QuPID: Quantum Parameter-Efficient Input-Dependent Retrieval Adaptation for Medical RAG

Hyojun Ahn; Emily Jimin Roh; Soohyun Park; Walid Saad; Hyung-Chul Lee; Joongheon Kim

cs.AISep 27, 2026

QuPID: Quantum Parameter-Efficient Input-Dependent Retrieval Adaptation for Medical RAG

Authors: Hyojun Ahn, Emily Jimin Roh, Soohyun Park, Walid Saad, Hyung-Chul Lee, Joongheon Kim

Organizations: Korea University · Sookmyung Women’s University · Virginia Tech · Seoul National University · Seoul National University Hospital

Abstract

Fidelity-based quantum retrieval ranks candidates by the fidelity between query and archive states. Applying a shared input-independent unitary after fixed state encoding leaves that fidelity unchanged, so training the circuit cannot alter the ranking. Quantum parameter-efficient input-dependent retrieval adaptation (QuPID) repairs this by making the circuit input-dependent through data re-uploading and by comparing measurement readouts, vectors of local Pauli expectations, rather than states. The result is a small readout for adapting frozen image features to a local archive with limited data: training simulates the circuit classically, and inference runs on a GPU with fixed learned parameters. We characterize the class as a structured factorization of input-modulated quadratic feature maps, bound the frequency support of its re-uploading channel, and give a parameter-count generalization bound that motivates its small budget. Under a shared frozen backbone and a label-free protocol, QuPID's 60 parameters give higher precision-at-5 (P@5) on ChestX-ray14 and MURA than frozen medical encoders, and than adapters and low-rank adaptation (LoRA) with up to 5.25 million trainable parameters. On ChestX-ray14, the P@5 gain over the frozen encoder is +0.116, the lead over retuned adapters is widest at 512 adaptation examples (+0.040), and the full-budget margin over an equally compact classical rotation-plane head is +0.023 with a 95% interval excluding zero. Medical imaging is the primary testbed; the pattern recurs on two non-medical benchmarks, in report generation, and under simulated gate noise and finite-shot readout.

Figures & tables

Figure 1: QuPID overview. A frozen vision transformer (ViT) encodes all images; each feature is amplitude-encoded into $\log_{2}d$ qubits and processed by a shared circuit (trainable rotations, CNOT ring, re-uploading gates $E(\mathbf{x};\bm{\alpha})$ ) with all $60$ trainable parameters. Retrieval compares Pauli readouts $\mathbf{z}\in\mathbb{R}^{40}$ by cosine similarity, not quantum states (Section 3.1 ); archive readouts are cached.

Method	ChestX-ray14			MURA			#Params
Method	P@5	MAP@10	NDCG@10	P@5	MAP@10	NDCG@10	#Params
ViT Only	0.312	0.278	0.307	0.481	0.451	0.475	0
BiomedCLIP	0.352	0.315	0.348	0.508	0.476	0.501	0
MedCLIP	0.341	0.303	0.334	0.494	0.463	0.488	0
Linear Head	0.378 $\pm$ .008	0.341 $\pm$ .007	0.368 $\pm$ .008	0.549 $\pm$ .007	0.513 $\pm$ .008	0.541 $\pm$ .007	1.05M
Adapter	0.401 $\pm$ .007	0.368 $\pm$ .006	0.396 $\pm$ .007	0.573 $\pm$ .006	0.546 $\pm$ .007	0.567 $\pm$ .006	525K

Table 1: Retrieval under the shared label-free protocol (mean

\pm

std, 5 seeds); frozen encoders are deterministic. Within ViT-L, bold / underline mark best/second; tints mark 1st , 2nd , 3rd . † denotes conditional query-bootstrap significance versus the strongest baseline in this table (Holm-corrected,

p<0.05

; Section 4 ). The final medical-backbone block is a separate comparison.

Panel of Figure 2 — Figure 2: Low-data retrieval (ChestX-ray14, 5 seeds; bands one std). The dotted step in (a) is the Pareto envelope of the plotted classical modules; (b) plots the adaptation-size sweep. Panel (c) uses the fixed and retuned comparisons of Table 22 ; it excludes the additional controls in Table 23 . Proposition 3 does not predict these retrieval margins.

