Bloch Sphere Explorer

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⟩ + e^(iφ)sin(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 see how each one moves the state vector.