Interactive Bloch Sphere Simulator for Quantum States
Explore single-qubit states and understand quantum rotations through interactive Bloch sphere visualization and circuit experiments.
Intuitive 3D State Exploration
Rotate the Bloch sphere in three dimensions. Inspect state vector coordinates (x, y, z) and polar angles θ and φ in real time.
Interactive Gate Rotations
Apply Pauli X, Y, Z, Hadamard, and Phase gates to see how the state vector orbits the sphere around specific axes.
Pure State Coordinates
Connect mathematical Dirac notation |ψ⟩ = cos(θ/2)|0⟩ + e^(iφ)sin(θ/2)|1⟩ directly to visual geometric coordinates on the sphere surface.
|0⟩ (θ = 0, z = +1)
│
│
|-i⟩ ───────────┼─────────── |+i⟩ (Y-axis)
│
╱ ╲
╱ ╲
|-⟩ ─────────┼─────╲────── |+⟩ (X-axis, θ = π/2, φ = 0)
╱ ╲
│ │
│ │
│
│
|1⟩ (θ = π, z = -1)
State Vector: |ψ⟩ = cos(θ/2)|0⟩ + e^(iφ) sin(θ/2)|1⟩
Bloch Vector: r = (sin θ cos φ, sin θ sin φ, cos θ)
Frequently Asked Questions
What is a Bloch sphere?
The Bloch sphere is a geometric representation of the two-dimensional state space of a single qubit, where every pure quantum state corresponds to a point on the unit sphere.
Can a Bloch sphere represent two entangled qubits?
No. Entangled states like Bell states cannot be fully represented on individual Bloch spheres because their state lives in an entangled 4-dimensional Hilbert space. In Quortup, multi-qubit systems are represented by both individual reduced Bloch spheres and the full statevector amplitude spectrum.