Generate Hamiltonian for specific parameter values
H_matrix = hamiltonian_func(t=1.0, U=2.5)

Documentation

Full documentation with tutorials and API reference is available at: https://qt.pages.quantumtinkerer.group/second_quantization/

Use Cases

• Quantum Many-Body Physics: Study interacting fermion systems
• Quantum Chemistry: Molecular Hamiltonians and electronic structure
• Condensed Matter: Hubbard models, topological systems, quantum dots
• Quantum Computing: Variational quantum algorithms, QAOA
• Education: Learn fermionic second quantization interactively

Core Functions

hilbert_space.to_matrix()

Convert symbolic fermionic expressions to matrix form using Jordan-Wigner transformation.

hilbert_space.make_dict_callable()

Create efficient callable functions from symbolic Hamiltonians for parameter sweeps.

hilbert_space.to_operators()

Decompose matrices back into symbolic fermionic operator expressions.

hilbert_space.basis_operators()

Generate basis for fermionic Hilbert spaces.

Requirements

• Python ≥ 3.11
• NumPy ≥ 2.0
• SciPy ≥ 1.8
• SymPy ≥ 1.13

Contributing

Contributions are welcome! Please see our repository for development setup and contribution guidelines.

License

BSD 3-Clause License. See LICENSE for details.