Reversible arithmetic, point 2 of #336: comparisons

[tatopenn-cell]

Point 2 of #336. Builds on #337 (contains its commit until #337 is merged).

• compare_registers(sv, n, a, b, out, op): |a, b, z⟩ → |a, b, z ⊕ [a op b]⟩, inputs unchanged; '<' is the comparator of Cuccaro et al. (quant-ph/0410184, Sect. 4.3), high bit of a − b
• compare_constant(sv, n, b, c, out, op): classical c; '<' is the most significant qubit after the reverse φADD(c) (Beauregard, quant-ph/0205095, Sect. 2.1, Fig. 4)
• op: '<', '>', '<=', '>=', '==', '!=' (derived by swapping operands and negating the output)

Tests: Cuccaro comparator circuit (1–3 bits) and Beauregard reverse φADD circuit (c < 2^n) built from engine gates, compared on every basis state; every comparison checked on every basis state; superposition gets entangled with the output.

Docs: Step 5 on api/arithmetic.md, nav label, README line.

[codecov]

Codecov Report

❌ Patch coverage is 98.61111% with 1 line in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
dense_evolution/circuits/arithmetic.py	98.57%	1 Missing ⚠️

📢 Thoughts on this report? Let us know!