Fault-tolerant resource product

scpn_quantum_control.fault_tolerant_resource_product turns the existing QEC resource primitives into one deterministic, digest-bound planning report for a bounded Kuramoto/XY request. It does not build another decoder or surface-code circuit.

Serialized reports use schema fault_tolerant_resource_product.v2. Stored reports with stale or unknown schema identifiers are refused by the immutable product contract.

The request pins oscillator count, evolution time, target precision, coupling density, Trotter steps, assumed physical error rate, syndrome-cycle duration, NISQ shots, and maximum odd code distance. The estimator then:

1. splits target precision equally across Trotter, logical-failure, and rotation-synthesis budgets;
2. selects the smallest odd distance whose phenomenological logical-error opportunities satisfy a conservative union bound;
3. reuses the existing 2d²-1 rotated-patch and 2d-1 repetition-scaffold register counts;
4. counts local and pairwise arbitrary Z-axis rotations from the declared coupling density; and
5. applies Selinger's conservative ceil(10 + 4 log2(1/epsilon)) Clifford+T Z-rotation estimate after allocating synthesis precision across all counted rotations.

from scpn_quantum_control.fault_tolerant_resource_product import (
    SyncProblemResourceRequest,
    build_fault_tolerant_resource_product,
    render_ft_resource_markdown,
)

request = SyncProblemResourceRequest(
    n_oscillators=4,
    evolution_time=1.0,
    target_precision=0.01,
    coupling_density=0.5,
    trotter_steps=8,
)
product = build_fault_tolerant_resource_product(request)
assert product.estimate.hardware_availability_claim_allowed is False
markdown = render_ft_resource_markdown(product)

Regime boundaries

The report keeps six regimes non-equivalent: classical reference, NISQ sampling, bit-flip-only repetition scaffold, unmeasured surface-code-shaped scaffold, bounded analog-feasibility dependency, and the fault-tolerant planning model. Register size never means a named device can execute the workload. The reported syndrome time is a floor for the assumed number of syndrome cycles; it excludes decoding, routing, feed-forward, magic-state factories, and logical-gate schedules, so it is not total runtime.

The Trotter allocation is a budget, not proof that a particular Hamiltonian and step count attain it. The surface-code logical-rate expression is a repository phenomenological ansatz. The existing SurfaceCodeUPDE operations remain structural proxies with no measured syndrome, decoder, or validated logical RZ/RZZ semantics.

Verified primary-source pins

• Horsman et al., Surface code quantum computing by lattice surgery
• Fowler et al., Surface codes: Towards practical large-scale quantum computation
• Selinger, Efficient Clifford+T approximation of single-qubit operators
• Google Quantum AI et al., Quantum error correction below the surface code threshold

These pins support architecture/scaling context and the declared synthesis estimate. They do not turn the product's simplified assumptions into a hardware-calibrated resource compiler.

Claim boundary

Conservative future-resource planning only. No available fault-tolerant hardware, validated logical RZ/RZZ, decoder integration, magic-state factory, total runtime, target-precision attainment, or fault-tolerant execution is claimed. The previous notebook's named-device register-size comparison is not an execution-feasibility result; this document is its claim-bounded successor.