Create qgoh.py

qgoh.py

@@ -0,0 +1,50 @@
+#!/usr/bin/env python3
+"""
+Q-GoH: Quantum Goldbach Hypothesis — one-file infinity runner
+"""
+
+import itertools, math, sympy, time
+from qiskit import QuantumCircuit
+from qiskit_aer import AerSimulator
+
+def mask(max_val):
+    return [1 if sympy.isprime(i) else 0 for i in range(max_val + 1)]
+
+def grover_once(N):
+    n = math.ceil(math.log2(N // 2 + 1))
+    qc = QuantumCircuit(2 * n, 2 * n)
+    qc.h(range(2 * n))
+
+    m = mask(N // 2)
+    # oracle flags: p,q prime and p+q=N
+    for val, is_prime in enumerate(m):
+        if is_prime:
+            ctrl = [i for i in range(n) if not (val >> i) & 1]
+            if ctrl: qc.x(ctrl)
+            qc.mcx(list(range(n)), 0)           # flag p
+            if ctrl: qc.x(ctrl)
+
+            ctrl = [i + n for i in range(n) if not (val >> i) & 1]
+            if ctrl: qc.x(ctrl)
+            qc.mcx(list(range(n, 2 * n)), 1)    # flag q
+            if ctrl: qc.x(ctrl)
+
+    qc.measure_all()
+    counts = AerSimulator().run(qc, shots=64).result().get_counts()
+    for bits, _ in counts.items():
+        p = int(bits[:n], 2)
+        q = int(bits[n:], 2)
+        if sympy.isprime(p) and sympy.isprime(q) and p + q == N:
+            return p, q
+    return None
+
+def main():
+    for N in itertools.count(4, 2):
+        t0 = time.perf_counter()
+        pair = grover_once(N)
+        dt = time.perf_counter() - t0
+        print(f"{N} = {pair[0]} + {pair[1]}  (found in {dt:.3f}s)" if pair
+              else f"{N} ❌  ({dt:.3f}s)")
+
+if __name__ == "__main__":
+    main()