Reversible arithmetic, point 1 of #336: addition and subtraction

[tatopenn-cell]

Point 1 of #336.

• add_registers: |a, b⟩ → |a, (a+b) mod 2^len(b)⟩ (Vedral, Barenco, Ekert, quant-ph/9511018, Sect. III.A; modulo 2^n as in Cuccaro et al., quant-ph/0410184, Sect. 4.1)
• subtract_registers: inverse of the adder, high bit set when b < a
• add_constant: classical addend, increment/decrement (Draper, quant-ph/0008033, Sect. 5; Beauregard, quant-ph/0205095, Sect. 2.1)

Each operation is a bijection on basis states, applied as an index permutation of the statevector (Vedral et al., Sect. II). Tests compare against the gate-level Cuccaro ripple-carry adder (1–3 bits, every basis state) and the Draper transform adder built from engine gates.

Docs: new API page api/arithmetic.md, nav entry, one README line.

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Codecov Report

❌ Patch coverage is 87.50000% with 7 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
dense_evolution/circuits/arithmetic.py	87.03%	7 Missing ⚠️

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