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_reservoirmaps 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 full4**nstring space.scpn_quantum_control.applications.qrc_baselinecompares 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_productcreates disjoint synthetic forecast/classification certificates and weighted exact Pauli-feature objectives.scpn_quantum_control.surrogatesfits 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_detectoruses 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.jsondata/quantum_reservoir_surrogates/quantum_reservoir_evidence.md- content digest
8b555933e6ec7f9b2ee3c885379ef87af11e1002ce4a2d119fa83f26507de41c
Scientific basis¶
- Fujii and Nakajima (2017) motivates fixed quantum dynamics with a trained classical readout.
- Schreiber, Eisert, and Meyer (2023) defines classical surrogates through bounded reproduction of quantum-model input-output relations and treats them as a natural honesty baseline.
- O'Leary et al. (2025) motivates radial-basis proposals followed by a true quantum-objective query.
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.