quantum-math-lab/README.md

Quantum Framework

Circuits, not slides. Real quantum computing.

A state-vector quantum circuit simulator with implementations of fundamental quantum algorithms, unsolved math problem compendium, and experimental emergence research. Built in Python with NumPy.

Features

• State-Vector Simulator — Dense complex NumPy arrays. Hadamard, Pauli-X/Y/Z, CNOT gates, custom unitaries, measurement with collapse.
• Bell States — Create and measure entangled qubit pairs.
• Probability Distributions — Inspect full probability distributions for any subset of qubits at any point.
• Measurement — Projective measurement with state collapse, configurable RNG for reproducibility.
• Problem Compendium — 10 landmark unsolved problems: Riemann Hypothesis, P vs NP, Navier-Stokes, and more.
• Emergence Research — Experimental trinary and emergence simulations in the lab.
• Automated Tests — Full pytest suite verifying simulator behavior.

Quickstart

git clone https://github.com/blackboxprogramming/quantum-math-lab.git
cd quantum-math-lab
pip install -r requirements.txt

# Run the simulator
python -c "
from quantum_simulator import QuantumCircuit
import numpy as np

# Create a Bell state
qc = QuantumCircuit(2)
qc.hadamard(0)
qc.cnot(0, 1)
print(qc.measure(rng=np.random.default_rng(42)))
"

# Run tests
pytest tests/

Simulator API

from quantum_simulator import QuantumCircuit
import numpy as np

qc = QuantumCircuit(3)       # 3-qubit register

# Gates
qc.hadamard(0)               # Hadamard on qubit 0
qc.pauli_x(1)                # Pauli-X (NOT) on qubit 1
qc.pauli_y(2)                # Pauli-Y on qubit 2
qc.pauli_z(0)                # Pauli-Z on qubit 0
qc.cnot(0, 1)                # CNOT: control=0, target=1

# Inspect
probs = qc.probabilities()   # Full probability distribution
result = qc.measure()         # Measure with collapse

Project Structure

quantum-math-lab/
├── quantum_simulator.py     # Core simulator: QuantumCircuit class
├── problems.md              # 10 unsolved math problems
├── requirements.txt         # numpy, pytest
├── lab/
│   ├── emergence.py         # Emergence simulation experiments
│   └── trinary_extended.py  # Trinary computing extensions
└── tests/
    ├── conftest.py
    └── test_quantum_simulator.py

Unsolved Problems Covered

1. Riemann Hypothesis
2. P vs NP
3. Navier-Stokes Regularity
4. Birch and Swinnerton-Dyer Conjecture
5. Hodge Conjecture
6. Yang-Mills Existence and Mass Gap
7. Goldbach's Conjecture
8. Twin Prime Conjecture
9. Collatz Conjecture
10. ABC Conjecture

Related Projects

• Simulation Theory — SHA-256 hash chains and computational reality
• Native AI Quantum Energy — AI quantum computing and energy simulation
• BlackRoad OS — The operating system for governed AI

Live Tools

• circuits.blackroad.io — Visual circuit designer
• simulator.blackroad.io — Browser-based quantum simulator

License

Copyright 2026 BlackRoad OS, Inc. — Alexa Amundson. All rights reserved.