See the qubit: Bloch sphere
Connect a pure qubit's direction to measurement probabilities and relative phase.
Intuition
The Bloch sphere is a map of single-qubit states, not the physical shape of a qubit. The north pole represents |0⟩ and the south pole |1⟩. Equatorial pure states have equal computational-basis probabilities.
Change θ to move between the poles. Change φ around the equator: the amplitudes' relative phase changes while the probabilities remain 50/50. Set θ to π/2 and φ to 0 for |+⟩. The sphere represents the same state described by its statevector.
The mathematics
Look a little deeper
This expression chooses a global-phase convention. At a pole, φ does not distinguish physical states. Pure states lie on the sphere; mixed states can lie inside it. The local state of an entangled qubit need not lie on the surface.
See a single qubit
The interactive state explorer requires the quantum simulator, which is not hosted in this preview.
Use it
Explore θ and φ above, then prepare |+⟩ using one H in the circuit lab. Inspect Bloch and Statevector.
This exercise uses the same server-side state and circuit checks as its linked practice problem.
Build your circuit
Click a gate to append it, or drag it onto a wire. CX uses the selected control; SWAP uses it as the second operand. Basis order: |qₙ … q₀⟩.
Returned logical circuit · before transpilation · q0 on top
Connect to code
qc = QuantumCircuit(1) qc.h(0)
These operations go inside a circuit-building program. Practice problems provide a complete solve() template.
Check your understanding
First complete the circuit exercise successfully.