[WIP] Add benchmarking for free-fermion quantum circuits

[Copilot]

Implementation plan for fermionic-computing-benchmark repository:

• Create project structure with proper Python packaging (setup.py, pyproject.toml, requirements.txt)
• Implement core fermionic simulation modules:
  • Matchgate operations and circuits
  • Free-fermion state representation using covariance matrix
  • Polynomial-time simulation algorithms
• Implement comparison baseline:
  • Exponential-time statevector simulation
  • Performance comparison utilities
• Implement Fermionic Machine Learning (FermiML) components:
  • Fermionic parameterized circuits
  • Training and optimization utilities
• Create benchmarking suite:
  • Performance benchmarks for various qubit counts
  • Comparison plots and analysis
• Add documentation and examples:
  • Update README with usage instructions
  • Add example notebooks or scripts
  • Include references to Gince et al. and Bravyi & Kitaev
• Add tests for core functionality
• Verify all components work together

Original prompt

A Python repository for efficient classical simulation of free-fermion quantum circuits (Matchgates) and Fermionic Machine Learning (FermiML). The project benchmarks the polynomial-time simulation of non-interacting fermions against exponential-time statevector simulations. Based on the work of Gince et al. (2024) and Bravyi & Kitaev.

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