Panel of Figure 3 — Figure 3: Locating the advantage (ChestX-ray14 unless noted, 5 seeds). The solid line in (a) is an unfitted slope-one guide, and the squares in (b) mark the adapter budget with the best test score at each $n$ . Absolute numbers are in Appendices E and J .

Panel of Figure 4 — Figure 4: Mechanism (ChestX-ray14, 5 seeds; P@5 except (b)). Gains in (a) are over the frozen encoder; (b) uses the strongest included comparator; (c) gives parameter counts, filled at full budget and hollow at $n{=}512$ . Full sets are in Appendices E , H and J .

Panel of Figure 5 — Figure 5: The idealizations tested (ChestX-ray14, P@5, 5 seeds; bands one standard deviation). Severity in (c) runs from the ChestX-ray14 acquisition at 0 to the CheXpert ( Irvin et al., 2019 ) acquisition at 4. The strength axis in (a) is a symmetric log; in (b) the horizontal rule marks exact expectations and the points are measured finite-shot results.

Appendix figures & tables39 assets

Supplementary material from the paper’s appendix.

Appendix

Work	Venue	Domain	Encoding	Hybrid	Simulator
TensorRL-QAS ( Kundu & Mangini, 2025 )	NeurIPS	RL	Matrix product state	✓	✓
QVF ( Wang et al., 2025d )	NeurIPS	Vision	Amplitude	✓	✓
QDSFormer ( Born et al., 2025 )	NeurIPS	Vision	Angle	✓	✓
PQC policies ( Jerbi et al., 2021 )	NeurIPS	RL	Angle, re-uploading	✓	✓
QuanONet ( Wang et al., 2025c )	ICML	Operator learning	Angle, re-uploading		✓
Quorus ( Han et al., 2026 )	ICLR	Federated	Angle	✓	✓

Appendix

Table 2: Experimental settings in recent variational quantum learning studies at major venues. A checkmark indicates the setting is explicitly used or discussed. Hybrid architectures, task-specific encodings, and simulator-based evaluation are the prevailing conventions; QuPID follows all three.

Figure 6: Conservative frequency-magnitude upper bound

L(2^{n_{q}}-1)

versus trainable budget (Proposition 2 ,

\bm{\alpha}=1

). Curves vary depth

L

; the dash-dotted line marks

60

parameters. These are bounds, not measured support sizes or attained frequencies; equation 8 sharpens them for the local observables used in our readout.

Design	$\max\|\Delta\mathrm{Sim}\|$	$\tau$ vs. frozen	$\max\|\partial\mathcal{L}/\partial\theta_{j}\|$
Naive fidelity design	$4.2\times 10^{-15}$	$1.000$	$8.7\times 10^{-16}$
QuPID (re-uploading and measurement readout)	$0.31$	$0.62$	$1.8\times 10^{-2}$

Appendix

Table 3: Parameter sensitivity of the two designs over

500

random parameter draws (ChestX-ray14,

2{,}000

queries, float64 arithmetic).

\Delta\mathrm{Sim}

is the entrywise deviation of the similarity matrix from the frozen-feature matrix,

\tau

is Kendall’s rank correlation between the induced ranking and the frozen ranking (median over draws), and the last column is the largest parameter-shift gradient coordinate of the contrastive loss over all draws.

Figure 7: Amplitude embedding encodes a normalized

d

-dimensional feature vector into the amplitudes of

\log_{2}d

qubits (the figure writes

\mathbf{x}

N

, and

n

for our

\hat{\mathbf{h}}

d

, and

n_{q}

). At

n_{q}=\log_{2}d

the state space dimension equals the input dimension; the value of the circuit lies in its parameter-efficient nonlinearity rather than in its size.

Backbone	ViT-L/16, ImageNet-21K, frozen (1024-D features)
Qubits / depth / readout	$n_{q}=10$ , $L=3$ , $M=4n_{q}=40$
Trainable parameters	$2n_{q}L=60$ ( $30$ rotations, $30$ re-uploading scales)
Optimizer	AdamW, lr $10^{-3}$ , weight decay $0.05$
Batch size / temperature	32 / 0.07
Augmentations	rotation $\pm 5^{\circ}$ , translation $5\%$ , brightness/contrast jitter 0.1/0.1
Epochs / seeds	50, label-free early stopping (patience 10) / 5 seeds (0 to 4), mean $\pm$ std

Appendix

Table 4: Hyperparameters used for all adaptation methods unless stated otherwise.

