ⰍⰖⰀⰐⰕⰖⰏ ⰀⰎⰃⰑⰓⰋⰕⰘⰏⰔ

ⰍⰖⰀⰐⰕⰖⰏ ⰀⰎⰃⰑⰓⰋⰕⰘⰏⰔ — ⰔⰘⰑⰂⰐ ⰋⰐ ⰗⰖⰎⰎ ⰄⰅⰕⰀⰋⰎ, ⰂⰋⰕⰘ ⰋⰕⰔ ⰒⰓⰑⰑⰗ: Ⰰ ⰄⰅⰕⰅⰓⰏⰋⰐⰋⰔⰕⰋⰜ ⰜⰑⰐⰕⰅⰐⰕ-ⰀⰄⰄⰓⰅⰔⰔ ⰓⰅⰜⰑⰏⰒⰖⰕⰀⰁⰎⰅ ⰗⰓⰑⰏ ⰕⰘⰅ ⰜⰑⰏⰒⰑⰐⰅⰐⰕ'Ⱄ ⰐⰀⰏⰅ.

☶10D

Quantum algorithms · quadratic → exponential

The quantum wave continues into the algorithm speedups — the whole spectrum of advantage. Grover's search finds the one marked item among N in about (π/4)√N steps, amplifying its amplitude until measurement almost certainly returns it — a quadratic speedup. Deutsch–Jozsa decides whether an n-bit function is constant or balanced in a single query, where a classical deterministic algorithm can be forced to make 2^(n−1)+1. And Simon's algorithm recovers a hidden period: every quantum run yields a string orthogonal to it, so O(n) runs determine it by linear algebra, while any classical method needs exponentially many — the first exponential quantum-classical separation, and the seed from which Shor's factoring grew. All three run exactly here on the deterministic simulator.

• ✓ Grover — quadratic searchfound item 42 of 64 in 6 iterations (~(π/4)√N), marked-probability 0.997 — quadratic speedup (provably optimal, not exponential)
• ✓ Deutsch–Jozsa — one querydecides constant vs balanced in 1 query (constant / balanced), where a classical deterministic algorithm may need 2^(n−1)+1
• ✓ Simon — the first exponential separationrecovers hidden period s=11 (recovered 11, every run orthogonal=true) — O(n) quantum vs Ω(2^(n/2)) classical, Shor's precursor
• the honest boundquery/oracle separations (Grover only quadratic, BBBV-optimal); the simulation has no speedup (Gottesman–Knill, 2^n memory); the real exponential at scale (Shor) needs the QFT + fault tolerance

Boundary: Three real, cited quantum algorithms on the deterministic state-vector simulator: Grover's search (1996; the existing grover primitive — found 42 of 64 in ~√N iterations), Deutsch–Jozsa (1992; one query decides the global property), and Simon's algorithm (1994; the parity oracle at n=2 with hidden s=0b11, every measured y orthogonal to s). HONEST BOUNDS: these are QUERY/oracle-complexity separations — Grover's quadratic speedup is provably optimal (Bennett–Bernstein–Brassard–Vazirani 1997), so it is NOT exponential; Deutsch–Jozsa and Simon's separations are against an oracle, not unconditional; and the SIMULATION itself carries no speedup (it is classical, costing 2^n memory, efficient here only because n is tiny / Clifford by Gottesman–Knill). The genuine exponential advantage at scale (Shor's factoring) needs the quantum Fourier transform plus fault tolerance — beyond this demonstration. Composes quantumImpossibleWaveThree.

✓ proven · content-address ef3f6330-2a8f-804f-a3da-80ab0b9beacc — declared, placed, mounted, and recomputable from the component's name.