VQE molecular ground state energy and materials simulation

Quantum computers can simulate quantum systems exponentially faster than classical computers for chemistry problems. The Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE) algorithms on QCOS enable molecular energy calculation, drug docking simulation, and materials discovery without classical exponential memory limits.

Why Quantum Chemistry?

Classical computers represent N-electron wave functions as 2ᴺ-dimensional vectors (memory scales exponentially with electron count), making exact simulation of molecules with more than ~50 electrons impossible. Quantum computers naturally encode quantum states, making them exponentially more efficient.

Molecule / System	Classical limit	QCOS Quantum Approach
H₂ (hydrogen)	Exact (2 electrons)	Benchmark / verification
LiH (lithium hydride)	FCI up to ~10 electrons	VQE on simulator
N₂ (nitrogen)	CCSD(T) approximation	VQE on cloud QPU
FeMo-co (nitrogenase)	Intractable	Target for fault-tolerant QC
Drug binding site	Classical MM/GBSA	Hybrid QM/MM with VQE

H₂ Ground State Energy (VQE)

Background

The hydrogen molecule is the canonical quantum chemistry benchmark. The second-quantized molecular Hamiltonian is:

H = Σ_p h_p a†_p a_p  +  Σ_pq h_pq a†_p a_q  +  ½ Σ_pqrs h_pqrs a†_p a†_q a_r a_s

is mapped to qubit operators via Jordan-Wigner or Bravyi-Kitaev transformations.

Python Example — H₂ VQE

import os
import time
import requests

API_KEY = os.environ["QCOS_API_KEY"]
BASE_URL = "https://api.softquantus.com"
HEADERS = {"Authorization": f"Bearer {API_KEY}", "Content-Type": "application/json"}

# Bond lengths to sweep (Ångströms)
bond_lengths = [0.5, 0.6, 0.7, 0.74, 0.8, 0.9, 1.0, 1.2, 1.5, 2.0]
energies = []

for r_angstrom in bond_lengths:
    resp = requests.post(
        f"{BASE_URL}/api/v1/algorithms/vqe",
        headers=HEADERS,
        json={
            "molecule": {
                "formula": "H2",
                "geometry": [
                    {"atom": "H", "x": 0.0, "y": 0.0, "z": 0.0},
                    {"atom": "H", "x": 0.0, "y": 0.0, "z": r_angstrom}
                ],
                "basis": "sto-3g",
                "charge": 0,
                "spin_multiplicity": 1
            },
            "backend": "statevector_simulator",
            "shots": 8192,
            "ansatz": "UCCSD",
            "optimizer": "COBYLA",
            "max_iterations": 150
        }
    )
    resp.raise_for_status()
    job_id = resp.json()["job_id"]

    # Poll
    while True:
        r = requests.get(f"{BASE_URL}/api/v1/jobs/{job_id}", headers=HEADERS).json()
        if r["status"] in ("completed", "failed"):
            break
        time.sleep(3)

    energy = r["result"]["ground_state_energy_hartree"]
    energies.append((r_angstrom, energy))
    print(f"  r = {r_angstrom:.2f} Å → E = {energy:.6f} Hartree")

# Find equilibrium geometry
eq = min(energies, key=lambda x: x[1])
print(f"\nEquilibrium bond length: {eq[0]:.2f} Å")
print(f"Ground state energy:     {eq[1]:.6f} Hartree")
print(f"Dissociation energy:     {energies[-1][1] - eq[1]:.6f} Hartree")

Drug-Receptor Docking (Hybrid QM/MM)

For pharmaceutical applications, QCOS supports hybrid quantum-classical simulations:

Quantum region (QM): Active site + drug molecule (VQE)
Classical region (MM): Protein scaffold (force fields)

# Submit drug-receptor docking
resp = requests.post(
    f"{BASE_URL}/api/v1/algorithms/vqe",
    headers=HEADERS,
    json={
        "problem_type": "drug_docking",
        "receptor_pdb": "7JU3",          # PDB ID or inline PDB string
        "ligand_smiles": "CC(=O)OC1=CC=CC=C1C(=O)O",  # Aspirin
        "binding_pocket": {
            "center": {"x": 12.4, "y": -3.2, "z": 8.1},
            "radius_angstrom": 8.0
        },
        "backend": "aws_sv1",
        "qm_electrons": 6,
        "ansatz": "hardware_efficient",
        "shots": 4096
    }
)
resp.raise_for_status()
job_id = resp.json()["job_id"]
print(f"Docking job: {job_id}")

Result includes binding energy (kcal/mol), binding pose, and comparison to classical MM/GBSA prediction.

Material Band Gap Calculation

Predict electronic band gaps for new semiconductor and battery materials:

resp = requests.post(
    f"{BASE_URL}/api/v1/algorithms/vqe",
    headers=HEADERS,
    json={
        "problem_type": "band_gap",
        "material": {
            "formula": "TiO2",
            "crystal_structure": "rutile",
            "lattice_constants": {"a": 4.594, "c": 2.958}
        },
        "backend": "statevector_simulator",
        "k_points": 4,
        "shots": 2048
    }
)

Full Chemistry Workflow

POST /api/v1/algorithms/vqe

`problem_type`	Description	Typical qubits
`molecular_energy`	Ground/excited state energies	4–30
`geometry_optimization`	Find minimum energy geometry	4–20
`reaction_pathway`	Transition states and barriers	6–24
`drug_docking`	Ligand binding energy	4–16
`band_gap`	Material electronic structure	8–32
`excited_states`	Absorption/emission spectra	4–20

Ansatz Selection Guide

Ansatz	Use when	Qubits	Depth
`UCCSD`	High accuracy needed, few qubits	4–12	Deep
`hardware_efficient`	Near-term QPU, moderate accuracy	2–20	Shallow
`ADAPT-VQE`	Balance accuracy/depth	4–16	Adaptive
`k-UpCCGSD`	Strongly correlated systems	4–14	Medium

Genomics use cases — VQE for protein structure prediction
Add a GPU and run quantum simulations on it — larger molecular simulations
Using QCOS: run quantum circuits end to end — submit a VQE job through the runtime API

​Why Quantum Chemistry?

​H₂ Ground State Energy (VQE)

​Background

​Python Example — H₂ VQE

​Drug-Receptor Docking (Hybrid QM/MM)

​Material Band Gap Calculation

​Full Chemistry Workflow

​Ansatz Selection Guide

​Related