Quantum Synth
Hear the H₂ Molecule
The simplest molecule. Two protons, two electrons, one covalent bond. Each energy level becomes a harmonic partial. Stretch the bond and hear the spectrum shift.
Thermal weighting (Ha)
Ground state pitch
Harmonic spacing
Harmonic Layers
How It Works
Energy → Frequency
Each energy eigenvalue of H₂ maps to an oscillator. The gap from ground state sets the pitch: f = 65 × 2⁻ΔE/1.2. These are the same transitions spectroscopists measure with light — now mapped to sound.
Boltzmann Weighting
Amplitude follows a thermal distribution: a = e⁻ΔE/kT. Low excitation emphasizes the fundamental. Crank it up and all levels contribute equally — like heating the molecule.
Bond Stretching
Pull the atoms apart and listen. Near equilibrium (0.74 Å), the ground state is deepest. At dissociation, energy levels converge and the harmonic structure collapses — the sound of a bond breaking.
Technical Details
Hamiltonian: H₂ in STO-3G minimal basis, Jordan-Wigner encoding on 4 qubits (16×16 matrix).
Eigenvalues: Full diagonalization (numpy.linalg.eigvalsh) at 28 bond distances from 0.3 to 3 Å.
Degeneracies arise from symmetry: orbital angular momentum, spin. H₂ has 4 spin-orbitals giving 16 eigenvalues, typically 9-10 unique levels.
Computed with PySCF + OpenFermion. Same pipeline used for our VQE hardware experiments on Tuna-9 and IBM Quantum.