siam_vqe

Variational Quantum Eigensolver (VQE) for single-impurity Anderson models (SIAM) in Qiskit, validated against EDRIXS / exact-diagonalization reference energies, with a hardware path on IBM Quantum.

The package is organized around a ladder of active-space levels:

• L0: Hubbard-dimer toy ground state (statevector), the algorithmic smoke test.
• L1: minimal NiO SIAM on real IBM Quantum hardware (the 02 notebook).
• L2 / L3: noise study and larger active spaces (in progress).

Every level checks the VQE energy against an independent ED/EDRIXS reference, so the quantum energy is never reported on its own.

How it works

The pipeline is a small set of composable stages, one module each:

• hamiltonian: builds the SIAM second-quantized Hamiltonian (impurity d-levels, correlated U, and a hybridized bath) for a chosen active space.
• mappings: fermion-to-qubit encoding (e.g. Jordan–Wigner) producing a qubit SparsePauliOp.
• ansatz: parameterized trial states (hardware-efficient or chemistry- inspired), sized to the active space.
• vqe_runner: the variational loop. A classical optimizer drives a Qiskit Estimator (statevector, noisy simulator, or real backend) to minimize ⟨H⟩.
• noise / hardware: Aer noise models and the qiskit-ibm-runtime glue (transpilation, error mitigation, job submission) for the hardware path.
• reference_ed / reference_edrixs: independent exact-diagonalization ground-state energies that every VQE result is checked against.

The L0→L3 ladder grows the active space one step at a time, so the algorithm is checked at each level before qubits are added: L0 is a two-site Hubbard dimer (statevector sanity check), L1 a minimal NiO SIAM run on IBM hardware, and L2/L3 add a noise study and larger d-shell active spaces.

Install

pip install -e ".[dev]"

Python 3.11+ required.

Run

pytest                      # unit tests
ruff check siam_vqe         # lint
mypy siam_vqe               # types
jupyter lab notebooks/      # driver notebooks

Layout

• siam_vqe/: the package (Hamiltonian build, fermion→qubit mappings, ansätze, VQE runner, noise model, hardware glue, ED/EDRIXS references)
• tests/: pytest suite
• notebooks/: driver notebooks per active-space level (L0 toy model, L1 NiO minimal hardware run) plus their result JSONs
• figures/: versioned result figures

Reference

Haverkort, Zwierzycki, Andersen, Phys. Rev. B 85, 165113 (2012); EDRIXS pedagogical examples 3 and 6.

License

MIT. See LICENSE.