Superposition
Superposition is the ability of a quantum system to be in a weighted combination of multiple basis states simultaneously, with complex amplitudes.
The principle
Quantum mechanics is linear: if |0> and |1> are valid states of a system, then so is any normalised combination a|0> + b|1>. This is superposition. It is a direct consequence of states living in a linear vector space where the equation of motion is linear.
Superposition is not ignorance about which state the system is really in. A qubit in (|0> + |1>)/sqrt(2) is not secretly 0 or 1; it is genuinely in both, and this can be demonstrated experimentally through interference effects that a hidden definite value cannot reproduce.
Amplitudes, not probabilities
The coefficients a and b are complex amplitudes. Probabilities are their squared magnitudes, |a|^2 and |b|^2. Because amplitudes are complex and can be negative or imaginary, two paths leading to the same outcome can cancel — destructive interference — something probabilities alone can never do. This is the essential difference from a classical probabilistic bit.
Creating superposition
Applying a Hadamard gate to |0> produces (|0> + |1>)/sqrt(2), an equal superposition. Applying it again returns exactly |0>, because the two amplitude paths to |1> cancel while the paths to |0> add. Running the same operation twice recovering the input is a signature of interference at work.
- Equal superposition: (|0> + |1>)/sqrt(2)
- Weighted: 0.8|0> + 0.6|1> (probabilities 0.64 and 0.36)
- Complex phase: (|0> + i|1>)/sqrt(2)
Fragility
Superposition is delicate. Uncontrolled interaction with the environment leaks phase information and destroys the coherent combination, a process called decoherence. Protecting superposition long enough to compute is one of the central engineering problems of quantum hardware, and it is the reason qubit coherence times are a headline specification.