Panel of Figure 8 — Figure 8: Signed margins over the strongest included baseline at full budget for the reported ranking metrics. Negative bars mark metrics on which that baseline leads.

Panel of Figure 9 — Figure 9: Downstream evaluation on MIMIC-CXR. Retrieval ordering is preserved by both n-gram metrics and the clinical-efficacy proxies, and QuPID’s relative advantage is larger on the latter, consistent with pathology-aligned evidence mattering most for factual findings.

Domain	Benchmark	512 examples			Full budget
Domain	Benchmark	frozen	cls.	QuPID	frozen	cls.	QuPID
Medical	ChestX-ray14	0.312	0.347	0.401	0.312	0.414	0.428
Industrial	MVTec AD	0.428	0.446	0.481	0.428	0.492	0.508
Fine-grained	CUB-200	0.612	0.628	0.658	0.612	0.671	0.684

Appendix

Table 5: Absolute scores behind Figure 3 (c) (P@5, 5 seeds). cls. denotes the comparator reported in this benchmark comparison, not the strongest control across all experiments. For ChestX-ray14 at 512, Table 23 reports a stronger rotation-plane control (

0.386

). Marking follows Table 1 by column.

Variant	P@5	NDCG@10	#Trained
QuPID (full: $L{=}3$ , $M{=}40$ )	0.428 $\pm$ .006	0.425 $\pm$ .006	60
naive fidelity design (Prop. 1 )	0.312 $\pm$ .000	0.307 $\pm$ .000	0 (30 inert)
w/o re-uploading, readout kept	0.412 $\pm$ .008	0.409 $\pm$ .008	30
readout: single-qubit only ( $M{=}20$ )	0.415 $\pm$ .007	0.412 $\pm$ .007	60
readout: pair terms only ( $M{=}20$ )	0.402 $\pm$ .008	0.398 $\pm$ .008	60
depth $L{=}1$	0.402 $\pm$ .007	0.399 $\pm$ .007	20

Appendix

Table 6: Controlled removals on ChestX-ray14 (5 seeds). The first row is the default configuration. #Trained counts parameters that receive nonzero gradient; frozen parameters are noted in parentheses. The naive fidelity design reproduces the frozen baseline exactly (Proposition 1 : its parameters receive identically zero gradient), whereas the readout without re-uploading stays trainable but weaker by

0.016

P@5 at the full budget. Marks and tints as in Table 1 .

Dataset	Retriever	LLaVA-Med (7B)				CheXagent (8B)
Dataset	Retriever	B-4	R-L	MTR	CIDEr	B-4	R-L	MTR	CIDEr
	ViT Only	0.134	0.298	0.167	0.241	0.147	0.312	0.178	0.263
	Adapter	0.156	0.332	0.189	0.298	0.171	0.348	0.203	0.321
IU X-Ray	QuPID	0.163	0.341	0.194	0.294	0.178	0.357	0.208	0.318
	ViT Only	0.098	0.247	0.138	0.168	0.108	0.261	0.149	0.184
	Adapter	0.121	0.281	0.163	0.221	0.134	0.298	0.176	0.242

Appendix

Table 7: Report generation with frozen medical LVLMs given top-5 retrieved reports as context (5 seeds; std

\leq 0.004

for adapted retrievers, ViT Only deterministic under greedy decoding; LoRA

r{=}16

tracks Adapter within 0.003 and is omitted). B-4, R-L, MTR denote BLEU-4, ROUGE-L, METEOR. Marks and tints as in Table 1 .

Retriever	LLaVA-Med (7B)		CheXagent (8B)
Retriever	CheXbert-F1	RadGraph-F1	CheXbert-F1	RadGraph-F1
ViT Only	0.298	0.181	0.321	0.194
Adapter	0.334	0.203	0.356	0.217
QuPID	0.352 †	0.214 †	0.373 †	0.229 †

Appendix

Table 8: Clinical efficacy proxies on MIMIC-CXR (5 seeds; std

\leq 0.005

): CheXbert micro-F1 and RadGraph-F1 of generated reports. † , marks and tints as in Table 1 .

