How do I simulate a roller-coaster loop?

Open this page and use the live Qubit Playground tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive a roller-coaster loop from your own measurements.

Use case · powered by Qubit Playground

Qubit Playground for a roller-coaster loop

Simulate a roller-coaster loop live in your browser. This runs the real Qubit Playground solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

For:Students Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders

Bloch Sphere

open full solver →

Bloch SphereLive

the state of a qubit

Controls

Presets

Polar angle θ (°)

Azimuth φ (°)

Every pure state of a single qubit is a point on the Bloch sphere. The north pole is |0⟩, the south |1⟩, and the equator holds equal superpositions differing only in phase φ. Quantum gates rotate this arrow — the geometric picture behind all single-qubit quantum computing.

▶ Run in Python

Data Inspector

P(|0⟩)0.750

P(|1⟩)0.250

Amplitude α0.866

Amplitude β0.50∠45°

Governing equation

∣ ψ ⟩ = cos \frac{θ}{2} ∣0 ⟩ + e^{i ϕ} sin \frac{θ}{2} ∣1 ⟩ = 0.87 ∣0 ⟩ + e^{i (4 5^{\circ})} 0.50 ∣1 ⟩

Reading this result: Polar angle θ sets the measurement odds: P(|0⟩)=cos²(θ/2)=0.75, so tilting toward a pole biases the qubit while φ only twists its phase.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

↓

Stern Gerlach

open full solver →

Stern-Gerlach ExperimentLive

spin measurement & projection

Controls

Presets

Analyzer angle θ (°)

Speed1×

Atoms prepared spin-up are measured along an axis tilted by θ. Quantum mechanics says each atom randomly comes out up or down, with probability cos²(θ/2) for up — never a fraction. At 90° it is a perfect coin flip; at 180° it always flips. The running tally converges to the Born-rule probability.

▶ Run in Python

Data Inspector

P(up) theory0.750

Measured up0.0%

Atoms1

Governing equation

P (↑) = cos^{2} \frac{θ}{2} = 0.750, P (↓) = sin^{2} \frac{θ}{2} = 0.250, θ = 6 0^{\circ}

Reading this result: Tilted by 60°, the analyzer still favors up: theory predicts P(up) = cos²(θ/2) ≈ 0.75, and the tally converges there.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

About this simulation

The full Qubit Playground tool models a roller-coaster loop with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

More you can do with Qubit Playground

Qubit Playground for a projectile from a cannon Qubit Playground for a bouncing ball Qubit Playground for a pendulum clock Qubit Playground for a car braking Qubit Playground for a satellite orbit Qubit Playground for a mass on a spring Qubit Playground for a skydiver's free fall Qubit Playground for a two-cart collision

Other ways to simulate a roller-coaster loop

Particle / N-Body for a roller-coaster loop Heat & Wave Fields for a roller-coaster loop GPU Compute (WebGPU) for a roller-coaster loop WebGPU Fluid for a roller-coaster loop GPU N-Body for a roller-coaster loop GPU PDE Solver for a roller-coaster loop

Frequently asked questions

How do I simulate a roller-coaster loop?: Open this page and use the live Qubit Playground tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive a roller-coaster loop from your own measurements.