Classical computers store information in bits that are always either 0 or 1. A quantum computer stores information in qubits, and a qubit's state is a superposition - a weighted combination of 0 and 1 described by two complex amplitudes. That single change ripples through everything: how information is processed, what "reading a value" means, and which problems become easier.
Superposition is arithmetic, not mystery
A qubit state can be written as α|0⟩ + β|1⟩, where |α|² + |β|² = 1. The amplitudes α and β are not probabilities themselves - they can interfere, cancel, and reinforce like waves. Probabilities only appear when you measure. You can build this intuition directly in the interactive lab's superposition panel, where amplitude and phase sliders show how a state vector becomes measurement statistics.
Gates are rotations
Quantum logic gates are unitary operations - reversible rotations of the state. A useful mental picture for one qubit is the Bloch sphere: every pure state is a point on a sphere, and every gate is a rotation of that sphere. The Hadamard gate takes |0⟩ to an equal superposition; the phase gates rotate around the vertical axis. The quantum computers page walks through the standard gate set with 3D visualizations.
Measurement collapses the story
Measurement is the only non-reversible step. Measuring a qubit along an axis returns a definite 0 or 1 with probabilities set by the amplitudes, and afterwards the state is whatever you observed. This is why quantum algorithms are choreographed so that wrong answers interfere destructively before anyone looks.
Entanglement: correlations with no classical explanation
Two qubits can be placed in a state such as the Bell state (|00⟩ + |11⟩)/√2, which cannot be described as "qubit A has some state and qubit B has some state." Measurement outcomes on the two qubits are correlated more strongly than any local hidden-variable model allows - that is the content of Bell inequality violations. The entanglement panel lets you rotate analyzer angles and watch the correlation curve depart from the classical bound.
Where the speedups come from
Quantum computers are not "trying all answers at once." Algorithms like Shor's factoring and Grover's search exploit interference and structure: they arrange amplitudes so that correct answers add up and incorrect ones cancel. That works only for problems with the right structure, which is why quantum advantage is domain-specific - simulation of quantum systems, certain algebraic problems, and some optimization and sampling tasks.
Keep going
- Study the formal backbone in the theory library - states, operators, and measurement.
- Run the lab panels for superposition, entanglement, and teleportation.
- Check the qubit state calculator to convert between amplitudes, angles, and probabilities.