FA-91078 / Quantum circuit simulation / Member archive

Bloch vector puts |0> at the south pole · case 03

|0> is reported with z = -1.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input [[ar, ai], [br, bi]] for a|0> + b|1> (possibly unnormalized). Return the Bloch vector [2Re(conj(a) b), 2Im(conj(a) b), |a|^2 - |b|^2] divided by |a|^2 + |b|^2, rounded to 6 decimals, or "zero-state" when the squared norm is below 1e-12.

Why this case matters

Bloch coordinates feed visualizers and single-qubit tomography checks; sign or scale slips put states on the wrong axis.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: random qubit 2	`[-0.888347, 0.410865, 0.205012]`	`[-0.888347, 0.410865, -0.205012]`	Failed

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