HPC Tier Module
Variational Quantum Eigensolver (VQE) Simulator
Classical VQE statevector simulation of H2, validated against the exact closed-form ground-state energy.
This tool runs inside GDBS HPC. What it computes and the authorities it applies are below.
The problem
Learning or prototyping VQE usually means a heavy quantum SDK, and the variational energy is typically checked against another approximation rather than against exact truth.
The local-first solution
This plugin runs a classical statevector simulation of VQE for the 2-qubit reduced H2 Hamiltonian in your browser, optimizes a hardware-efficient ansatz with a deterministic golden-section search, and validates the energy against the exact lowest eigenvalue from closed-form 4x4 diagonalization. Deterministic f64 math, nothing uploaded.
What it does
Exact f64 complex-statevector simulation of the 6-term Pauli-sum H2 Hamiltonian
Particle-number-aware hardware-efficient single-rotation ansatz with an analytic E(theta) witness
Deterministic golden-section optimizer (no randomness, same answer every run)
Per-iteration energy recorded for the convergence chart
Exact ground-state reference by closed-form 2x2/4x4 diagonalization (no iterative solver)
Energy gap to the exact eigenvalue tested below chemical accuracy (1.6e-3 Hartree)
Honest scope
EXACT: the statevector linear algebra, Pauli-to-matrix construction, analytic E(theta), golden-section arithmetic, and closed-form eigenvalues in f64. The six Pauli coefficients are bond-length-indexed, basis-dependent cited constants (O'Malley 2016 / Kandala 2017 at R=0.7414 A, STO-3G) you confirm - always surfaced. NOT modeled: larger active spaces/bases, hardware/shot noise, error mitigation, multi-parameter trainability, excited states, or the full dissociation curve. A teaching/verification tool, not production electronic-structure guidance.
Authorities cited
- O'Malley, P. J. J. et al. (2016). Scalable Quantum Simulation of Molecular Energies. Phys. Rev. X 6, 031007. DOI 10.1103/PhysRevX.6.031007. (The H2 / STO-3G 2-qubit reduced Hamiltonian and its g0..g5 Pauli coefficients vs bond length.)
- Kandala, A. et al. (2017). Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242-246. DOI 10.1038/nature23879. (Hardware-efficient ansatz; H2 ground-state energy within chemical accuracy.)
- Peruzzo, A. et al. (2014). A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213. DOI 10.1038/ncomms5213. (Original VQE: Rayleigh-Ritz variational principle E(theta) = <psi(theta)|H|psi(theta)> >= E_ground.)
- McClean, J. R., Romero, J., Babbush, R., Aspuru-Guzik, A. (2016). The theory of variational hybrid quantum-classical algorithms. New J. Phys. 18, 023023. DOI 10.1088/1367-2630/18/2/023023. (Hybrid VQE objective and expectation estimation.)
- Helgaker, T., Jorgensen, P., Olsen, J. (2000). Molecular Electronic-Structure Theory. Wiley. (STO-3G minimal basis; second-quantized molecular Hamiltonian; chemical accuracy ~1 kcal/mol ~ 1.6e-3 Hartree.)
- Nielsen, M. A., Chuang, I. L. (2010). Quantum Computation and Quantum Information, 10th anniv. ed. Cambridge. Sec. 4.2-4.3 (Pauli operators, single-qubit rotations, controlled gates) and the variational/expectation formalism.
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Run VQE against exact truth
Run the simulation in your browser with nothing uploaded, then save the convergence chart and exact-energy gap to a Sandbox workspace or attach them to a Worklog case.