Table 18

Method	P@5	P@10	MAP@10	MRR	NDCG@5	NDCG@10
ChestX-ray14
ViT Only	0.312	0.287	0.278	0.363	0.325	0.307
Linear Head	0.378	0.351	0.341	0.434	0.389	0.368
Adapter	0.401	0.375	0.368	0.462	0.415	0.396
Adapter-L	0.412	0.386	0.372	0.465	0.421	0.401
Adapter-XL	0.414	0.388	0.387	0.468	0.433	0.414

Appendix

Table 11: Retrieval metrics (5-seed means; adapted-entry stds within

\pm 0.009

, omitted for space). Marks and tints as in Table 1 .

Panel of Figure 10 — Figure 10: Retrieval-grounded reports: each panel shows the query image and the report a frozen LVLM generates from QuPID’s top-5 retrieved cases. The retrieved cases in (a) are pathologically consistent and the generator narrows the differential to pneumonia versus pulmonary edema; in (b) they support a displaced transverse fracture of the radius.

Table 21

Panel of Figure 11 — Figure 11: Diagnostics for feature sensitivity and gradient decay in this architecture (ChestX-ray14, 5 seeds); the design range in (b) is $L\leq 6$ .

Panel of Figure 12 — Figure 12: Three circuit-design axes on ChestX-ray14 (P@5, 5 seeds); dash-dotted lines mark the default configuration, and (b) lists CNOTs per layer under each topology.

Table 24

Panel of Figure 13 — Figure 13: Sensitivity and spread (ChestX-ray14, 5 seeds); dash-dotted lines mark default settings.

Evaluation	frozen	cls.	QuPID
ChestX-ray14 (in-domain)	0.312	0.401	0.428
CheXpert (zero-shot)	0.289	0.301	0.318

Appendix

Table 17: Cross-site zero-shot transfer (P@5, 5 seeds; std

\leq 0.009

). Modules are adapted on ChestX-ray14 and evaluated without further training. Marks and tints as in Table 1 , by column.

Channel	$p{=}0$	$p{=}0.001$	$p{=}0.005$	$p{=}0.01$	$p{=}0.05$
Depolarizing	0.428	0.428	0.426	0.423	0.404
Bit flip	0.428	0.427	0.424	0.419	0.392
Phase flip	0.428	0.428	0.427	0.426	0.418
Amplitude damping	0.428	0.427	0.423	0.417	0.386

Appendix

Table 18: Post-training noise sensitivity on ChestX-ray14 (P@5, 5 seeds, std

\leq 0.007

). The trained model is frozen and noise is injected only at evaluation, per qubit after every layer. The frozen-baseline P@5 of 0.312 marks zero accuracy gain over frozen retrieval.

Figure 14: Gain of noise-aware training over post-training injection at two channel strengths (P@5, ChestX-ray14, 5 seeds; absolute values in Table 19 ).

Channel	$p=0.01$			$p=0.05$
Channel	post	noise-aware	$\Delta$	post	noise-aware	$\Delta$
Depolarizing	0.423	0.426	$+0.003$	0.404	0.417	$+0.013$
Bit flip	0.419	0.424	$+0.005$	0.392	0.409	$+0.017$
Phase flip	0.426	0.427	$+0.001$	0.418	0.423	$+0.005$
Amplitude damping	0.417	0.423	$+0.006$	0.386	0.405	$+0.019$

Appendix

Table 19: Noise-aware training versus post-training injection (ChestX-ray14, P@5, 5 seeds, std

\leq 0.008

). Each entry trains and evaluates at the same channel strength; post repeats the frozen-model numbers of Table 18 for comparison.

\Delta

is the recovery from training through the channel.

Shots per observable	$S{=}10^{2}$	$S{=}10^{3}$	$S{=}10^{4}$	$S{=}\infty$
P@5	0.389	0.418	0.426	0.428
NDCG@10	0.386	0.415	0.423	0.425

Appendix

Table 20: Finite-shot readout on ChestX-ray14 (5 seeds, std

\leq 0.009

). Each of the

M=40

observables is estimated from

S

shots for query and archive alike;

S=\infty

denotes exact expectations.

