Understand
Quantum Mechanics
one step at a time.

Classical computers store information as bits — tiny switches that are either off (0) or on (1). Quantum computers use qubits, which can be in a blend of both states at once. Quantum Lab lets you see, manipulate, and measure qubits in real time directly in your browser.

Every module is self-contained. You don't need to complete them in order — dip in wherever your curiosity takes you.

Quantum Lab runs entirely in your browser — nothing to install. Here's the fastest path from zero to your first quantum state.

A qubit (quantum bit) is the basic unit of quantum information. Unlike a classical bit that is strictly 0 or 1, a qubit exists as a combination of both until it's measured.

Mathematically, we write a qubit state as a superposition:

Here α and β are complex amplitudes. Their squared magnitudes — |α|² and |β|² — give the probability of each outcome and always sum to 1.

Superposition is often described as "being in two states simultaneously," but more precisely: a qubit in superposition has a definite quantum state — one that doesn't correspond to a single classical outcome until measured.

Think of it like a coin spinning in the air. It's not heads and tails — it's in a well-defined spin state that will resolve to one side when it lands.

The Hadamard gate is the most common way to create superposition. Applied to |0⟩, it produces |+⟩ — a 50/50 chance of measuring either outcome.

When two qubits become entangled, their states are no longer independent. Measuring one instantly determines the outcome of measuring the other — no matter how far apart they are. Einstein famously called this "spooky action at a distance."

The maximally entangled two-qubit states are called Bell states. The most common, |Φ⁺⟩, reads:

If you measure qubit A and get |0⟩, qubit B will always be |0⟩. The outcomes are correlated, but neither is predetermined — both happen with equal probability.

Real qubits don't stay in superposition forever. They interact with their environment — stray fields, thermal vibrations — and gradually lose their quantum properties. This is called decoherence.

T₁ (relaxation time) measures how long a qubit holds its energy before decaying from |1⟩ to |0⟩. T₂ (dephasing time) measures how long the phase of a superposition stays coherent. T₂ is always ≤ 2·T₁.

The Decoherence module lets you tune both T₁ and T₂ and watch coherence drain away in real time. The state vector spirals inward toward the center of the sphere as the qubit becomes a "mixed state."

Visualize a single qubit as a point on a unit sphere. Every pure qubit state maps to exactly one point on the surface — the north pole is |0⟩, the south pole is |1⟩, and the equator holds all equal-weight superpositions. You can also drag the arrow tip directly on the sphere to set any custom state.

Quantum gates are reversible linear transformations on qubit states — they rotate the Bloch vector. Unlike classical logic gates, every quantum gate can always be undone. This module lets you build and replay circuits of up to 8 gates on a single qubit starting from |0⟩.

This module renders two Bloch spheres side by side — Qubit A (left, green) and Qubit B (right, blue). A stream of animated particles connects the two spheres to visualise their quantum link. When the qubits are entangled, the individual Bloch vectors become undefined — only the joint two-qubit state is well-defined.

Real qubits don't hold their quantum state forever. Environmental noise causes two distinct types of decay. This module lets you tune both timescales and watch fidelity drain away in real time, with a live sparkline chart tracking the history.

Quick definitions for the terms you'll encounter throughout the lab.