Variational Quantum Simulation of Antiferromagnetic Hamiltonians

Part of ARPA Quantum Logical Systems — QONDRA  ·  qondra@arpacorp.net

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What this is

spinq-vqe simulates the quantum many-body physics of Mn₃Sn — a Kagome antiferromagnet that demonstrated 40-picosecond spin-orbit torque switching (UTokyo, 2026). We use Variational Quantum Eigensolvers (VQE) to approximate its ground state and compare directly to spectroscopic data.

Two parallel research threads:

• VQE on the Kagome lattice: ground-state energy, entanglement structure, barren plateau diagnostics, exact diagonalization benchmarks.
• SOC material screening via QAOA: classical MLP surrogate on spin Hall angle data, used as oracle for a QAOA composition optimizer.

Important

NB04 scientific scope. The committed data/mp_theta_sh.csv combines Materials Project descriptors with a fixed, illustrative θ_SH oracle. Its 12 target values reproduce the k=3 surrogate/QAOA workflow; they are not a row-wise set of verified measurements. The notebook demonstrates an optimizer comparison on this committed oracle, not materials discovery or quantum advantage. See data/theta_sh_sources.md and the machine-readable data/theta_sh_provenance.csv.

Structure

spinq-vqe/
├── src/spinq_vqe/
│   ├── kagome.py        # Kagome lattice graph + Heisenberg Hamiltonian
│   ├── ansatz.py        # HVA, HEA, MERA variational ansatze
│   ├── vqe.py           # COBYLA (primary) + Adam (diagnostic) VQE runners
│   ├── entanglement.py  # Von Neumann entropy, mutual information
│   ├── utils.py         # Publication-quality plot helpers
│   ├── surrogate.py     # MLP surrogate for spin Hall angle prediction
│   ├── qaoa.py          # QAOA circuit + optimizer for material selection
│   └── dmrg.py          # TeNPy DMRG reference energies (NB06)
├── notebooks/           # Executable research notebooks
├── figures/             # Generated plots
├── data/                # ED/VQE/QAOA CSVs, mp_theta_sh.csv, statevectors
├── scripts/             # fetch_mp_theta_sh.py — refresh MP dataset (optional)
├── docs/                # Guides and API reference → docs/README.md
├── OVERVIEW.md          # Full program description + research context
└── REFERENCES.md        # Full bibliography (50+ references)

Install

python -m venv .venv
.venv\Scripts\activate        # Windows
source .venv/bin/activate     # Linux / macOS
pip install -e ".[dev]"

Conda users:

conda env create -f environment.yml
conda activate spinq-vqe

Requires Python ≥ 3.11. Core: pennylane ≥ 0.39, numpy, scipy, networkx, matplotlib.
Optional: pip install -e ".[data]" adds scikit-learn, mp-api, pandas (for SOC QAOA notebooks).
Optional: pip install -e ".[dmrg]" adds physics-tenpy (for DMRG comparison, NB06).

SOC QAOA data (NB04): uses committed data/mp_theta_sh.csv (no API key needed). To refresh from Materials Project:

cp .env.example .env          # add MP_API_KEY from materialsproject.org/api
pip install -e ".[data]"
python scripts/fetch_mp_theta_sh.py

Notebooks

#	Notebook	Notes
01	01_kagome_hamiltonian.ipynb	lattice, ED baseline, figures
02	02_vqe_run.ipynb	COBYLA seed stats (mean ± std), 9.66% best error, Adam barren plateau
03	03_entanglement.ipynb	entropy profile, MI matrix, sublattice correlations
04	04_soc_qaoa.ipynb	surrogate MLP, QAOA p=1/2/3, material ranking, landscape diagnostic
05	05_scaling_analysis.ipynb	N=9/12/18 scaling, gradient variance, barren plateau
06	06_dmrg_comparison.ipynb	TeNPy DMRG vs ED/VQE, χ convergence, entanglement profile

Key results

Ground-state energy (VQE vs DMRG)

DMRG (TeNPy) is the primary classical reference for system sizes beyond sparse ED. VQE errors are quoted relative to DMRG E₀.

N	Seeds	Mean E₀	Std E₀	Best E₀	Error vs DMRG	Notes
9	5	−1.23572	0.02852	−1.28456	9.66%	HEA d=3, 27 params
12	3	−1.21520	0.02026	−1.23859	16.33%	HEA d=2, 24 params
9	—	—	—	−1.42190399	—	DMRG = ED, gap Δ ≈ 0
12	—	—	—	−1.48041803	—	DMRG reference
18	—	—	—	−1.49962859	—	DMRG = ED, gap Δ = 0.037
24	—	—	—	−1.50936790	—	DMRG only (beyond ED)

Adam / HEA d=3 at N=9 stalls at +0.141 (barren plateau). COBYLA mean ± std and per-seed distributions are in data/vqe_results.csv, data/vqe_seeds_n9.csv, and figures/vqe_seed_distribution.png (regenerate via NB02).

Why COBYLA, not Adam: The |0⟩⊗N initial state is a Z-basis eigenstate — all IsingXX/YY/ZZ gradients cancel to exactly zero by SU(2) symmetry. COBYLA uses function evaluations directly and is immune to this.

Entanglement structure (N=9 statevector)

Metric	Value	Interpretation
Mean single-site entropy	0.9066 bits	Near-maximal → strong quantum fluctuations
Max single-site entropy	1.000 bits	7 of 9 sites maximally entangled
Sublattice I(A:B)	3.689 bits	Strong inter-sublattice correlations
Sublattice I(A:C), I(B:C)	2.235 bits	C sublattice also correlated
Mean pairwise MI	0.227 bits	Non-local correlations (spin liquid signature)

SOC material selection via QAOA

Method	Total θ_SH	Selected	Notes
QAOA p=1	3.049	W, Ta, Bi₂Se₃	Best QAOA depth — still sub-optimal
QAOA p=2	3.049	W, Ta, Bi₂Se₃	Same selection as p=1
QAOA p=3	−0.451	W, Ta, Pd	Deeper circuit — worse on this oracle
Greedy (classical)	4.259	Bi₂Se₃, CrTe₂, Mn₃Sn	Optimal on surrogate oracle
Sim. annealing	4.259	Mn₃Sn, CrTe₂, Bi₂Se₃	Matches greedy

Tests

pip install -e ".[dev]"
pytest tests/ -v

Six test modules covering all library functions. Runs in under 90 seconds on CPU. See docs/testing.md for the full guide.

Docs

→ OVERVIEW.md — research narrative, key results, and literature context.
→ docs/README.md — physics background, ansatz guide, API reference, notebook guide.
→ docs/testing.md — test suite guide, coverage map, extending tests.

References

See REFERENCES.md for the full bibliography.
Key: Sachdev (1992), Yan/Huse/White (2011), Wiersema et al. (2020), Kandala et al. (2017), Cerezo et al. (2021), Farhi et al. (2014).

Citation

If you use this software, please cite CITATION.cff:

Peilivanidis, V., & ARPA Quantum Logical Systems (QONDRA). (2026). spinq-vqe: Variational Quantum Simulation of Antiferromagnetic Hamiltonians (v0.1.5). https://doi.org/10.5281/zenodo.21628505

Use the concept DOI above for the code artifact (always resolves to the latest archived version). Cite any related paper DOI separately once the manuscript is published.

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License: MIT  ·  Contact: qondra@arpacorp.net