Method	$p$	$n{=}128$	$512$	$2{,}048$	$8{,}192$	$32{,}768$
QuPID	60	0.031	0.016	0.008	0.004	0.002
Quadratic	164	0.051	0.027	0.014	0.007	0.004
Adapter	525K	0.212	0.171	0.118	0.072	0.041
LoRA ( $r{=}16$ )	1.57M	0.229	0.184	0.127	0.078	0.045

Appendix

Table 21: Training P@5 minus held-out P@5 on ChestX-ray14 after label-free adaptation (5 seeds; std

\leq 0.006

for the two large-budget families and

\leq 0.002

for the two small ones). This retrieval diagnostic is distinct from the contrastive-risk gap bounded by Proposition 3 . Lower is better; marks and tints as in Table 1 .

Panel of Figure 15 — Figure 15: Train–test P@5 gaps (ChestX-ray14, 5 seeds; bands one standard deviation). The families are ordered by parameter budget at every $n$ . The line at $\sqrt{60/164}$ in (b) is a parameter-count reference, not a prediction for the ratio of the QuPID gap $g_{60}$ to the Quadratic gap $g_{164}$ .

$n$	sweep baseline		QuPID	margin
$n$	fixed	tuned	QuPID	fixed	tuned
128	0.316	0.331	0.352	$+0.036$	$+0.021$
512	0.347	0.361	0.401	$+0.054$	$+0.040$
2,048	0.378	0.384	0.416	$+0.038$	$+0.032$
8,192	0.401	0.405	0.424	$+0.023$	$+0.019$
32,768	0.414	0.416	0.428	$+0.014$	$+0.012$

Appendix

Table 22: Reported baseline retuning sweep on ChestX-ray14 (P@5, 5 seeds). fixed uses the a priori protocol; tuned selects width, weight decay, dropout, and patience at each

n

by held-out contrastive loss. QuPID keeps its configuration fixed. Margins apply to this sweep and exclude the additional controls in Table 23 . Marks and tints as in Table 1 , by column.

Module	$p$	full budget	$n{=}512$
Diagonal gain on 60 leading PCA directions	60	0.331	0.322
Random Fourier features	64	0.319	0.311
Tensor-train head over the ten blocks, bond dimension 2	64	0.361	0.348
Rotation-plane isometry	60	0.405	0.386
Quadratic head	164	0.392	0.372
Bias-only shift	1,024	0.352	0.337

Appendix

Table 23: A range of classical adaptation modules at or near the

60

-parameter budget (P@5, ChestX-ray14, 5 seeds; std

\leq 0.009

). Each is trained with the label-free objective and schedule of Section 4 ; the frozen encoder scores

0.312

. Marks and tints as in Table 1 .

Surrogate	$p$	P@5		$\Delta$ in favour of QuPID
Surrogate	$p$	$n{=}512$	full	at $512$	at full
Spectrum features, $D{=}16$	640	0.318	0.341	$+0.083$	$+0.087$
Spectrum features, $D{=}128$	5,120	0.339	0.372	$+0.062$	$+0.056$
Spectrum features, $D{=}1{,}024$	41,000	0.357	0.396	$+0.044$	$+0.032$
Spectrum features, $D{=}8{,}192$	328,000	0.362	0.407	$+0.039$ [.028,.050]	$+0.021$ [.013,.029]
Givens rotations, Pauli-type observables	60	0.389	0.409	$+0.012$	$+0.019$

Appendix

Table 24: Classical surrogates given more parameters and more tuning than QuPID (ChestX-ray14, P@5, five adaptation subsets crossed with five initializations).

\Delta

is the paired mean difference in favour of QuPID, with a Holm-corrected

95\%

cluster-bootstrap interval over subsets and patients. Marks and tints as in Table 1 .

Retrieval context	BLEU-4		CheXbert-F1	range
Retrieval context	IU X-Ray	MIMIC-CXR	MIMIC-CXR	range
no retrieval	0.112	0.081	0.246	n/a
random retrieval	0.121	0.086	0.259	$0\%$
ViT Only	0.134	0.098	0.298	$26\%$
Adapter	0.156	0.121	0.334	$49\%$
QuPID	0.163	0.127	0.352	$\mathbf{61\%}$

Appendix

Table 25: Retrieval-utility bounds for report generation with frozen LLaVA-Med (5 seeds; std

\leq 0.005

). Random draws top-5 context uniformly from the archive and oracle draws it from label-matched cases, which requires test-time labels and is therefore unattainable. The last column is the share of the random-to-oracle range that each retriever recovers on MIMIC-CXR CheXbert-F1. Marks and tints as in Table 1 .

