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Towards Scaling Quantum Fine-Tuning of Foundational Time Series Models for Classification

Sang Hyub Kim, Julien Baglio, Rajiv Krishnakumar, Chi Chen, Oliver Knitter, Jonathan Mei, Claudio Girotto, Masako Yamada, Frederik F. Flöther, Martin Roetteler

arXiv:2609.05408v1quant-phcs.ET

TL;DR

The paper examines whether quantum heads can exploit time-series foundation-model embeddings and how hybrid quantum fine-tuning should scale. It fine-tunes a frozen Chronos backbone for PSML-5 classification, comparing quantum and classical heads and introducing wings that add input bandwidth through sparse one-way coupling. The quantum head beats the benchmark baseline and a larger classical MLP on identical inputs, while wing-based scaling improves balanced accuracy when added qubits carry new sample-matched information.

  • Problem

    Whether quantum fine-tuning transfers to time-series foundation models and how such heads should scale remains open.

  • Method

    The study attaches quantum and classical classification heads to frozen Chronos embeddings and introduces wings that expand a fixed-depth core’s input bandwidth.

  • Results

    The quantum head surpasses the strongest PSML-5 baseline and achieves 1.7–2.0 percentage points higher balanced accuracy than a larger classical head on identical inputs.

  • Takeaways & Limitations

    Quantum scaling helps when added qubits carry additional sample-matched inputs, whereas added circuit capacity without new information provides no gain.

Abstract

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Time-series foundation models produce rich embeddings, but whether quantum models can exploit them, and how far hybrid classical-quantum architectures scale, remains unclear. We address this by fine-tuning Chronos for power-grid event classification (PSML-5) with a quantum head on the model's embeddings. Grouping embeddings by physical sensor type before summarization already surpasses the best published baseline built for this benchmark, and with finer-grained features the quantum head outperforms a larger classical multilayer perceptron on identical inputs by 1.7-2.0 percentage points of balanced accuracy. Yet the gains saturate: past a point, feeding more information to the same fixed-width register yields no improvement. We show the bottleneck is neither the supply of information nor circuit expressiveness, but the bandwidth of the data intake. To overcome this limitation, we introduce the wing module, a self-contained few-qubit circuit that feeds additional information into the core circuit through a sparse, one-way coupling. Under a preregistered four-seed protocol, we attach wings to a fixed 12-qubit core with fixed features. Balanced accuracy increases with each added wing, from 83.6% with no wings (13 qubits, including a post-selection qubit) to 85.2% with two (19 qubits). Ablations establish that a circuit enlarged without new information gains nothing, while a wing fed information from the wrong sample harms accuracy. These results reframe scaling for quantum fine-tuning: added qubits help when they carry added inputs, not merely more parameters. Wings offer a modular and stable route to widening that bandwidth.

I. INTRODUCTION

The paper asks whether quantum fine-tuning transfers from text to time-series foundation models and how such hybrid heads should scale. It introduces a wing architecture to increase quantum data intake while holding core depth fixed.

  • Foundation models support downstream adaptation with less data and compute than training from scratch.
  • Quantum fine-tuning places a parameterized quantum circuit head on frozen foundation-model representations to pursue accuracy and parameter-efficiency gains.
  • Time-series classification tests this approach under multivariate, multi-class inputs containing short transient structure and substantial variation.
  • Wings add three-qubit feature-processing blocks through sparse one-way couplings, increasing intake without increasing core depth or fully connected width.
  • The study converts a forecasting model into a PSML multi-class event classifier and reports performance above the benchmark’s best specialized classical baseline.
  • The experiments test whether a fixed-width quantum head saturates as additional sketch fingerprints are supplied and whether intake capacity, rather than feature supply, limits performance.

A. Dataset and Baseline

The study uses PSML-5, a physically consistent power-system benchmark designed to test classification under strong nuisance variation. It follows the reference preprocessing and compares against the published MLSTM-FCN result using balanced accuracy.

