This simulator places a classical bit and a qubit side by side. Flip the classical bit to see its only two possible states, then dial the qubit's superposition angle and relative phase to see how much richer — and how continuous — a qubit's state space really is before measurement forces a single 0-or-1 outcome.
• A classical bit rendered as a simple 0/1 toggle with no in-between states. • A qubit rendered as a vector on the Bloch sphere, driven by a superposition-angle slider (theta) and a relative-phase slider (phi). • Live measurement-probability bars for P(0) and P(1) that track theta in real time. • An explicit |psi> = alpha|0> + beta|1> equation that updates with every slider move. • Amplitude magnitude readouts (|alpha|, |beta|) alongside the probabilities they produce.
• Flip the classical bit and note that nothing about it can ever be "a little bit 1" — only 0 or only 1. • Set theta to 90 degrees for an equal 50/50 superposition, then sweep phi from 0 to 360 degrees and confirm the probability bars never move — phase alone is invisible to this measurement. • Set theta to 0 or 180 degrees to recover the two classical-looking basis states |0> and |1> as special cases of the qubit's general state.
Although relative phase does not change P(0) or P(1) on its own, it fixes exactly where on the equator of the Bloch sphere the state vector points. Every interference-based quantum algorithm exploits that hidden phase information by recombining amplitudes with a later gate — turning an invisible phase difference into a visible, and useful, probability difference, as the Quantum Phase and Quantum Interference labs demonstrate directly.
A classical bit always has a definite value, 0 or 1, with nothing in between. A qubit's state is described by two complex amplitudes and can be any point on the Bloch sphere — a genuine superposition — until it is measured, at which point it randomly collapses to 0 or 1 with probabilities set by those amplitudes.
Not on its own. A single measurement in the computational basis only reads out |alpha|^2 and |beta|^2, so relative phase alone does not change P(0) or P(1). Phase becomes measurable once the qubit passes through another gate that recombines the amplitudes, as later interference labs show.
A single qubit still only yields one classical bit of information when measured — you cannot read out its continuous amplitudes directly. Its advantage comes from how many qubits can be combined and manipulated together before that one measurement, not from squeezing extra bits out of one qubit.
It models a single, isolated, noise-free qubit with instantaneous, ideal gates. Real qubits are subject to decoherence, gate errors and measurement noise that this idealized teaching model does not simulate.