Interactive Laboratory

QUANTUMLAB

Experience quantum mechanics through interactive visualizations. Manipulate qubits, build quantum circuits, and explore quantum phenomena in real-time.

Choose Experiment

Quantum Superposition

Superposition Balance

50:50

Wave Function Visualization

Qubit exists in superposition of both states simultaneously

|0⟩

|1⟩

Measurement Probabilities

|0⟩ Probability

50%

|1⟩ Probability

50%

Current State

|ψ⟩ = 0.707|0⟩ + 0.707|1⟩

Superposition: Before measurement, the qubit exists in both states simultaneously. The wave functions represent the probability amplitudes.

Measurement: Observing the qubit collapses the wave function to a definite state (|0⟩ or |1⟩) according to the probability distribution.

Understanding

QUANTUMMECHANICS

SUPERPOSITION

Quantum superposition allows a qubit to exist in multiple states simultaneously until measured. The wave function represents probability amplitudes for each possible state.

Wave Function: Describes quantum state probability distribution

Collapse: Measurement forces definite state (|0⟩ or |1⟩)

Probability: Determined by amplitude squared (|ψ|²)

Interference: Wave functions can constructively or destructively combine

QUANTUM GATES

Quantum gates manipulate qubits through unitary transformations. Unlike classical gates, quantum gates are reversible and can create superposition and entanglement.

Hadamard (H): Creates superposition from |0⟩ or |1⟩

Pauli-X: Quantum NOT gate, flips |0⟩ ↔ |1⟩

Pauli-Z: Phase flip gate, changes sign of |1⟩

CNOT: Two-qubit gate for creating entanglement

KEYCONCEPTS

Superposition

|ψ⟩ = α|0⟩ + β|1⟩

A qubit can exist in a linear combination of basis states simultaneously. The amplitudes α and β are complex numbers satisfying |α|² + |β|² = 1.

Measurement

P(0) = |α|²  •  P(1) = |β|²

Measuring a qubit collapses its superposition to either |0⟩ or |1⟩. The probability of each outcome is given by the squared magnitude of its amplitude.

Entanglement

|ψ⟩ = (|00⟩ + |11⟩) / √2

Two or more qubits become correlated in ways impossible classically. Measuring one qubit instantaneously affects the others, regardless of distance.