primitive · G11

Period-finding backend of Shor (N = 15, a = 7)

Control register (m = 4) in |+⟩⁴, two work qubits encode the compiled periodic function f(x) = x mod 4 (the same period as ord₁₅(7) = 4). Inverse QFT on the control register, no final swap (bit-reversal absorbed in the host decoder). Continued-fractions on the non-zero peaks recovers r = 4.

period_decode_verified · recovered r = 4 · peak share on {0,4,8,12} = 1.0000 · 2048 shots

← frontier card

Control-register histogram (k ∈ 0..15)

Top peaks

0, 4, 8, 12

Continued-fractions candidates

2, 4, 4

LCM (recovered r)

Kernel snippet

open in Playpond ↗

from quantum.nadarasa_g11_lib import (
    guppy, qubit, h, x, cx, rz, measure, result, angle, cphase_h,
)

@guppy
def program() -> None:
    c0 = qubit()
    c1 = qubit()
    c2 = qubit()
    c3 = qubit()
    w0 = qubit()
    w1 = qubit()

    # Control register in |+>^4 (sweep x = 0..15 in superposition).
    h(c0); h(c1); h(c2); h(c3)

    # Compiled f(x) = x mod 4 into the work register: w_j = c_j for j<2.
    cx(c0, w0)
    cx(c1, w1)

    # Inverse QFT on (c0, c1, c2, c3), no final swap.
    h(c3)
    cphase_h(c3, c2, -0.5)
    h(c2)
    cphase_h(c3, c1, -0.25)
    cphase_h(c2, c1, -0.5)
    h(c1)
    cphase_h(c3, c0, -0.125)
    cphase_h(c2, c0, -0.25)
    cphase_h(c1, c0, -0.5)
    h(c0)

    result("c0", measure(c0))
    result("c1", measure(c1))
    result("c2", measure(c2))
    result("c3", measure(c3))
    result("w0", measure(w0))
    result("w1", measure(w1))