Hadamard
1/√2 × [ 1 1 ; 1 −1 ]Mixes both amplitudes. Applying it twice is the identity.
Check the numbersQBIT / Technical explorationsClassical simulation · Real mathematics
Beyond the basics
Quantum technology.
Look beneath the signal. Follow amplitudes through interference, trace a rotation, and inspect the operators that change a qubit.
01 / Paths & phase
Same odds. Different futures.
A sign can change everything.
Interference bench
q₀ |0⟩H→ ψ
H splits the amplitude evenly. Either measurement outcome has a 50% chance.
H|0⟩ = (|0⟩ + |1⟩)/√2Computed stateIdeal / noiseless
0.7071 |0⟩
+ 0.7071 |1⟩
| 0 ⟩50.00 %
| 1 ⟩50.00 %
02 / Continuous control
A state, through every angle.
From a certain zero to a certain one.
Rotation sweep
P(0) = cos²(θ/2) · P(1) = sin²(θ/2)Ry( 60 °)|0⟩Live
0.8660 |0⟩
+ 0.5000 |1⟩
| 0 ⟩75.00 %
| 1 ⟩25.00 %
The angle changes amplitudes continuously. A full turn gives −|0⟩: the sign changes, but the measurement probabilities return to their starting values.
03 / The operators
Gates are linear algebra.
Rows separated by “;”. Angles in radians.
Pauli X
[ 0 1 ; 1 0 ]Swaps |0⟩ and |1⟩ amplitudes — a bit flip.
Check the numbersPauli Z
[ 1 0 ; 0 −1 ]Negates the |1⟩ amplitude — a phase flip.
Check the numbersY rotation
[ cos(θ/2) −sin(θ/2) ; sin(θ/2) cos(θ/2) ]Continuously rotates a state using an angle θ.
Check the numbers04 / Inside the engine
No black box.
A small system with exact rules.
Complex amplitudes
Each state stores real and imaginary parts for α and β. Measurement probabilities use |α|² and |β|², not just their real parts.
Unitary evolution
H, X, Z and Ry preserve the total probability. Gate order matters: the same ingredients can produce different final states.
Local computation
These experiments run in your browser on classical hardware. They model one ideal qubit, without physical noise or a connection to quantum hardware.
Keep exploring