Implement quantum simulator and unsolved problems for Quantum Math Lab

[blackboxprogramming]

Description

The README for Quantum Math Lab describes a minimal quantum computing simulator in quantum_simulator.py and a file problems.md summarizing major unsolved math problems, but these files are absent from the repository. Without these files the project is non-functional.

Proposed work

• Create a quantum_simulator.py module implementing a QuantumCircuit class with basic gates (Hadamard, Pauli‑X), a controlled NOT gate, measurement, and state vector management using NumPy. Use the features described in the README (simulate circuits, apply gates and measure) as guidance and draw inspiration from the existing simulator in the Native AI Quantum Energy Lab【521547631455444†L0-L27】.
• Include comprehensive docstrings and usage examples for each method.
• Write tests using pytest to verify that single‑qubit gates, entanglement and measurement produce expected probabilities.
• Create a problems.md file containing succinct descriptions of ten major unsolved problems in mathematics. Take inspiration from the problems listed in the Native AI Quantum Energy Lab’s problems.md file, which summarises the Riemann Hypothesis, P vs NP, Navier–Stokes existence and smoothness, and other conjectures【746733578561328†L9-L91】. Adapt the descriptions in your own words and cite authoritative references where appropriate.
• Update the README to link to the new simulator and problem files and provide instructions for installing dependencies and running the simulator.

Acceptance criteria

• The repository includes a fully implemented quantum_simulator.py with a working QuantumCircuit class and accompanying docstrings.
• A problems.md file is added with high‑level descriptions of at least ten unsolved mathematical problems similar to those described in the Native AI Quantum Energy Lab’s problems list【746733578561328†L9-L91】.
• Pytest tests verify correct operation of the quantum simulator and are included in a tests/ directory.
• The README is updated with instructions on running the simulator and reading the problem summaries.

[blackboxprogramming]

@copilot @dependabot @Blackroad @cadillac @codex @lucidia @cecilia @GitGuardian @blackboxprogramming @slackbot @blackroadagents

I can’t merge right now. Please:

1. set up tests, 2) run full CI, 3) fix failing checks and review comments, 4) re-run CI, 5) add/keep queue:ready when green.
   Block prod deploys until protections are strict and all checks pass. Thanks.

[chatgpt-codex-connector]

Summary

• Implemented a state-vector QuantumCircuit simulator with common gates, custom unitary support, probabilistic measurement, and measurement result helpers for interactive experimentation. quantum_simulator.pyL33-L290
• Added pytest coverage for single-qubit gates, entanglement, and measurement behaviour along with path configuration for local imports. tests/test_quantum_simulator.pyL1-L61 tests/conftest.pyL1-L6
• Documented setup and usage instructions, captured ten referenced unsolved problems, and recorded dependency and ignore metadata for the project. README.mdL1-L68 problems.mdL1-L83 requirements.txtL1-L2 .gitignoreL1-L5

Testing

• ✅ pytest

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