[DOCS] Add algorithm complexity comparison table to README #4
Description
Enhancement Request
Add a comprehensive comparison table showing the computational complexity, memory requirements, and use cases for all supported quantum algorithms.
Motivation
New users often ask "which algorithm should I use?" but have to dig through code comments to understand the trade-offs between QFT, Grover, Shor, GHZ, and Bell algorithms.
Proposed Addition
Add this table to the README.md in the "Advanced Algorithms" section:
| Algorithm | Time Complexity | Memory Usage | Best For | Max Qubits* |
|---|---|---|---|---|
| QFT | O(n²) gates | Most efficient | Shor's algorithm, frequency analysis | 25+ |
| Grover | O(√N) iterations | Moderate | Database search, optimization | 20+ |
| Shor | O(n³) gates | High | Factorization, cryptography | 18+ |
| GHZ | O(n) gates | Light | Multi-party entanglement | 25+ |
| Bell | O(n) gates | Lightest | Basic entanglement, benchmarking | 25+ |
*Approximate limits on typical hardware
Additional Documentation Needed
- Brief explanation of when to use each algorithm
- Link to relevant research papers
- Performance benchmarks on different hardware
Implementation Notes
- Good first issue for new contributors
- Requires no code changes, only documentation
- Should match the current performance characteristics in
test_ultimate_scaling.py
Acceptance Criteria
- Table added to README.md
- Accurate complexity information
- Links to algorithm implementations
- Brief usage recommendations
- Consistent with current code performance