Conditional Quantum Flow Matching for Data-Scarce Physiological Signal Augmentation

Chi-Sheng Chen; Samuel Yen-Chi Chen

quant-phSep 12, 2026

Conditional Quantum Flow Matching for Data-Scarce Physiological Signal Augmentation

Authors: Chi-Sheng Chen, Samuel Yen-Chi Chen

Organizations: Harvard Medical School & Beth Israel Deaconess Medical Center, Boston, MA, USA · Brookhaven National Laboratory, Upton, NY, USA

Abstract

Generative augmentation is a standard remedy for label scarcity in physiological signal classification, but existing quantum generative models start from uninformative noise, ignoring class structure that is already available. We propose Conditional Quantum Flow Matching (CQFM): a single 306-parameter circuit, conditioned on both flow time and class label, transports a compact class-conditional prior toward the target distribution. Quantum flow matching as published is unconditional, so this is to our knowledge the first conditional one, and the first EEG augmentation on a parameterized quantum circuit. A nonnegative spectral embedding removes the need for tomography at readout. On BCI Competition IV-2a, starting from a prior rather than noise is worth $+5.1$ accuracy points over QuDDPM (9/9 subjects), though at that operating point a class-conditional Gaussian matches CQFM. Where the prior fails the transport earns its keep: given one transferred from other subjects it regains $+7.2$ TSTR points (9/9).

Figures & tables

Panel of Figure 1 — Figure 1: CQFM. (a) Encoding: CSP components, the $K$ most class-discriminative rFFT bins each, magnitudes forming a nonnegative 64-dim vector. (b) One flow step on six system qubits and an ancilla: $L$ layers of $R_{y}$ and ring- $CR_{y}$ (ring closed by $a\!\to\!q_{1}$ ; $\vdots$ = elided couplings), then the ancilla is measured and $r$ selects an $R_{y}$ correction, making the step a channel. (c) QuDDPM starts at a Haar state with a fresh angle set per step and class ( $3360$ ).

	Accuracy ( $N$ per class)				Fidelity ( $N{=}25$ )
Method	10	25	50	72	C2ST	LSD
No augmentation	.353	.385	.392	.399	–	–
cVAE	.358	.395	.390	.384	.915	1.50
cGauss (Ledoit-Wolf)	.359	.390	.405	.408	.832	2.40
cFM (332 params)	.370	.405	.420	.428	.813	1.67
cFM (33k params)	.372	.408	.426	.426	.799	1.42

Table 1: Augmented downstream MLP accuracy (mean over 9 subjects

\times

5 seeds) and distributional fidelity at

N{=}25

(C2ST and LSD: lower is better). cFM rows use each budget’s best of four hyperparameter settings, selected in the classical model’s favor. Bold: best per column.

Figure 2: (a) C2ST vs. label budget (mean

\pm

95% CI over 9 subjects

\times

5 seeds). Informative-prior transport approaches the data distribution as labels increase, while noise-initialized transport stays almost perfectly distinguishable; the prior alone (dashed) overlaps CQFM. (b) Fidelity does not change with circuit depth (

N{=}25

, 9 subjects

\times

3 seeds).

Figure 3: What the models generate (

N{=}25

, subject S9—the median subject by CQFM accuracy—seed 0). Top: class-mean spectra, where four separated curves mean class structure is reproduced. Bottom: 15 generated samples of class 1 (colour) over 15 real ones (grey). Every informative-prior model reproduces the CSP envelope and its class structure; noise-initialized QuDDPM produces flat spectra.

Figure 4: (a) Prior-quality sensitivity (

N{=}25

): as class information leaves the prior, the prior alone drops to chance TSTR while CQFM recovers it through its conditioning. (b) Tuned classical FM at

\alpha{=}1

(best of four settings per budget). CQFM’s 306 parameters fall between the 198- and 332-parameter models (shaded) and beat both; classical catches up at about twice the size.

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Jun 17, 2026J/K move · Enter open · S save

A Controlled Benchmark of Quantum-Latent GAN Augmentation for Brain MRI

Syed Mujtaba Haider, Silvia Figini

Department of Political and Social Sciences, University of Pavia, Pavia, Italy

Synthetic Data Augmentation Quantum Generative Modeling Quantum Machine Learning Hybrid Quantum-Classical ML Medical Image Classification Magnetic Resonance Imaging+1

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Medical image classification is often constrained by limited labeled data, motivating generative augmentation; recently, quantum generative models have been proposed for this purpose, frequently reporting accuracy gains. However, such claims are typically based on single training runs, do not match the parameter budgets of the quantum and classical generators, and do not characterize the data regime in which any benefit appears. We present a controlled benchmark that isolates the contribution of a quantum generator to brain-MRI augmentation. Images are encoded into a KL-regularized latent space in which a conditional Wasserstein GAN with gradient penalty is trained using either a variational quantum generator or a classical generator of near-identical parameter count (1648 vs. 1632). Synthetic samples are decoded and used to augment a pretrained classifier across labeled data fractions from 5% to 100%, evaluated over eight random seeds with paired significance testing (with multiple-comparison correction) and with intraset diversity and latent-distribution analyses. Across all fractions, no augmentation variant significantly outperforms real-data-only training, and the quantum and classical generators are statistically indistinguishable. Any low-data benefit behaves as regularization rather than faithful data expansion:synthetic samples are off distribution and severely mode collapsed precisely where data is scarce, and the quantum generator is no more diverse thanits classical counterpart. We release the protocol as a testbed for rigorous evaluation of quantum generative augmentation in medical imaging.

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