Formulon Physics 1.000

What's new in Formulon 1.0

Formulon 1.0 introduces the Quantum-Informed Physical AI Engine, a hybrid quantum-classical research module for learning mappings between physical feature representations and noisy quantum measurements.

Core capabilities

• Classical physics computation
• Quantum-computing modules
• Physics-informed machine learning
• Quantum-informed physical AI
• Noisy quantum simulation
• Physical feature extraction
• Reconstruction and classification
• Interactive visualizations
• Modular Python API

Formulon Physics is a modular computational-physics library containing 234 public scientific formula functions across classical mechanics, electromagnetism, waves/optics, thermodynamics, fluids, modern physics, mathematical physics and series. It also provides optional PennyLane/Qiskit quantum-computing examples.

Design principles

1. Formula first: functions implement familiar textbook/engineering relations.
2. Boundary-aware: inputs are checked for mathematical validity and common model assumptions.
3. No fake universal limits: classical quantities such as velocity and gravity are not capped at arbitrary values. Relativistic limits are applied only where the model requires them.
4. Units are explicit: numeric APIs use SI values; optional Pint helpers provide dimensionality and conversion.
5. Documented assumptions: formulas state their model and intended use.
6. Optional quantum stack: PennyLane and Qiskit are not imported by the core package.

Installation

python -m venv .venv
source .venv/bin/activate
pip install .

With units and quantum examples:

pip install '.[all]'

Or individually:

pip install '.[units]'
pip install '.[pennylane]'

Unit-aware workflow

from formulon.units import quantity, to_si

length = quantity(5, 'ft')
time = quantity(2, 's')
speed = length / time
print(to_si(speed))

Pint is used for explicit unit conversion/dimensionality rather than silently changing the numeric API. Pint supports quantities, conversions and dimensionality checks. citeturn0search0turn0search2

Quantum examples

Grover search

from formulon.quantum_computing.grover import grover_search

result = grover_search(3456, num_qubits=12)
print(result.target_binary, result.found_state, result.success_probability)

Legendre quantum encoder/decoder

The encoder maps (x) to (P_0(x),...,P_{d-1}(x)), uses (RY(rccos(P_n))), and therefore has (\langle Z angle=P_n) ideally. Finite-shot computational-basis measurement gives sampled outcomes; the decoder reconstructs the classical coordinate from estimated Legendre features.

PennyLane is an open-source platform for quantum computing and QML; Formulon's quantum layer is intentionally optional. citeturn0search5

Boundary philosophy

A bound belongs in the validator only when it is a mathematical requirement or a clearly stated model assumption. Examples:

• mass > 0 for formulas that divide by mass;
• radius > 0 where (1/r) occurs;
• absolute temperature (T \ge 0) K;
• volume > 0 for ideal-gas relations;
• emissivity (0\le\epsilon\le1);
• angles restricted only where the formula's geometry requires it;
• relativistic speed (|v|<c) only for relativistic formulas.

Classical velocity is not globally capped at (c), because the classical formula itself is not a relativistic model.

Formula catalog

formulon.formula_catalog exposes machine-readable metadata for all 234 public formula functions:

from formulon.formula_catalog import FORMULA_COUNT, get_formula
print(FORMULA_COUNT)
print(get_formula('projectile_range'))

The catalog records the module, signature, validation rules, description and primary real-world use case.

Testing

The release includes import tests, formula-catalog tests and optional quantum tests. A release should be tested in a clean virtual environment on the target Linux/Python versions before publication.

Scope

This is scientific/educational software, not a substitute for validated engineering codes, safety-critical design, medical decisions or certified numerical simulation. Every formula should be used within its documented assumptions.