Two-Qubit CNOT Gate Visualizer

Initial Two-Qubit State

Define the initial state of your two-qubit system. This is a 4-dimensional complex vector:

$|\psi\rangle = \alpha_{00}|00\rangle + \alpha_{01}|01\rangle + \alpha_{10}|10\rangle + \alpha_{11}|11\rangle$

Remember that the sum of the squares of the magnitudes of all amplitudes must be 1: $|\alpha_{00}|^2 + |\alpha_{01}|^2 + |\alpha_{10}|^2 + |\alpha_{11}|^2 = 1$.

A common starting point for entanglement is the state $|+\rangle|0\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |10\rangle)$, which is set as the default.

α₀₀ Real Part:

α₀₀ Imaginary Part:

α₀₁ Real Part:

α₀₁ Imaginary Part:

α₁₀ Real Part:

α₁₀ Imaginary Part:

α₁₁ Real Part:

α₁₁ Imaginary Part:

Apply CNOT Gate

The **CNOT (Controlled-NOT) gate** flips the target qubit if the control qubit is $|1\rangle$. If the control is $|0\rangle$, the target remains unchanged.

This gate is essential for creating **entanglement**.

Control Qubit:

Target Qubit:

Quantum Circuit Diagram

Qubit 1: |0> --- Qubit 2: |0> ---

Resulting Two-Qubit State

Complex Amplitudes:

α₀₀:

α₀₁:

α₁₀:

α₁₁:

Measurement Probabilities:

P(|00⟩):

P(|01⟩):

P(|10⟩):

P(|11⟩):

The **complex amplitudes** show the full quantum state, including phase information crucial for entanglement.

The **measurement probabilities** tell you the likelihood of observing each classical outcome when you measure the qubits.