Quantum Phase Shifter — Gate Calibration on the Bloch Sphere

Phase-Shift Angle φ

φ 0.000° (0.000 rad)

Target Gate

Fidelity to target100.0%

CALIBRATED — exact gate

Target

Identity

Angle error Δφ

0.000°

Resulting state |ψ⟩

(|0⟩ + |1⟩)/√2

How it works

The qubit starts in the equal superposition |+⟩ = (|0⟩+|1⟩)/√2, a point on the Bloch sphere's equator. A phase shifter applies the single-qubit gate P(φ) = diag(1, e^iφ), leaving |0⟩ untouched and multiplying |1⟩ by e^iφ. The result, (|0⟩+e^iφ|1⟩)/√2, is still on the equator — just rotated by φ. Sweep the slider and watch the state vector spin around the equator in real time.

P(φ)|+⟩ = (|0⟩ + e^{iφ}|1⟩)/√2
φ = 0    → Identity
φ = π/4  → T gate
φ = π/2  → S gate
φ = π    → Z gate

Fidelity between the current state and a target gate's exact angle φ_t is F = cos²((φ−φ_t)/2) — it equals 1.0 only when the phase shifter is calibrated to the exact angle. Any miscalibration doesn't fail randomly: it silently implements a different, well-defined (but wrong) gate, which is why real photonic and superconducting phase shifters need sub-degree precision.

φ slider — the continuous phase shift applied by the device; drag it to see the state sweep smoothly around the equator.
Quick-jump buttons — snap exactly to the four named special angles.
Target gate — pick the gate you're trying to calibrate the shifter to implement.
Fidelity readout — how close the current φ is to the target's exact required angle; 100% only at an exact match.

State vector |ψ⟩ Equator (all φ) Target angle Named gate markers

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