Tools / Interactive models

Interactive models of quantum states

Small models that run in the browser: one qubit, then two, then three, then any number of symmetric spins. Each exposes the parameters of one construction and shows the numbers beside the drawing. Nothing you set leaves the page, and every control has a keyboard equivalent.

Available

The models

04 tools

  1. Visualizer

    Single-qubit state visualizer

    Point a qubit state on the Bloch sphere by dragging or by setting its two angles. Aim the axis of any unitary with the green axis handle, apply the named gates or a gate you build from that axis, angle and phase, measure the qubit, and read the amplitudes behind the picture.

    Explore the controls
    • Bloch sphere
    • Gates X, Y, Z, H, S, T
    • Draggable rotation axis
    • Any unitary from an axis, angle and phase
    • Measurement and collapse
    • The two amplitudes behind the picture

  2. Visualizer

    Two-qubit state visualizer

    Every vector of a two-qubit state in one complex plane: four amplitude arrows at their true lengths and angles over a heat map of the concurrence, plus the needle that measures entanglement. The same state is redrawn in Schmidt form on one Bloch sphere, where the first qubit's basis is unit length and the second qubit's vectors carry the branch amplitudes as their lengths. Stretch and turn the arrows by hand, press Normalize to restore the weights, and build a Bell state with CNOT.

    Explore the controls
    • Four amplitude vectors in one plot
    • Lengths and phases you can drag
    • One-click normalization
    • Schmidt form on one sphere
    • Concurrence needle
    • Concurrence heat-map background
    • Phase and length keys
    • CNOT, CZ and SWAP
    • Measurement of either qubit

  3. Visualizer

    Three-qubit state visualizer

    Eight amplitude arrows in one complex plane, plus the relative-state view: choose a reference qubit and the state splits into two two-qubit branches, one for each value of that qubit. Each branch is drawn in its own Schmidt bases, so one Bloch sphere carries a plane per branch, and the branch probability sets its opacity. Where the planes cross they name one shared basis; drag the sphere to orbit it.

    Explore the controls
    • Eight amplitude vectors in one plot
    • Any qubit as the reference
    • Two Schmidt planes in one sphere
    • The shared basis where the planes meet
    • Drag to orbit the sphere
    • Branch weights and Schmidt angles
    • Lengths and phases you can drag
    • CNOT, CZ and SWAP on any pair
    • Measurement of any qubit

  4. Visualizer

    Majorana constellation explorer

    A symmetric state of many qubits drawn as one point per spin on one Bloch sphere. Drag the stars, or prepare a cat, coherent, Dicke or single-excitation state, and read the amplitudes, the collective spin and the geometric measure of entanglement. The page states exactly which states the picture can and cannot describe.

    Explore the controls
    • One star per symmetric spin
    • Draggable stars on an orbitable sphere
    • Amplitudes beside the picture
    • Spin length and geometric measure
    • Cat, coherent, Dicke and single-excitation presets
    • Keyboard control of every star

Planned

In preparation

Each will follow the rule used above: one idea, every parameter exposed, and the mathematics beside the picture.

How these tools are built

Each model is a small programme that runs in the page: no account, no server, and no tracking. Where a drawing depends on a physical parameter, the static page still shows a meaningful state, and the controls always have a keyboard path — sliders for continuous values, buttons for everything else.

They are companions to the courses and the research handbook. If a model contradicts your calculation, the calculation is the arbiter.