Single-qubit gates are reversible transformations, and the Bloch sphere gives you a geometric picture of how they move a qubit's state.
The Bloch sphere is one of the fastest ways to see the difference between a basis flip (X gate), a phase rotation (Z or S gate), and the loss of purity caused by entanglement (state moves inside the sphere).
The Bloch sphere turns an abstract quantum state into a direction you can see. Every pure single-qubit state maps to a point on the surface of a sphere. The north pole is , the south pole is , and the equator represents equal superpositions with different phases. Applying a gate moves this point to a new location on the sphere. This visual picture makes it much easier to understand what each gate does.
sits at the north pole and at the south pole. The Hadamard gate () moves to an equatorial point (an equal superposition). The Z gate rotates the state around the vertical axis, changing the phase without moving it toward or away from the poles. Try this in the simulator -- the Bloch sphere panel shows exactly these movements.
Pure one-qubit states can be represented as points on the surface of the Bloch sphere. The coordinates (bx, by, bz) encode both the amplitude balance and the relative phase. Gates such as X, Z, and H correspond to rotations or reflections on this sphere. When a qubit is entangled with other qubits, its individual state may appear inside the sphere rather than on the surface -- this means some of its information is shared with the other qubits.
Open the simulator and see this concept in action. Watch how the state changes and compare it to what you just learned.
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