USEL

USEL () is an open-source, CPU-only scientific computing framework focused on quantum physics simulations and numerical methods.

Version 1.0 establishes the mathematical and computational foundation — matrix and linear algebra utilities, numerical solvers, FFT-based frequency analysis, random number generation, configuration/IO/logging utilities, and a CLI — for future quantum mechanics, computational physics, and quantum information modules.

Features

• Runs efficiently on standard consumer hardware, no GPU required
• Operates within 8 GB RAM
• Cross-platform (Windows, Linux, macOS)
• Modular, extensible architecture
• Fully typed, PEP 8 compliant codebase

Installation

uv sync
uv run usel version

Or, for local development:

git clone https://github.com/usel/usel.git
cd usel
uv sync --group dev

See the examples directory for more, including eigenvalue solving, ODE integration, FFT analysis, and numerical integration.

Command Line Interface

uv run usel version
uv run usel doctor
uv run usel benchmark --size 200
uv run usel info
uv run usel config path/to/config.yaml
uv run usel test

Modules

Module	Description
usel.math	Matrix creation, algebra, norms, FFT transforms
usel.linalg	Eigenvalues/vectors, SVD, QR, LU, Cholesky
usel.solvers	Root finding, ODE solvers, numerical integration
usel.random	Random matrices, vectors, and distributions
usel.utils	Timing, profiling, validation, precision control
usel.logging	Console/file loggers, performance logger
usel.config	YAML/JSON/TOML configuration loading
usel.io	CSV/JSON/NumPy binary/text file I/O
usel.cli	Command line interface

Non-Goals (v1.0)

This release intentionally excludes the Schrödinger equation, quantum circuits/gates/qubits, machine learning, chemistry simulation, GPU/cloud computing, and AI integration. These are planned for future releases (see CHANGELOG.md and the roadmap below).

Roadmap

• v1.0 — Schrödinger Module

  • Non-relativistic quantum state evolution
  • Grid, operator, and Hamiltonian construction
  • Multiple time-evolution schemes (Crank-Nicolson, split-operator, RK4)

• v2.0 — Dirac Equation Module

  • Relativistic 1D Dirac equation solver
  • Spinor algebra and Pauli/Dirac matrix library
  • Matrix-exponential propagation

• v3.0 — Maxwell Equation Module

  • Electromagnetic field simulations
  • Symbolic and numerical field solvers

• v4.0 — Black-Scholes Module

  • Analytical option pricing, Greeks, and put-call parity
  • Implied volatility and Black-Scholes PDE solver
  • Monte Carlo pricing with variance reduction

Still more planning is going on this.

Development

uv sync --group dev
uv run pytest
uv run ruff check .
uv run black --check .
uv run pytest --cov=./ --cov-report xml

Documentation

Full documentation is built with MkDocs:

uv run mkdocs serve

Contributing

Contributions are welcome! See CONTRIBUTING.md for guidelines.

Security

USEL performs no telemetry, no network communication, and no data collection. It is fully offline capable.

License

MIT — see LICENSE.