  • PSML contains multivariate millisecond-resolution synchrophasor recordings of physically distinct power-grid disturbances.
  • PSML-5 contains five disturbance classes: generator trip, branch trip, branch fault, bus trip, and bus fault.
  • After filtering, the benchmark contains 549 samples with 91 channels and 960 time steps per sample.
  • The benchmark uses balanced accuracy because severe class imbalance makes standard accuracy less appropriate.
  • Same-class events vary in baseline, onset timing, peak amplitude, and grid location, while class-level signatures remain detectable.

B. Foundation Models

Chronos provides the frozen time-series foundation-model backbone, with encoder representations reused as classification features. The authors select Chronos over TimesFM provisionally and leave systematic backbone comparison outside scope.

  • Chronos tokenizes scaled time-series values and was pretrained for probabilistic forecasting on real and synthetic series.
  • The study uses Chronos-T5-base, extracting frozen per-timestep encoder states as downstream classification features.
  • The base variant has 200M parameters and d_model = 768, with embeddings extracted independently per channel and concatenated.
  • Chronos showed a modest but consistent preliminary downstream-classification edge over similarly sized TimesFM under the shared protocol.
  • Systematic comparison across foundation-model backbones is outside scope because Chronos-2, Lag-Llama, and TimeGPT were not evaluated.

III. TRAINING & FINE-TUNING PIPELINE

The pipeline mean-pools frozen Chronos embeddings, builds classical and quantum heads, and scales quantum intake through wings carrying separate feature streams. Wings couple sparsely and one-way into a fixed-depth core while post-selection keeps the readout grammar fixed.

  • Shared representation: Each of 91 channels yields a 768-dimensional mean-pooled embedding over the 960-step window, which forms the shared raw feature vector.
  • Parallel heads: The classical MLP uses 1.2–3.0 million trainable parameters, whereas the 12-qubit quantum head uses 3,240.
  • Feature construction: Features include type-group mean/std summaries and sketch fingerprints designed to preserve local or transient structure.
  • Wing scaling: The wing experiments keep the core’s 96-fingerprint feature set bit-identical while assigning each wing its own feature stream.
  • Wing scaling: Each wing uses a separate encoder and fixed CNOT couplings into the core; wings do not couple to one another, and core depth remains fixed.
  • Readout and simulation: The post-selection qubit is present at every rung, and only |0⟩ outcomes are retained; the ladder begins at 13 qubits and circuits are noiselessly simulated.

A. Hyperparameter optimization

The study uses five-fold cross-validation and controlled feature-specific ablations to optimize and compare the classical and quantum classification heads.

  • A. Hyperparameter optimization: Five-fold cross-validation on the training split uses mean balanced accuracy as the hyperparameter-selection objective.Optuna’s TPE search tunes the classical head across optimization and architecture settings, while the quantum search additionally varies quantum-specific parameters.
  • A. Hyperparameter optimization: The sketch-fingerprint quantum experiment reuses the unchanged 12-qubit core and varies only fingerprint dimension as a controlled ablation.The engineered-feature classical head is retuned using the same search space for its longer input.

B. Classification Results

Chronos with sensor-type pooling substantially improves PSML-5 classification, while finer fingerprints reveal a quantum-head advantage that saturates at fixed width.

  • B. Classification Results: 74.43% versus 74.20% balanced accuracy shows that a frozen Chronos-base backbone with a plain classical head already matches the published benchmark.This comparison is made before the paper’s feature-engineering steps.
  • B. Classification Results: 81.93% quantum and 82.10% classical balanced accuracy result from type-group mean/std pooling, the largest single jump for both heads.At this zero-fingerprint budget, the two heads are comparable.
  • B. Classification Results: From fingerprint budget two onward, the quantum head leads the classical head on bit-identical cached inputs.Its saturation trajectory is 84.21% → 84.29% → 84.39% → 84.37% at budgets 8, 16, 96, and 160, roughly 1.7–2.0 percentage points above the classical plateau.
  • B. Classification Results: 84.29% at budget 16 versus 84.39% at budget 96 suggests fixed 12-qubit width, rather than the feature family, is the binding constraint.The 16→96 transition changes from base-sketch to base+raw features, so it is a family switch rather than simply more of the same fingerprint.

C. Qubit Scaling

The wing experiment scales a fixed core by adding three-qubit modules with separate feature streams, while preserving the readout grammar and evaluating rung performance under repeated-seed validation.

