Bloch Sphere Explorer
A single qubit has infinite possible states. The Bloch sphere maps every one of them to a point on a unit sphere — quantum gates become rotations.
What is a qubit?
A classical bit is either 0 or 1. A qubit exists in a superposition of
both simultaneously: |ψ⟩ = α|0⟩ + β|1⟩, where
α and β are complex numbers satisfying
|α|² + |β|² = 1. When you measure a qubit, it
collapses — you get |0⟩ with probability |α|² or |1⟩ with
probability |β|². Before measurement, the qubit carries far more
information than a classical bit.
The Bloch sphere
Because the global phase of a qubit is physically unobservable, every
single-qubit state can be parameterized by just two angles:
|ψ⟩ = cos(θ/2)|0⟩ + eiφsin(θ/2)|1⟩.
This maps each state to a unique point on the surface of a unit sphere.
The north pole is |0⟩, the south pole is |1⟩, and the equator holds
equal superpositions like |+⟩ and |−⟩. Orthogonal quantum states
are antipodal — on opposite sides of the sphere.
Quantum gates as rotations
Single-qubit quantum gates correspond to rotations of the Bloch sphere. The X gate (quantum NOT) rotates π around the x-axis, flipping |0⟩ to |1⟩. The Hadamard gate H rotates π around the diagonal axis between x and z, turning |0⟩ into the superposition |+⟩. The T gate performs a small π/4 rotation around z — a subtle phase shift that is one of the key ingredients for universal quantum computation. Try applying gates above to build intuition for how they transform states.
Quantum Computing for Computer Scientists
Microsoft Research talk by Andrew Helwer. The clearest introduction to quantum computing fundamentals for people who already know how to code.