Interactive Quantum Simulations with TypeScript
Bell State Creator
Create and measure maximally entangled two-qubit Bell states.
Bell states are maximally entangled pure states of two qubits.
State Vector:
Entanglement Entropy:
Measurement Probabilities:
$$|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$$
Quantum Gate Visualizer
Apply quantum gates and observe state transformations.
Pauli gates, Hadamard, Phase gates transform quantum states.
Result State:
Amplitudes:
$$\sigma_X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, \quad H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$$
Entanglement Analysis
Analyze entanglement using information theory functions.
Comprehensive entanglement analysis using entropy, concurrence, and negativity.
Entanglement Entropy:
Concurrence:
Negativity:
Type:
$$S(\rho) = -\text{Tr}(\rho \log_2 \rho)$$
Multi-Qubit States
Generate GHZ and W states for multi-particle entanglement.
GHZ and W states demonstrate multi-particle entanglement patterns.
State Vector:
Components:
Dimension:
Norm:
$$|\text{GHZ}_n\rangle = \frac{1}{\sqrt{2}}(|0\rangle^{\otimes n} + |1\rangle^{\otimes n})$$
Angular Momentum States
Create spin states using angular momentum operators.
Eigenstates of the angular momentum operators with definite eigenvalues.
State |j,m⟩:
Jz eigenvalue:
J² eigenvalue:
$$J_z |j,m\rangle = \hbar m |j,m\rangle, \quad J^2 |j,m\rangle = \hbar^2 j(j+1) |j,m\rangle$$
1D Quantum Random Walk
Simulate a quantum particle on a 1D lattice using a Hadamard coin operator. Observe quantum spreading behavior through step-by-step evolution.
A quantum random walk combines coin flips (coin operator) with conditional position shifts. Unlike classical walks with peaked distributions, quantum walks show interference and spread faster across the lattice.
(5-31, odd numbers work best)
Current Step:
0
Total Probability:
1.0000
Center of Mass:
—
Variance:
0.0000
Max Probability:
—
Spread Width:
—
Position Distribution:
$$|\psi(t+1)\rangle = S(C \otimes I)|\psi(t)\rangle$$
Quantum Circuit Simulator
Build quantum circuits using Hadamard and CNOT gates.
Create Bell states from computational basis using quantum circuits.
Circuit Steps:
$$|\psi\rangle = \text{CNOT} \cdot (H \otimes I) |00\rangle$$
Quantum Fidelity Analyzer
Compare quantum states using inner product and fidelity.
Quantify overlap and similarity between quantum states.
Fidelity:
⟨ψ|φ⟩:
$$F(\psi, \phi) = |\langle\psi|\phi\rangle|^2$$