Superposition

A quantum system existing in multiple states simultaneously until measured.

Superposition is perhaps the most famous feature of quantum mechanics. A quantum system in superposition is not in one definite state but rather in a combination of multiple possible states at once.

The Concept

Consider a qubit. Classically, a bit is either 0 or 1. A qubit in superposition is both 0 and 1 simultaneously:

$$|\psi ⟩=\alpha |0⟩+\beta |1⟩$$

This is not the same as:

• Being 0 or 1 but we don’t know which (that’s classical uncertainty)
• Switching rapidly between 0 and 1
• Being “kind of” 0 and “kind of” 1

Superposition is genuinely being in multiple states at once, a distinctly quantum phenomenon with no classical analog.

Measurement and Collapse

When you measure a qubit in superposition, you get a definite result:

• $|0⟩$ with probability $|\alpha {|}^2$
• $|1⟩$ with probability $|\beta {|}^2$

After measurement, the superposition is destroyed. The qubit is now in the measured state. This is called wavefunction collapse or state collapse.

Creating Superposition

The most common way to create superposition is with the Hadamard gate:

$$H|0⟩=\frac{1}{\sqrt{2}}(|0⟩+|1⟩)=|+⟩$$

This takes a qubit in state $|0⟩$ and puts it in an equal superposition.

Multi-Qubit Superposition

With $n$ qubits, you can create superposition over $2^n$ states:

$$|\psi ⟩=\sum _{x=0}^{2^n-1}{\alpha }_x|x⟩$$

For example, 3 qubits can be in superposition over 8 states (000, 001, 010, 011, 100, 101, 110, 111) simultaneously.

This is often called quantum parallelism, but be careful! You can’t simply “read out” all $2^n$ values. Measurement gives you just one result.

Why It Matters

Superposition is essential for:

• Quantum parallelism: Processing multiple possibilities simultaneously
• Quantum interference: Making wrong answers cancel out (see Interference)
• Quantum speedups: Algorithms like Grover’s exploit superposition

Common Misconception

Superposition ≠ randomness. A qubit in state $|0⟩$ is not in superposition. It will definitely measure as 0. A qubit in superposition has specific amplitudes that determine measurement probabilities and can interfere with other amplitudes.

See also: Qubit, Hadamard Gate, Measurement, Quantum Parallelism