Shor's Algorithm: Phasor-Sum Interference Map

Number to Factor

N 15

Base a (coprime to N) 7

Inspect output k 0

Live Readouts

True order r (a^r≡1 mod N)

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Measured x₀ (2nd register)

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Measured k (after QFT)

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Estimated period r̃

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Pick N and a, then run.

Phasor step (one collapsed x)

Resultant vector Σ (current k)

Spectrum — true period peaks

Spectrum — measured outcome

How it works

This is the 2D counterpart to the 3D bar-chart period-finding visualizer. Instead of rendering the QFT output as bar heights in a 3D scene, it draws the actual complex-plane arithmetic that produces those heights: an Argand (phasor) diagram. For a chosen output index k, the collapsed register's M surviving values of x each contribute one unit step e^(2πikx/Q) in the complex plane; the diagram chains these steps head-to-tail exactly like a vector-addition polygon.

step_i = e^(2πi k xᵢ / Q),  i = 0…M-1  (unit-length phasors)
Σ = step_0 + step_1 + … + step_{M-1}   (drawn as the connected chain)
P(k) = |Σ|² / (M·Q)                    (properly normalised QM probability, Σ_k P(k) = 1)

When k sits exactly on a multiple of Q/r, every step points the same direction — the chain walks in a straight line and closes far from the origin, giving a tall spectrum bar. Off a peak, the steps' directions wind around evenly and the chain curls back near the origin, cancelling almost to nothing. The bottom strip plots P(k) for every k so you can see the whole spectrum while the top diagram animates the mechanism behind whichever k is currently selected — auto-scan sweeps k continuously and rebuilds the phasor chain live, or drag the slider to inspect any single k by hand.

N / a — the composite to factor and the random base; only bases coprime to N are offered.
Register qubits n — resolution of the frequency register; a larger Q gives more, sharper peaks to inspect.
Inspect output k — freezes the phasor diagram on one output index; auto-scan turns off while you drag it.
Measure output register — samples one k from the real P(k) distribution and runs the same continued-fraction extraction as the 3D version to recover a candidate period r̃ (and, when even, the classical gcd factors of N).

All of the number theory here — modular exponentiation, the exact discrete Fourier sum, continued fractions — is exact and independently computed for this 2D view; only the exponential quantum speed-up itself is what a real device would add.