Skip to content

Quantum Reservoir Computing and Classical Surrogates

This page defines the bounded quantum reservoir computing (QRC), matched classical baseline, and differentiable classical-surrogate surfaces.

Production Surfaces

The QRC surface preserves the existing reservoir and adds certificate layers:

  • scpn_quantum_control.applications.quantum_reservoir maps classical inputs through Kuramoto-XY Hamiltonian evolution and Pauli expectation features, then fits a ridge readout. Exact-statevector allocation is budget checked, oversized input vectors are refused, and Pauli labels are generated without enumerating the full 4**n string space.
  • scpn_quantum_control.applications.qrc_baseline compares QRC with a deterministic ESN at equal feature count. The held-out comparison continues ESN state from training into validation instead of resetting it.
  • scpn_quantum_control.applications.quantum_reservoir_product creates disjoint synthetic forecast/classification certificates and weighted exact Pauli-feature objectives.
  • scpn_quantum_control.surrogates fits a Gaussian radial-basis surrogate, exposes its analytic input gradient, rejects train/validation leakage, and certifies held-out values and gradients against the exact local objective.
  • scpn_quantum_control.analysis.qrc_phase_detector uses exact dense ground-state Pauli features as a small-system phase-detector reference.

Held-out QRC / ESN certificates

import numpy as np

from scpn_quantum_control.applications import (
    ReservoirTaskKind,
    certify_reservoir_training,
    generate_synthetic_reservoir_task,
)

K = np.array([[0.0, 0.65], [0.65, 0.0]])
dataset = generate_synthetic_reservoir_task(
    ReservoirTaskKind.CLASSIFICATION,
    n_train=18,
    n_validation=8,
    seed=4139971,
)

certificate = certify_reservoir_training(
    dataset,
    K,
    omega=np.array([0.15, -0.1]),
    alpha=0.1,
    max_weight=1,
    t=0.8,
    seed=4139971,
)

The committed deterministic evidence uses 18 training and 8 validation rows for each synthetic task. Both systems have six readout features:

Synthetic task QRC validation MSE ESN validation MSE Lower MSE
Nonlinear classification 0.0696474284 0.0913905636 QRC
One-step forecast 0.890831726 0.0195529047 ESN

The result is intentionally mixed. It establishes two working held-out certificate paths, not a general performance result. The forecast row is also a direct negative control against presenting QRC as the default winner.

Classical Baseline

classical_esn_feature_matrix implements a deterministic ESN reference with:

  • seeded input and recurrent weights;
  • recurrent matrix rescaled to the requested spectral radius;
  • leaky state update;
  • ridge readout through classical_esn_ridge_regression.

Callers can request a deliberately unmatched reservoir_size, but certificate evidence requires equal feature count and reports the capacity match explicitly.

Differentiable classical surrogate

The bounded surrogate is a regularised Gaussian radial-basis model. Fitting stores SHA-256 identities for every training row and the target vector. Certification rejects any validation row that overlaps the training set.

On the frozen two-parameter weighted-Pauli objective, 25 training points and 16 disjoint validation points produced:

Gate Frozen threshold Observed Result
Held-out RMSE <= 0.01 0.000422869640 pass
Held-out maximum absolute error <= 0.025 0.000791764885 pass
Held-out R-squared >= 0.98 0.999994691 pass
Analytic-gradient maximum error <= 0.02 0.000893768362 pass

The gradient reference uses central differences of the exact local statevector objective at four disjoint points. It is not an analytic quantum gradient or a hardware-gradient result.

Exact-validated co-design proposal

propose_and_validate_surrogate_step(...) converts the surrogate gradient into a norm-bounded, unapplied ControllerProposal, then evaluates both current and candidate parameters through the caller's exact local objective. The frozen evidence candidate improved the exact objective from 0.0123150159 to -0.0490886919. The acceptance flag records that exact local observation only; the function does not emit a co-design safety decision or apply an update.

Regenerate and byte-check the evidence with:

PYTHONPATH=src python scripts/run_quantum_reservoir_surrogate_evidence.py
PYTHONPATH=src python scripts/run_quantum_reservoir_surrogate_evidence.py --check

Committed custody:

  • data/quantum_reservoir_surrogates/quantum_reservoir_evidence.json
  • data/quantum_reservoir_surrogates/quantum_reservoir_evidence.md
  • content digest 8b555933e6ec7f9b2ee3c885379ef87af11e1002ce4a2d119fa83f26507de41c

Scientific basis

These papers motivate the architecture. They do not validate this repository's specific fidelity thresholds, tasks, or proposal policy.

This is functional evidence for wiring and bounded task behaviour. It is not an isolated-core production benchmark.

Explicit Boundaries

  • The QRC feature map is exact-statevector and small-system bounded.
  • The phase detector is an exact dense reference, not a scalable reservoir simulator.
  • The ESN baseline is a deterministic NumPy reference comparator, not an accelerated service path.
  • The bounded simulation-only multimodal schema now supplies a classical forecasting product, but the quantum-reservoir evidence owner adds no adapter to it. No real clinical, grid, or plasma data is admitted by either product.
  • Differentiable notebook curriculum expansion is outside the reservoir evidence scope and is not represented as complete.
  • No hardware QRC, provider execution, unseen-domain generalisation, closed-loop control, optimisation advantage, publication, or deployment claim is made.