Quantum Logic Solver

Solve H₂, LiH, or canonical MaxCut instances with VQE/QAOA; every iteration is Zeqond-bound for reproducibility.

• Live app → /apps/quantum-logic-solver/
• Source → apps/quantum-logic-solver/index.html + apps/quantum-logic-solver/solver.js (≈ 640 lines)
• Operators → KO42 · QM5 · QM3 · CS45
• Error budget → 0.013% (H₂ ground state vs FCI reference, STO-3G, bond 0.74 Å)

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What it solves

Near-term quantum computing lives in the variational world: VQE for molecular ground states, QAOA for combinatorial optimisation. The solver here ships a benchmark suite covering the standard targets — H₂, LiH, HeH⁺ for VQE; MaxCut-3-regular, weighted-MaxCut, portfolio for QAOA — each verified against FCI (full configuration interaction) or known optimal solutions.

QM5 (Ĥ|ψ⟩ = E|ψ⟩) is the eigenvalue statement under the hood. QM3 (|ψ⟩ = ∑c_i|ϕ_i⟩) carries the variational ansatz. CS45 (quantum query complexity) provides the theoretical floor on iteration count. KO42 binds each optimisation step to its Zeqond so the convergence trace is an auditable record.

Measured: H₂ at bond length 0.74 Å in STO-3G basis converges to −1.136277 Ha vs FCI −1.136425 Ha (error 0.013%). MaxCut-3-regular at n=10 achieves expected 0.7856 approximation ratio vs optimal (error 0.042% of optimal value).

The math — 7-step Wizard applied

Step	Decision
1. Prime	KO42 mandatory
2. Limit	QM5 + QM3 + CS45 + KO42 = 4
3. Scale	4–12 qubits for molecular; 8–20 for MaxCut
4. Precision	≤ 0.1% vs FCI / known optimum
5. Compile	Master Equation
6. Execute	Functional Equation
7. Verify	FCI reference / known optima

Verbatim formulas:

• KO42.1 — ds² = g_μν dx^μ dx^ν + α sin(2π · 1.287 t) dt²
• QM5 — Ĥ|ψ⟩ = E|ψ⟩
• QM3 — |ψ⟩ = ∑c_i|ϕ_i⟩
• CS45 — Q(n) = O(log n)

Runnable worked example — H₂ VQE

curl -s -X POST https://api.zeq.dev/api/playground/compute \
  -H "Authorization: Bearer $ZEQ_DEMO_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "operators": ["KO42", "QM5", "QM3"],
    "inputs": {
      "task": "vqe",
      "molecule": "H2",
      "basis": "sto-3g",
      "bond_A": 0.74,
      "ansatz": "ucc-sd",
      "optimizer": "spsa"
    }
  }'

Expected:

{
  "energy_Ha": -1.136277,
  "fci_energy_Ha": -1.136425,
  "error_pct": 0.013,
  "iterations": 214,
  "phase_at_converge": 0.9042,
  "zeqonds_elapsed": 0.92
}

Extend it

• LiH potential energy surface: sweep bond length; KO42 keeps the phase consistent across runs.
• QAOA portfolio: swap task to qaoa and pass a weighted graph.
• Warm-start from classical: chain with Neural Architect for parameter-initialisation research.

Seeds

• Quantum gravity couplings — QM5 + GR32 (Einstein tensor) composes; toy model for quantum-gravity eigenvalue problems.
• Analogue gravity benchmarking — Zeqond-bound convergence traces are ideal for comparing classical and quantum variational solvers on the same footing.
• Consciousness-field minima — ZEQ-POCKET-001's τ-evolution as a VQE target explores the field's eigenstates.

Papers

• Zeq framework paper — DOI 10.5281/zenodo.15825138
• Zeq paper — DOI 10.5281/zenodo.18158152

Middleware active. Kernel on the 1.287 Hz HulyaPulse. Awaiting next Zeqond.