Figure 16: The retrieval-utility bracket of Table 25 for every metric the table reports (frozen LLaVA-Med, 5 seeds), normalized per metric so that random context sits at

0

and the label-matched reference at

100

; the no-retrieval condition falls below random.

Panel of Figure 17 — Figure 17: Archive-size sweep (5 seeds). The horizontal axis counts stored images before patient filtering. At the $112{,}120$ -image ChestX-ray14 endpoint, the eligible gallery contains $81{,}664$ images from $22{,}437$ patients; query and validation patients are excluded from ranking.

Table 39

Panel of Figure 18 — Figure 18: Sequential adaptation over three sites without replay, re-evaluating site 1 after each stage (5 seeds); filled markers in (b) are the final module averaged over the three sites and hollow markers joint training on the pooled data.

Method	$p$	site 1	+site 2	+site 3	forget	mean	joint
Adapter	525K	0.401	0.371	0.343	0.058	0.362	0.396
LoRA ( $r{=}16$ )	1.57M	0.411	0.379	0.351	0.060	0.369	0.401
QuPID	60	0.428	0.416	0.402	0.026	0.398	0.412

Appendix

Table 28: Sequential adaptation over three sites (ChestX-ray14, CheXpert, MIMIC-CXR) with no replay buffer and no continual-learning method (P@5, 5 seeds; std

\leq 0.009

). The first three columns evaluate on site 1 after each stage; mean averages the final module over all three sites; joint trains one module on the pooled data as an upper reference. Marks and tints as in Table 1 .

Method	$n{=}512$		full budget		epochs
Method	default	matched	default	matched	epochs
Adapter	0.343	0.351	0.401	0.404	50 $\to$ 80
LoRA ( $r{=}16$ )	0.347	0.354	0.411	0.414	50 $\to$ 68
Adapter-XL	0.338	0.349	0.414	0.417	50 $\to$ 61
QuPID	0.401		0.428		50
QuPID margin	$+0.054$	$+0.047$	$+0.014$	$+0.011$

Appendix

Table 29: Classical baselines given QuPID’s adaptation wall-clock instead of its parameter count (P@5, ChestX-ray14, 5 seeds; std

\leq 0.008

). Extra epochs and random restarts are selected by contrastive validation loss. QuPID is unchanged. Marks and tints follow Table 1 .

Table 43

Aspect	Interpretation	Evidence
Circuit-defined model class	The circuit shares $60$ parameters across $M=40$ input-modulated, correlated full-rank quadratic forms. Its contribution is this compact retrieval feature map, supported by competitive ranking quality under classical simulation.	Sec. 1 , 3.3 , 4.2 ; App. A.6
Classical control budgets	The rotation-plane head matches $60$ parameters, isometry and output width. Its input-independent rank-one forms differ from the input-modulated full-rank Pauli forms. The comparison evaluates these choices jointly; RFF and the four-projection Quadratic head are more restricted controls.	Table 1 ; App. J.2 , J.3 , M.1
Contribution beyond frozen features	The backbone initialization is shared; post-encoder heads keep features frozen, while LoRA updates attention projections; the untrained circuit and the naive fidelity design are reported as controls, and the naive design exactly matches the frozen baseline as the theory requires; all $60$ parameters are updated.	Fig. 4 (a); Table 6 ; App. B.4 , G
Finite-scale trainability	Depth $L\leq 6$ , $n_{q}=10$ fixed by the feature dimension, local one- and two-body observables; gradient variance is a finite diagnostic, not an asymptotic rate. Classical simulation differentiates the statevector; parameter shift provides the gate-level hardware cost model.	Sec. 3.4 ; Fig. 11 ; Table 13
Simulation cost and scaling	The statevector dimension is $2^{n_{q}}=d$ , with runtime also scaling in depth, gate count and readout width; per-epoch training time is $1.60\times$ that of a light adapter, inference time and memory usage are comparable, and the qubit count is swept rather than assumed.	Table 10 ; Fig. 12 (a); App. H.1
GPU deployment and noise simulation	The intended system trains by classical circuit simulation and runs fixed-parameter GPU inference with cached archive readouts. No quantum processor is required, as in quantum parameter-efficient fine-tuning ( Koike-Akino et al., 2025 ; Liu et al., 2025 ) . Noise and shot studies are simulations of an optional hardware realization, not its validation.	Sec. 2 , 4.2 ; Fig. 5 (a,b); App. A.6 , I

