Analog Kuramoto Backends

SPDX-License-Identifier: AGPL-3.0-or-later

The analog Kuramoto backend interface compiles a validated K_nm, omega problem into native programme schemas for three hardware families:

• Neutral-atom arrays using Rydberg interaction geometry.
• Circuit-QED resonator networks using tunable exchange couplers.
• Continuous-variable modes using phase rotations and beam-splitter terms.

This layer is a compiler interface, not a cloud submission client. Provider adapters can consume the emitted dictionaries and translate them into concrete SDK objects while preserving the same coupling, detuning, sign, and duration metadata.

Usage

import numpy as np

from scpn_quantum_control.hardware import compile_analog_kuramoto

K = np.array([[0.0, 0.5, -0.25], [0.5, 0.0, 0.125], [-0.25, 0.125, 0.0]])
omega = np.array([0.1, -0.2, 0.3])

program = compile_analog_kuramoto(
    K,
    omega,
    platform="circuit_qed",
    duration=1.25,
)

Provider-specific exports

The generic programme can be exported into provider-specific design payloads without submitting a job:

from scpn_quantum_control.hardware import export_provider_payload

neutral_program = compile_analog_kuramoto(
    K,
    omega,
    platform="neutral_atoms",
    duration=1.25,
)

pulser_plan = export_provider_payload(neutral_program, "pulser")
bloqade_plan = export_provider_payload(neutral_program, "bloqade")

For circuit-QED pulse-level design studies:

circuit_qed_program = compile_analog_kuramoto(
    K,
    omega,
    platform="circuit_qed",
    duration=1.25,
)

ibm_pulse_plan = export_provider_payload(circuit_qed_program, "ibm_pulse")

Each ProviderAnalogPayload records the provider target, required platform, SDK module name, local SDK availability, serialisable payload, and limitations. can_submit is always False in this layer. Provider exports are design artefacts and must not be reported as analogue hardware execution.

The returned AnalogKuramotoProgram contains:

• coupling_terms: upper-triangular native couplings with magnitude and phase.
• drive_terms: per-oscillator detunings from omega.
• feedback_terms: optional FIM feedback terms for H_FIM(lambda) = -lambda M^2 / n.
• payload: platform-specific serialisable programme schema.
• metadata: oscillator count, coupler count, native term, scaling, and user metadata.

FIM feedback compilation

The compiler can include the static collective term used in the SCPN/FIM Hamiltonian paper:

program = compile_analog_kuramoto(
    K,
    omega,
    platform="circuit_qed",
    duration=1.25,
    lambda_fim=4.0,
)

The Hamiltonian identity is:

-lambda M^2 / n = -lambda I - (2 lambda / n) sum_{i<j} Z_i Z_j.

The global shift is recorded as fim_global_energy_shift; the pairwise feedback terms are emitted as feedback_terms and mirrored into the platform payload. This is a native-programme schema for follow-up platform work, not evidence that a specific cloud provider accepts or faithfully executes the term.

Platform Schemas

Neutral atoms emit native_ahs_v1 payloads with:

• square-grid register coordinates,
• local detunings,
• Rydberg interaction terms with equivalent radii,
• optional FIM feedback terms for an Ising-style collective interaction,
• a three-point global Rabi envelope.

Circuit-QED emits exchange_resonator_v1 payloads with:

• mode-frequency detuning terms,
• flat-top tunable exchange couplers,
• sign encoded as phase 0 or pi.
• optional cross-Kerr-style FIM feedback terms.

Continuous-variable platforms emit cv_gaussian_schedule_v1 payloads with:

• phase rotations for natural frequencies,
• beam-splitter operations for non-zero couplings,
• coupling sign encoded in the beam-splitter phase.
• optional number-feedback terms for the collective FIM proposal.

Provider Export Schemas

Pulser exports require neutral_atoms programmes and emit pulser_sequence_plan_v1 with:

• register coordinates keyed by site,
• rydberg_global channel metadata,
• Rabi envelope points,
• local detunings,
• Rydberg interaction terms,
• optional FIM feedback design terms.

Bloqade exports require neutral_atoms programmes and emit bloqade_ahs_plan_v1 with:

• atom positions,
• piecewise-linear Rabi amplitude and phase schedules,
• local detunings,
• Rydberg interaction terms,
• optional FIM feedback design terms.

IBM pulse-level exports require circuit_qed programmes and emit qiskit_pulse_schedule_plan_v1 with:

• mode-frequency detuning terms,
• exchange-coupler channel plans,
• optional cross-Kerr-style FIM feedback design terms.

These provider payloads intentionally stop before SDK object construction or cloud execution. A future executable adapter must add provider-unit calibration, backend capability checks, and an explicit submission approval gate.

Execution Plan Gate

Provider exports can now be wrapped in an approval-gated execution plan:

from scpn_quantum_control.hardware import prepare_provider_execution_plan

plan = prepare_provider_execution_plan(
    pulser_plan,
    calibration={
        "calibration_id": "local-emulator-units-v1",
        "duration_unit": "us",
        "coupling_unit": "rad/us",
        "detuning_unit": "rad/us",
    },
    approved=False,
)

The execution plan is still non-submitting. It records whether the provider SDK is locally importable, whether execution has been explicitly approved, whether the path is emulator-only, and whether SDK-object construction is allowed. Cloud submission is deliberately rejected by this function; a separate provider runner with a project-specific approval, budget, and calibration gate is required before any QPU or provider-cloud claim can be made.

Registry Integration

The backend is registered as analog_kuramoto in the scpn_quantum_control.backends entry-point group and is pre-registered for source checkouts:

from scpn_quantum_control.hardware import get_backend

backend = get_backend("analog_kuramoto")
assert backend.is_available()

The stable Kuramoto facade also exposes compile_analog_program(problem, ...) for callers that already use KuramotoProblem.