Reversible arithmetic, point 3 of #336: modular arithmetic

[tatopenn-cell]

Point 3 of #336. Builds on #337 and #338 (contains their commits until they are merged).

• add_registers_mod: |a, b⟩ → |a, (a+b) mod N⟩ (Vedral, Barenco, Ekert, quant-ph/9511018, Sect. III.B)
• add_constant_mod: classical addend, optional controls (Beauregard, quant-ph/0205095, Sect. 2.2, doubly controlled φADD(a)MOD(N))
• multiply_add_mod: |x, b⟩ → |x, (b + a·x) mod N⟩, optional controls (Beauregard Sect. 2.3 CMULT; Vedral Sect. III.C)
• multiply_mod: in place x → a·x mod N for gcd(a, N) = 1, optional controls (Vedral Sect. II; Beauregard Fig. 7); N = 2^n with odd a is plain multiplication
• power_mod: |x, y⟩ → |x, y·a^x mod N⟩, with y = 1 the modular exponentiation of Shor's algorithm (Vedral Eq. 1, Sect. III.D)

Values ≥ N are left unchanged so every map stays a permutation (unitary).

Tests compare each function with the paper's construction built from already-tested blocks and engine gates, on every basis state: Beauregard modular adder (Fig. 5), sum of controlled modular additions (Eq. 2), controlled-U_a with controlled swap (Fig. 7), chain of controlled multiplications (Vedral III.D); plus 7^x mod 15, plain ×odd mod 2^n, norm on random states, coprime check.

Docs: Step 6 (7^x mod 15) on api/arithmetic.md, details, nav label, README line.

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Codecov Report

❌ Patch coverage is 99.15966% with 1 line in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
dense_evolution/circuits/arithmetic.py	99.14%	1 Missing ⚠️

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