feat: add QUBO→ILP and CircuitSAT→ILP reductions

[GiggleLiu]

Summary

• Add QUBO → ILP reduction via McCormick linearization (src/rules/qubo_ilp.rs)
• Add CircuitSAT → ILP reduction via Tseitin-style gate constraint encoding (src/rules/circuit_ilp.rs)
• Both reductions are feature-gated behind ilp-solver
• All problem types can now reach ILP (fixes Add ILP reduction paths for CircuitSAT, MaxCut, QUBO, SpinGlass #83)

Details

QUBO → ILP: Linearizes quadratic binary terms using McCormick envelope constraints. For each non-zero off-diagonal Q_ij, introduces an auxiliary binary variable y_ij = x_i · x_j with constraints y ≤ x_i, y ≤ x_j, y ≥ x_i + x_j - 1.

CircuitSAT → ILP: Encodes boolean gates as linear constraints over binary variables. NOT, AND, OR, XOR, and Const gates are each translated into tight linear constraint formulations. This provides a direct 1-step path, more efficient than the 3-step CircuitSAT→SpinGlass→QUBO→ILP route.

Test plan

• 3 unit tests for QUBO→ILP (closed-loop, diagonal-only, 3-variable)
• 5 unit tests for CircuitSAT→ILP (AND, OR, XOR, nested, multi-assignment closed-loop)
• Full test suite passes (1503 unit + 91 integration + 43 doc = 1637 tests)
• Clippy clean with -D warnings
• Disambiguated reduce_to() calls in existing CircuitSAT→SpinGlass tests

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 96.26168% with 12 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.33%. Comparing base (7267e16) to head (aec9e56).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/rules/circuit_ilp.rs	93.43%	9 Missing ⚠️
src/rules/qubo_ilp.rs	94.54%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #85      +/-   ##
==========================================
- Coverage   96.35%   96.33%   -0.02%     
==========================================
  Files         193      197       +4     
  Lines       26722    27037     +315     
==========================================
+ Hits        25747    26047     +300     
- Misses        975      990      +15     

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[GiggleLiu]

1. clean up plan files
2. update all documents

[Copilot]

Pull request overview

This pull request adds two new reduction rules to enable all problem types to reach ILP, addressing issue #83:

1. QUBO → ILP via McCormick linearization of quadratic binary terms
2. CircuitSAT → ILP via Tseitin-style gate constraint encoding

Both reductions are feature-gated behind the ilp-solver feature and follow established patterns in the codebase.

Changes:

• Add QUBO→ILP reduction with McCormick linearization for binary products
• Add CircuitSAT→ILP reduction with linear constraint encodings for boolean gates
• Disambiguate reduce_to() calls in existing CircuitSAT→SpinGlass tests to avoid type inference conflicts
• Add comprehensive unit tests for both new reductions

Reviewed changes

Copilot reviewed 8 out of 8 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
src/rules/qubo_ilp.rs	QUBO→ILP reduction implementation using McCormick constraints for quadratic term linearization
src/unit_tests/rules/qubo_ilp.rs	Three unit tests covering closed-loop verification, diagonal-only case, and 3-variable case
src/rules/circuit_ilp.rs	CircuitSAT→ILP reduction with gate-specific linear constraint encodings (NOT, AND, OR, XOR, Const)
src/unit_tests/rules/circuit_ilp.rs	Five unit tests covering AND, OR, XOR, nested expressions, and multi-assignment circuits
src/rules/mod.rs	Module registration for both new reductions under ilp-solver feature flag
src/unit_tests/rules/circuit_spinglass.rs	Explicit type annotations to disambiguate reduce_to() calls after adding CircuitSAT→ILP
docs/plans/2026-02-18-ilp-reduction-paths-impl.md	Implementation plan document with step-by-step instructions
docs/plans/2026-02-18-ilp-reduction-paths-design.md	Design document explaining the reduction algorithms and mathematical formulations

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