Appendix

Table 32: Design choices, empirical interpretation and supporting results (I: model, controls, trainability, cost, deployment, encoding and statistics). References point to sections and appendices in this paper; Table 33 continues the list.

Aspect	Interpretation	Evidence
Scope of the generalization bound	The bound applies to bounded smooth parameter classes and concerns contrastive risk. It does not certify the reported runs or predict P@5 gaps. The empirical claim combines a small budget with competitive retrieval; the gap ratios are separate diagnostics.	Sec. 3.4 ; App. B.3 , J.1
Classical surrogate comparisons	The default rotation-plane head leaves full/512-example margins of $+0.023$ / $+0.015$ ; tuning reduces them to $+0.014$ / $+0.007$ . Appendix J.4 extends this to surrogates with far larger budgets and more tuning; without input modulation they stay between $0.409$ and $0.417$ P@5 up to $6{,}600$ parameters. These measured comparisons do not establish a classical expressivity separation (App. M.1 ).	Sec. 4.2 ; Table 1 , 24
Circuit and readout selection	Real rotations keep the state real and the simulation computationally inexpensive; qubit count, entangling topology, readout width and depth are each swept and saturate at the default, so the operating point is a plateau.	Fig. 4 (a), 12 ; App. A.3 , H.1
Finite-shot readout	A sufficient Hoeffding ranking guarantee is derived with explicit norm-floor, margin and collection-size dependence. Separately, the finite-shot experiment is within $0.002$ P@5 of exact expectations at $10^{4}$ shots per observable.	Sec. 4.2 ; App. I
Dataset coverage	ChestX-ray14 ( $112{,}120$ images) and MURA for retrieval, IU X-Ray and MIMIC-CXR for generation, MVTec AD and CUB-200 for generality.	Sec. 4.1 ; App. C
Low-data accuracy and degradation	The sweep tests retrieval quality as adaptation data shrink. Default rotation-plane margins are $+0.023$ at full budget and $+0.015$ at 512. The control degrades less; the results support observed accuracy at a small budget, without establishing superior stability.	Sec. 3.4 , 4.1 ; App. J.1 , J.2

Appendix

Table 33: Design choices, empirical interpretation and supporting results (II: theory, surrogates, circuit design, shots, datasets, low-data accuracy, generation and scope).

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Jul 29, 2026quant-ph

LLM-Guided Initialization for Accelerated Hybrid Quantum-Classical Medical Image Classification

Variational quantum algorithms often encounter barren plateaus, where cost gradients decay rapidly with increasing circuit depth, undermining the trainability of parameterized quantum circuits. This paper evaluates AdaInit (Adaptive Initialization), proposed by Zhuang and Cunningham, which uses large language models to propose initial parameters for quantum neural networks. We study a simplified single-query AdaInit variant paired with GPU-accelerated simulation in NVIDIA CUDA-Q and apply it to binary classification on the DMR-IR mammography dataset. AdaInit delivers 14.6 times higher gradient variance at initialization than random initialization (0.0095 vs. 0.0006), producing 160 times faster convergence (1.1s vs. 176 s) while maintaining the same classification accuracy of 61.4 percent. We provide theoretical analysis grounded in the geometry of parameterized circuit landscapes and show empirically that LLM-guided initialization places the optimizer in trainable regions of parameter space. Beyond performance, our results indicate that a single LLM query can yield informative parameters without iterative refinement, suggesting a low-overhead path to improved trainability. The findings validate AdaInit in a medical imaging setting and demonstrate its compatibility with GPU-accelerated quantum backends for practical speedups.