  • C. Qubit Scaling: Three-qubit wings receive per-channel feature streams and affect the fixed core only through sparse, one-way entangling gates.The core depth remains constant, allowing qubit count and circuit intake to increase through modular attachments.
  • C. Qubit Scaling: 83.63% < 84.62% < 85.23% balanced accuracy corresponds to 13, 16, and 19 qubits with zero, one, and two wings.The 12-qubit reference is 83.39%, and all values are reported as four-seed means at each rung’s selected peak learning rate.
  • C. Qubit Scaling: 83.01% < 83.63% < 84.08% < 84.87% remains the ordering at one shared learning rate for the 12-qubit reference and 13q, 16q, and 19q configurations.This selection-free comparison preserves the wing-count trend without per-rung tuning.
  • C. Qubit Scaling: Figure 3 plots balanced accuracy against wing count, with four-seed means and standard-deviation error bars, alongside a 12-qubit reference and the 74.2% published baseline.The ladder and reference use internal five-fold cross-validation on the training split, whereas the published baseline averages ten initializations on the designated train/test split.
  • C. Qubit Scaling: Two outer 13-qubit seed-42 learning-rate points carried truncation flags, and the 12-qubit reference curve was nonunimodal.In the auxiliary best-run analysis, a single 12-qubit reference run can exceed the zero-wing rung’s best run.

1) Attribution Ablations:

The ablations separate the effect of added circuit capacity from the information carried by wing payloads. Increasing parameters without new information does not preserve the intact two-wing model’s performance, while mismatching payloads removes the gain and can underperform the wingless model.

  • Attribution design: The ablations hold inputs, protocol, and training budget fixed to test whether two-wing gains arise from capacity or payload information.The two variants are evaluated at their own best learning rate over multiple seeds.
  • Capacity-only ablation: Increasing rotation parameters from 150 to 204 without adding information tests circuit capacity independently of the intact two-wing inputs.The unshared circuit starts identically to the shared circuit, while features remain unchanged.
  • Payload-correspondence ablation: Shuffling wing inputs across samples preserves dimensionality, distribution, and parameter count but breaks correspondence between each payload and its sample.Core inputs remain intact, isolating the role of sample-matched wing information.
  • Interpretation: The ablations indicate that wing benefits come from payload information rather than added circuit capacity, with broken correspondence removing the gain and underperforming the wingless model.This conclusion is supported by both the capacity-only and shuffled-payload comparisons.

V. DISCUSSION AND CONCLUSION

The study finds that quantum fine-tuning transfers to PSML-5 and that scaling helps when added qubits carry additional inputs. It also characterizes PSML as a difficult but separable task dominated by nuisance variation.

  • Quantum fine-tuning on frozen Chronos embeddings beats the strongest specialized PSML-5 baseline.
  • 1.7–2.0 percentage points more balanced accuracy is achieved by the quantum head than by a larger classical counterpart on identical inputs.
  • Fixed-width quantum intake saturates with richer information, motivating wings that expand input bandwidth through a separate feature stream.
  • Accuracy rises with wing count because wings carry new information; enlarging a circuit without new information provides no gain, while wrong-sample information harms accuracy.
  • PSML structure: PSML combines high intra-class waveform variation with detectable class structure: inter-class distance ratios remain above 1 at 1.13–1.17.
  • Feature construction: Type-group pooling replaces 91×768 dimensions with six summary vectors in R^4608, while fingerprints restore local and transient structure smoothed by mean/std pooling.

APPENDIX F PREREGISTERED ONE-SHOT TEST EVALUATION

The preregistered one-shot evaluation tests frozen checkpoints on PSML’s untouched 110-sample split. It compares per-checkpoint and ensemble results with cross-validation references and reports a generalization gap.

  • 110 samples comprise PSML’s untouched one-shot test split, evaluated by inference only on frozen fold checkpoints.
  • Test scores sit 4–5 percentage points below the cross-validation means.
  • Table IV reports per-seed fold-mean balanced accuracy for the qubit-scaling ladder and the 12-qubit reference.
  • Per-checkpoint test scores are reported as means and standard deviations over 20 fold checkpoints, while ensemble scores average four per-seed ensembles.
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