Quantum Math Lab

Quantum Math Lab pairs a lightweight quantum circuit simulator with concise summaries of landmark unsolved problems in mathematics. The project is designed for experimentation and self-study: you can build and inspect quantum states in pure Python while browsing short descriptions of famous conjectures.

Features

• State-vector simulator implemented in quantum_simulator.py with Hadamard, Pauli-X and controlled-NOT gates, custom unitaries and measurement utilities.
• Problem compendium in problems.md covering ten influential open problems such as the Riemann Hypothesis, P vs NP and the Navier–Stokes regularity question.
• Automated tests demonstrating the simulator’s behaviour, built with pytest.

Getting started

1. Install dependencies

   python -m venv .venv
   source .venv/bin/activate
   pip install -r requirements.txt  # see below if the file is absent

   If a requirements.txt file is not present, simply install NumPy and pytest:

   pip install numpy pytest

2. Experiment with the simulator

   from quantum_simulator import QuantumCircuit
   
   circuit = QuantumCircuit(2)
   circuit.hadamard(0)
   circuit.cnot(0, 1)
   print(circuit.probabilities())  # {'00': 0.5, '11': 0.5}
   result = circuit.measure(rng=np.random.default_rng())
   print(result.counts)

3. Review the unsolved problems by opening problems.md for high-level summaries and references.

Running the tests

Use pytest to execute the simulator tests:

pytest

The test suite verifies single-qubit gates, entanglement via the controlled-NOT operation and measurement statistics.

Disclaimer

This project does not attempt to solve the problems listed in problems.md and is not a substitute for full-featured quantum computing frameworks such as Qiskit or Cirq. It is an educational sandbox for experimenting with qubit states and learning about open questions in mathematics.