DIRECTORY / SANDBOXES / QUANTUM-WALK.HADAMARD

1D QUANTUM RANDOM WALK

Hadamard coin operator, unitary state evolution, and ballistic quantum wave propagation.

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QUANTUM WALK LATTICE

// QUANTUM COIN MATRIX (Ĥ)

TIME STEPS (t) 0

SPREADING VELOCITY: O(t) Ballistic

PROBABILITY SUM (Σ|ψ|²): 1.0000

CLICK CANVAS: Wavefunction Collapse (Observation) | CYAN PEAKS: Constructive Interference | DASHED: Classical Binomial

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RESEARCH & LEARNING VAULT // Quantum Random Walk & Wavefunction Superposition

Hadamard coin operator, quantum interference peaks, and click-to-measure wavefunction collapse.

ACADEMIC & ALGORITHMIC REFERENCE

// HISTORICAL ORIGINS

Introduced by Aharonov, Davidovich, and Zagury in 1993, quantum walks demonstrate quadratic speedup over classical random walks and form the foundation for quantum search algorithms.

// GOVERNING EQUATIONS

\hat{H} = \frac{1}{\sqrt{2}}\begin{pmatrix}1 & 1 \\ 1 & -1\end{pmatrix}, \quad \psi(x, t) = \begin{pmatrix}\alpha_x \\ \beta_x\end{pmatrix}, \quad P(x) = |\alpha_x|^2 + |\beta_x|^2, \quad \sigma \sim O(t)

// BROWSER IMPLEMENTATION

Maintains complex probability amplitudes for Left and Right chiral spins across a 201-site lattice. Applies unitary coin operations and spatial shift operators, producing constructive interference wavefronts.

// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOX

1Quantum Wavefront Observation

🎯 Action:Let the quantum walk evolve to t=40, then click anywhere on the canvas.

✨ Observe:The multi-peaked interference wave collapses instantly into a single classical particle position with a Geiger counter click.

// CURATED PAPERS, RFCS & RESOURCES

Quantum Random Walkspaper

By Y. Aharonov, L. Davidovich, & N. Zagury (Phys. Rev. A, 1993)

The seminal paper introducing discrete-time quantum random walks in quantum optics.