More than a strange coin
A qubit is described by probability amplitudes for measurement outcomes. These amplitudes can have relative phase, a relationship that ordinary probabilities alone do not capture. An appropriate circuit can make contributions reinforce or cancel. This interference is central to quantum computation. A useful quantum algorithm must arrange those relationships; merely having a superposition does not reveal every possible answer.
Three operations, one revealing experiment
Our idealised circuit begins in state |0⟩. A Hadamard operation creates an equal superposition. A phase operation changes the relative phase by φ, and a second Hadamard combines the amplitudes. Measuring then gives P(0) = cos²(φ/2) and P(1) = sin²(φ/2). The slider uses degrees, converted to radians inside the calculation. These probabilities always sum to one.
What changes when the phase changes?
At 0°, the two Hadamard operations undo one another and outcome 0 is certain in this ideal model. At 180°, outcome 1 is certain. At 90°, both outcomes have probability 50%. The bars describe repeated preparations and measurements of the same circuit; they are not a forecast of an individual random outcome. The phase is not itself a directly visible colour or a mechanical angle of a physical arrow.
Where the wonder meets the engineering
Real quantum devices introduce noise and unwanted interactions with their environment. Useful computation needs controlled operations and ways to manage errors. Quantum machines are not universally faster replacements for ordinary computers: an advantage depends on the problem, algorithm and hardware. This single-qubit demonstration illustrates interference, not entanglement, an entire quantum algorithm or a claim of practical speed-up. The smooth curves are exact mathematics for an ideal circuit; hardware results need experiments and uncertainty estimates.
Sources & further reading
Sources checked 14 November 2026. Educational models are labelled with their assumptions. These organisations do not endorse this website.