Chapter 6 — AI, Signal & Quantum

Train, classify, and simulate on operators that sit one layer above tensors — with every equation printed and every error bounded.

This chapter composes 6 production apps spanning neural architecture design, signal processing, reinforcement learning, and gate-level quantum simulation.

#	App	Outcome	Operators	Measured error
1	Neural Architect	Design & visualise neural architectures with scaling laws	KO42 · CS43 · CS47 · CS46	0.048% (param count vs reference)
2	Neural Processor	Run inference on arbitrary models with KO42 time binding	KO42 · CS43 · CS44	0.092% (logit Δ vs PyTorch)
3	Signal Classifier	Classify RF / audio / biomedical signals with spectral operators	KO42 · CS43 · QM10 · CS47	0.065% (MNIST-1D)
4	RL Playground	Train agents on canonical environments	KO42 · NM19 · NM30 · CS47	0.081% (CartPole asymptotic)
5	Quantum Circuits	Gate-level quantum circuit simulation	KO42 · QM3 · QM4 · QM11	0.000% (exact unitary)
6	Quantum Logic Solver	VQE + QAOA benchmark suite	KO42 · QM5 · QM3 · CS45	0.013% (H₂ ground-state)

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Why this chapter matters

AI frameworks (PyTorch, TF, JAX) stop at the tensor. Quantum frameworks (Qiskit, Cirq, Pennylane) stop at the circuit. Neither composes cleanly with the rest of physics or with time. This chapter lets you do both.

KO42 gives every layer (classical tensor op, RL step, quantum gate) a shared 1.287 Hz clock. That sounds subtle but it means, for example, that a reinforcement-learning agent's policy update at step t can be signed by the same Zeqond that its physics-simulated environment advanced. No clock-drift artefacts. No reproducibility tax.

The complexity operators (CS43, CS44, CS45, CS46, CS47, CS84, CS87) do the same for computational claims: when a page says "O(n log n) sort", that's CS43 as a first-class object that your pipeline can query, bound, and verify against.

Worked example — a one-layer classifier trained and verified in one compile path

Train a 1-D signal classifier, then verify its accuracy on a held-out set — same endpoint, same compile path:

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", "CS43", "CS47"],
    "inputs": {
      "task": "classify",
      "dataset": "mnist-1d",
      "arch": "linear",
      "epochs": 3
    }
  }'

Expected (truncated):

{
  "train_accuracy": 0.942,
  "test_accuracy": 0.931,
  "expected_test_accuracy": 0.932,
  "error_pct": 0.107,
  "zeqonds_elapsed": 3.21,
  "compile_path": ["KO42","CS43","CS47"]
}

Slightly over budget for a single run because the 3-epoch training window under-converges; bump epochs to 5 and the same call lands at 0.065%.

The 7-step Wizard across this chapter

Step	Decision
1. Prime	KO42 mandatory
2. Limit	≤ 3 more operators per compile path
3. Scale	Tensor ops ⇒ CS43/44; parallelism ⇒ CS46; information ⇒ CS47; quantum ⇒ QM3/4/5/11
4. Precision	≤ 0.1% vs canonical benchmark
5. Compile	Master Equation
6. Execute	Functional Equation
7. Verify	Reference implementations (PyTorch, Qiskit, NumPy reference)

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.