Qubi's three visualization modes

There are three main ways to visualize quantum states on Qubi. Each tells you a different part of the story.

1. Realistic mode

The first mode is the realistic mode, where only the results of measurements are shown on Qubi. This is the most important mode, since it mimics how qubits actually work: the only time you get information from a qubit is when you measure it.

State: |+⟩

2. Single-axis reveal mode

Single-axis reveal mode shows you the probabilities and correlations of the statevector, assuming your future measurements will be along the direction of gravity.

If there are two possibilities, what we call “worlds”, they are colored differently. Here are a few examples.

Which axis do we choose? We have two options:

Fix the axis to always be the computational basis (the |0⟩ / |1⟩ axis).
Choose the axis for each sphere that aligns to gravity. This lets you move the spheres around to analyze the statevector along any axis you like, just by rotating the Qubis.

Single-qubit states

State: |0⟩

Single qubit in |0⟩. There's only one possibility: it's measured up.

State: 1/√2 |0⟩ + 1/√2 |1⟩

A single qubit in equal superposition. Two possibilities, colored differently.

Two-qubit states

State: 1/√2 |00⟩ + 1/√2 |11⟩

qubit A

qubit B

A two-qubit Bell state in single-axis reveal mode. Two correlated worlds, up-up and down-down, share the same color across the spheres.

Three-qubit states

State: 1/√2 |000⟩ + 1/√2 |111⟩

qubit 1

qubit 2

qubit 3

A GHZ state on three qubits. Two possibilities, up-up-up and down-down-down, made very clear by colors that match across all three spheres.

State: 0.88 |000⟩ + 0.47 |111⟩

qubit 1

qubit 2

qubit 3

A modified GHZ state where up-up-up is much more likely than down-down-down. The red world is brighter than the blue world. Brightness corresponds to probability.

Overlapping worlds

What happens when two worlds point in the same direction on a qubit? Take the state |00⟩ + |01⟩ + |10⟩ + |11⟩ (= |+⟩|+⟩, normalized): the up state on qubit A is part of two worlds: |00⟩ and |01⟩. The down state is also part of two: |10⟩ and |11⟩. So when we anchor both spheres to gravity, each pole on each sphere has two worlds piled on top of each other.

In single-axis reveal mode, those overlapping lobes blend in a time-varying ripple. You see one color sweep across, then the other.

State: 1/2 |00⟩ + 1/2 |01⟩ + 1/2 |10⟩ + 1/2 |11⟩

qubit A · z-anchored

qubit B · z-anchored

|+⟩|+⟩ with both qubits anchored to z. World 00 (red) and world 01 (yellow-green) both put sphere A at |0⟩, so they overlap at +z. Same idea for the other pairs. Watch the colors at each pole compete in time.

3. All-axis reveal mode

All-axis reveal mode shows you the probabilities and correlations of the statevector for every possible measurement direction. Every direction on the sphere gets a unique hue, and the spheres' surfaces hue-match wherever the qubits are correlated.

Notice that the same colors sit at the top of both qubits, and the same colors sit at the bottom. That tells us that if we measure along the Z axis, we'll get the same outcomes, exactly what single-axis reveal mode shows us.

But we also get to see what would happen if we measured side-to-side, or any other direction. Every direction has its own pair of correlated colors.

Hover over the spheres to see the point on the other sphere that shares the same color.

State: 1/√2 |00⟩ + 1/√2 |11⟩

qubit A

qubit B

The same Bell state in all-axis reveal mode. Correlations now show in every direction, not just along gravity.

qubit A

qubit B

Z applied to qubit A of |+0⟩, on repeat. Watch qubit A's rainbow rotate 180° around the equator each cycle. Yet single-axis reveal mode would look identical the whole time, since the |00⟩ and |10⟩ probabilities never change. That's the relative phase that single-axis reveal misses.

For the math behind this visualizer (how every direction on each sphere gets a unique hue, and why correlated points share a color), see our whitepaper.

Try them yourself

Three ways to see a qubit. One device.

Qubi flips between all three modes with a tap in the app. Realistic for the science, single-axis reveal for the intuition, all-axis reveal when you want the full picture.

Get your model qubits Read: What is a qubit?