Testing Tolerance Framework

This section is under development. Content will be migrated from CIP-0004 documentation.

The qig test suite uses scientifically-derived tolerance categories for numerical validation.

Tolerance Categories

Category A: Machine Precision Operations (≤ 1e-14): Pure algebraic operations with minimal error accumulation
Category B: Quantum State Properties (≤ 1e-12): Fundamental quantum constraints (unit trace, hermiticity)
Category C: Entanglement & Information Metrics (≤ 1e-10): Information-theoretic quantities sensitive to eigenvalue ratios
Category D: Analytical Derivatives (≤ 1e-8): Error propagation in quantum Fisher information metric
Category E: Numerical Integration (≤ 1e-6): ODE solver convergence and long-time stability
Category F: Physical Validation (≤ 1e-4): Statistical significance for physical claims
Category G: BCH Approximation Residuals (~0.1 · ‖θ‖²): The Hamiltonian extraction formula \(F\,\eta \approx A\,\theta\) (where \(F_{rc} = \sum_b f_{rbc}\,\theta_b\)) is only leading-order correct. The Kubo-Mori kernel embedded in \(A\) contributes \(O(\|\theta\|^2)\) corrections outside \(\operatorname{col}(F)\). For \(\|\theta\|\sim 0.05\) the irreducible residual is \(\sim 10^{-3}\). Tests that verify this residual use the bound \(0.5\,\|\theta\|^2\) rather than a fixed numerical tolerance. See tests/test_generic_hamiltonian.py::test_extraction_consistency_multiple_points and CIP-0009 (Correction note: extraction formula accuracy).

For complete documentation, see: