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Quantum PCA for Gene-Expression Data — 2D Rotatable Projection

Interactive 2D simulator: drag to rotate a projected gene-expression sample cloud as classical power-iteration PCA converges on its principal axes, while a real quantum-phase-estimation histogram (the Nielsen-Chuang Dirichlet-kernel formula) resolves the same eigenvalue alongside it.

Computational Biology & Quantum Computing2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version

A cohort of simulated gene-expression samples is generated with a tunable correlation between three marker genes, then reduced two ways side by side. Classically, power iteration on the empirical covariance matrix converges to the principal axes, drawn as rods through a hand-rotated projection of the 3-gene point cloud — drag the view to inspect it from any angle. Quantum Principal Component Analysis instead treats that covariance matrix as a density operator and recovers its eigenvalues through Quantum Phase Estimation — the histogram panel computes the real QPE measurement-outcome distribution (the Dirichlet-kernel formula from Nielsen & Chuang) for the dominant eigenvalue, so raising the ancilla-qubit count visibly sharpens the estimate exactly as it would on real quantum hardware.

⚙ Under the hood

Drag to rotate a hand-projected gene-expression sample cloud as classical power-iteration PCA converges on its principal axes, while a real quantum-phase-estimation histogram (the Nielsen-Chuang Dirichlet-kernel formula) resolves the same eigenvalue alongside it — all rendered on a plain 2D canvas.

Quantum ComputingBioinformaticsPCAPhase EstimationGenomics2D Canvas

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install