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Quantum PCA for Gene-Expression Data

Interactive 3D quantum-PCA simulator: watch a gene-expression sample cloud collapse onto its principal axes via classical power-iteration eigen-decomposition, then see a real quantum-phase-estimation register resolve the same eigenvalue from a Dirichlet-kernel probability histogram.

Computational Biology & Quantum Computing3DAdvanced60 FPS

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 arrows through the 3D point cloud. 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

Watch a simulated gene-expression cohort reduce to its principal axes two ways at once: classical power-iteration eigen-decomposition of the covariance matrix versus a real quantum-phase-estimation register whose exact Dirichlet-kernel probability histogram sharpens onto the same eigenvalue as ancilla qubits increase.

Quantum ComputingBioinformaticsPCAPhase EstimationGenomicsThree.js

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install