Superposition

Superposition is the principle that a quantum system can be in multiple states simultaneously until measured.

Think of it like a coin spinning in the air — it's neither heads nor tails until it lands. But unlike a coin, the qubit truly IS in both states at once, not just unknown.

Example: After applying a Hadamard gate to |0⟩:

|ψ⟩ = (1/√2)|0⟩ + (1/√2)|1⟩

This means there's a 50% chance of measuring 0 and a 50% chance of measuring 1.

The Hadamard gate (H) is the most common way to create superposition:

H|0⟩ = (|0⟩ + |1⟩)/√2 → Equal superposition

H|1⟩ = (|0⟩ - |1⟩)/√2 → Equal superposition with relative phase

The matrix representation is:

H = (1/√2) × [[1, 1], [1, -1]]

Try it in the Circuit Builder! Apply H to a qubit starting in |0⟩ and observe the probabilities become 50/50.

Superposition enables quantum parallelism — the ability to process multiple inputs simultaneously.

With n qubits in superposition, you can represent 2ⁿ states at once:

• 1 qubit → 2 states

• 10 qubits → 1,024 states

• 50 qubits → over 1 quadrillion states!

This exponential scaling is what gives quantum computers their potential advantage over classical computers for certain problems.