The HP Lattice Model

A discretized coordinate system mapping complex 3D amino geometry directly into binary Hamiltonian penalty states.

Concept

In the Hydrophobic-Polar (HP) model, standard amino sequences are translated into binary identifiers: H for hydrophobic (e.g., Leucine, Valine) and P for polar (e.g., Arginine, Serine). The lattice mapping represents continuous molecular dynamics onto a simple cubic or tetrahedral grid, ensuring self-avoiding walks where sequence contacts provide negative energy rewards.

Penalty Systems in Quantum Circuits

When simulating the HP model inside qiskit, specific geometry rules are governed by an applied Hamiltonian:

• Turn Penalties: Prevents backtracking onto an immediately previous coordinate.
• Distance Penalties: Limits the peptide bond distances structurally to exactly 1 lattice unit.
• Contact Energies: Applies the global optimization goal by granting energy reductions every time two 'H' types occupy adjacent spatial coordinates.

Implications on VQE/QAOA Outcomes

Because the interactions are radically simplified compared to atomic-level quantum chemistry, HP algorithms on early NISQ hardware demonstrate algorithm viability rather than rendering exact real-world physics. It is purely a mathematical optimization demonstration.