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FRC Pulsed-Shot QAOA Scheduling

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

scpn_quantum_control.control.qaoa_pulsed_cost and scpn_quantum_control.control.frc_pulsed_qaoa schedule capacitor-bank firing for a field-reversed-configuration (FRC) pulsed-compression shot by minimising a control-grade physics cost with QAOA.

This is a control adapter, not a transport solver: the high-fidelity FRC physics is owned by SCPN-FUSION-CORE. The cost function evaluates the published closed forms of the quantities the scheduler trades off, and the FRCPlasmaSurrogate parameters can be matched to a FUSION run.

Cost function

frc_pulsed_shot_cost(schedule, target_b_profile, available_capacitor_energy_J, objective) returns the weighted sum of four dimensionless penalties:

Term Physics Reference
s-parameter deviation s = R_s / rho_i, flux-compression scaling Steinhauer, Phys. Plasmas 18, 070501 (2011)
bank energy over budget fired banks × energy-per-bank vs budget —
MRTI growth gamma = sqrt(A_T k g - k² B² / (mu0 (rho_h+rho_l))), amplitude a0 exp(∫gamma dt) Velikovich, Phys. Plasmas 14, 022701 (2007); Sefkow, Phys. Plasmas 21, 072711 (2014)
tilt-mode margin kinetic stabilisation via S*/E Belova, Phys. Plasmas 8, 1267 (2001) 
from scpn_quantum_control.control.qaoa_pulsed_cost import FRCQAOAObjective, frc_pulsed_shot_cost
import numpy as np

objective = FRCQAOAObjective(
    target_s_parameter=2.5, bank_energy_budget_J=5e5,
    mrti_amplitude_max_m=1e-2, tilt_margin_required=0.3,
)
cost, components = frc_pulsed_shot_cost(
    np.array([1, 0, 1, 1, 0, 1, 1, 0]), np.linspace(0.5, 4.0, 8), 1e6, objective,
    return_components=True,
)

Optimisers

The cost is a general (non-quadratic) function of the binary schedule, so the QAOA cost layer is the exact diagonal phase separator exp(-i gamma diag(cost)) (Farhi, Goldstone, Gutmann, arXiv:1411.4028).

  • optimal_schedule — exact brute-force minimum (reference, horizon ≤ 16).
  • classical_sqp_schedule — SciPy SLSQP relaxation plus rounding (classical NMPC-style baseline).
  • solve_frc_pulsed_qaoa — multi-restart p-layer QAOA used as a sampler.

On the documented test cases QAOA reaches the brute-force optimum (within the 5 % acceptance band).

Acceleration

The MRTI growth integral (the per-evaluation physics kernel) dispatches to a Rust kernel that matches the NumPy reference to 1e-12 relative tolerance; the scalar penalties stay in Python.

Measured per-call wall-time (release build, median of 7, scripts/bench_frc_pulsed_qaoa.py, artefact results/frc_pulsed_qaoa_benchmark.json, functional_non_isolated):

profile length NumPy Rust speed-up
8 25.8 µs 0.44 µs 59×
256 25.5 µs 1.42 µs 18×
1 024 28.5 µs 4.43 µs 6.5×
4 096 47.7 µs 16.8 µs 2.9×

The Rust kernel is the fastest measured backend at every profile length (NumPy's per-call overhead dominates on short profiles), so it sits at the top of the dispatch chain.

Consumers

SCPN-MIF-CORE imports frc_pulsed_shot_cost and FRCQAOAObjective for shot-sequence optimisation; SCPN-FUSION-CORE supplies the high-fidelity FRC physics and SCPN-CONTROL the NMPC comparison.