FA-91199 / Quantum circuit simulation / Member archive

Grover planner takes asin of the marked fraction instead of its square root · case 04

For N=1024, M=1 the planner asks for about 804 iterations instead of 25.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input [N, M]. "invalid" if N < 1, M < 0 or M > N; "no-solution" if M == 0; if 2M >= N return {"iterations": 0, "success": M/N}; else theta = asin(sqrt(M/N)), k = floor(pi/(4 theta)) and success = sin^2((2k+1) theta). Probabilities rounded to 6 decimals.

Why this case matters

Choosing the Grover iteration count wrongly overshoots the amplitude peak and collapses the success probability.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression: N=16 M=3	`{"iterations": 4, "success": 0.98402}`	`{"iterations": 1, "success": 0.949219}`	Failed

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