feat(simulator): add QuantumState interface and local DensityMatrixSi…

[Aditya12313]

…mulator

• Add QuantumState abstract base class for state representations
• Implement DensityMatrixState and local DensityMatrixSimulator for offline execution
• Fix 2D list parsing bug in quantum_info.DensityMatrix._init_from_array
• Add comprehensive test suite in tests/test_density_matrix_simulator.py

Summary

This PR adds a generic QuantumState interface and introduces a local DensityMatrixSimulator backend, enabling offline and noisy circuit simulations without cloud dependencies. It also resolves a 2D array parsing bug in quantum_info.DensityMatrix.

Key Changes

1. QuantumState Abstract Interface (qpiai_quantum/simulator/state.py):
   • Defines a standard interface for quantum state representations (single-qubit gates, multi-qubit gates, unitary evolution, Kraus channels, measurement statistics).
2. DensityMatrixState & DensityMatrixSimulator (qpiai_quantum/simulator/density_matrix.py):
   • Implements two-sided tensor gate transformations: $\rho \to U \rho U^\dagger$.
   • Supports Kraus operator channel application: $\rho \to \sum_i K_i \rho K_i^\dagger$.
   • Includes state helpers (pure_state, maximally_mixed), information-theoretic metrics (purity, von_neumann_entropy), and subsystem partial_trace (specifically optimized for 2-level qubit registers).
   • Implements BaseSimulator interface, returning standard QasmSimulatorResult.
3. Bug Fix in quantum_info.DensityMatrix._init_from_array:
   • Fixed conditional branch handling in _init_from_array so 2D numeric and complex nested lists properly initialize self.data.
4. Unit Tests (tests/test_density_matrix_simulator.py):
   • 10 comprehensive tests covering gates, mixed states, partial trace, Kraus channels, and quantum_info.DensityMatrix interoperability.

Verification

• All 10 tests in tests/test_density_matrix_simulator.py and existing simulator unit tests pass cleanly.