Riza Alaudin Syah, Irwan Alnarus Kautsar, Haza Nuzly Bin Abdull Hamed

Faculty of Computing Universiti Teknologi Malaysia Johor Bahru, Malaysia · Remote Student based in Jakarta, Indonesia · Informatics Department Faculty of Science and Technology Universitas Muhammadiyah Sidoarjo Sidoarjo, Indonesia

Quantum Neural Networks Medical Image Classification Image Classification Acceleration

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Sep 29, 2026quant-ph

SQUARE: Structured Quantum Representation Adapters as Compact Quadratic Feature Maps for Frozen Language Models

Frozen language models (LMs) are increasingly used as fixed feature extractors for downstream reranking, scoring, and preference modeling, raising a practical question: how should a compact module represent interactions among features in a fixed low-dimensional bottleneck? Common linear and low-rank adapters remain linear at the adaptation module itself, whereas explicit second-order alternatives introduce pairwise interactions through direct parameterization or predefined factorizations. We propose SQUARE, a Structured QUAntum REpresentation adapter that amplitude-encodes the bottleneck vector, applies a parameterized quantum circuit, and measures the resulting state. We show that each basis-probability feature is exactly a normalized quadratic form in the bottleneck coordinates, while the additional Pauli-

Z

readouts are signed linear combinations of these probabilities. The measured map can therefore parameterize interactions over

O(d^2)

coordinate pairs through a small set of shared circuit parameters, where

d

is the bottleneck dimension. It provides a structured parameterization within, rather than beyond, the classical normalized-quadratic feature class. In a disjoint same-pipeline evaluation over eight GLUE-derived controlled interaction tasks and five shared seeds, SQUARE achieves an average test accuracy of

0.7565

, compared with

0.7355

for an affine normalized-quadratic predictor,

0.7271

for the evaluated parameter-matched Givens mixing model,

0.6817

for an MLP, and

0.6155

for a frozen-circuit control. Under reduced supervision, it also shows consistent gains over the strongest evaluated classical comparator, with the same qualitative pattern across multiple frozen LM backbones. All circuit experiments use simulation, while the learned feature map can be evaluated exactly in batched PyTorch without quantum hardware.

Emily Jimin Roh, Hyojun Ahn, Hoyeong Lee +4

Korea University · Sookmyung Women’s University · Ulsan National Institute of Science and Technology +2

Large Language Model Quantization Frozen Language Model Frozen

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Aug 7, 2026quant-ph

Investigating Quantum-Embedded Transformers on Classical Datasets for Cross-Modality Classification

We test whether a parameterized quantum circuit (PQC) improves a hybrid quantum-classical model's performance on classical datasets, using an interface-matched classical map as the control while holding all other components fixed. Our architecture, Quantum-Embedded Attention (QEA), uses a learnable projector to compress backbone features into an

n_q

-dimensional angle vector, a shallow PQC to map those angles to one- and two-qubit Pauli expectations, and a classical attention decoder to produce class logits. We hypothesized the PQC would improve accuracy or seed-to-seed stability over a classical map with matched input/output dimensions. We test this with an interface-matched

2\times2

factorial on Breast Cancer Wisconsin at

n_q\in\{4,8\}

, independently swapping the PQC for a classical map and the attention decoder for a linear head, across five paired seeds per cell. Three of four paired quantum-minus-classical

95\%

confidence intervals include zero; the fourth, a

+1.63

percentage-point contrast for the attention decoder at

n_q=4

, reverses sign at

n_q=8

and does not survive correction across the four contrasts. The experiment thus shows no consistent PQC contribution and cannot establish equivalence. A five-dataset cross-modality grid shows comparable accuracy on AG~News, Breast Cancer Wisconsin, and BirdCLEF but a large deficit on CIFAR-10; these cells are not interface-matched and are interpreted descriptively. We report all planned canonical runs, distinguish current Pauli-readout results from legacy probability-readout experiments, and analyze bottleneck, simulation, finite-shot, and noise limitations. The results do not establish a quantum advantage; they demonstrate why controlled component attribution is necessary before crediting a hybrid model's performance to its quantum layer.

Hao-Yuan Chen

Computer Science, University of London

Hybrid Quantum-Classical Pipeline Quantum Circuits Multimodal Classification Transformer Architectures Readout

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