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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

arXiv:2609.33351v1cs.AIcs.LG

TL;DR

Medical retrieval may have few local adaptation examples, while shared input-independent unitary fidelity leaves rankings unchanged. QuPID uses input-dependent re-uploading and measurement readouts; with 60 parameters, it reports higher P@5 on ChestX-ray14 and MURA than frozen encoders, adapters, and LoRA, with broader tests in generation and non-medical retrieval.

  • Problem

    Medical retrieval needs adaptation when diagnostically distinct cases are poorly separated by frozen features, yet local archives may offer few adaptation examples and shared-unitary fidelity cannot learn a different ranking.

    Source: §1 · pp. 1–2

  • Method

    QuPID adapts frozen features with a shared circuit made input-dependent by data re-uploading and compares local-Pauli measurement readouts rather than states.

    Source: §1 · p. 2, §3.3 · p. 4

  • Results

    With 60 parameters, QuPID achieves higher P@5 than adapters and LoRA with up to 5.25M parameters on ChestX-ray14 and MURA; it also improves factual generation metrics over Adapter.

    Source: §4.1 · pp. 6–7

  • Takeaways & Limitations

    The reported results support circuit-defined measurement features as a practical route to parameter-efficient retrieval adaptation under classical GPU execution.

    Source: §5 · p. 9

    The method uses pooled frozen-backbone features and cannot recover information averaged away by CLS aggregation; the generation metrics lack clinician assessment.

    Source: §5 · p. 9

Abstract

from arXiv · show

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.

1 INTRODUCTION

The introduction asks whether a tiny readout can adapt medical retrieval when local data are scarce, and explains why shared-unitary fidelity retrieval cannot learn. QuPID instead combines input-dependent re-uploading with measurement readouts, then evaluates a 60-parameter feature map against larger and compact alternatives.

1 INTRODUCTION

  • Pooled image features can make diagnostically distinct cases nearly collinear, while RAG built on that geometry can retrieve inconsistent evidence and result in hallucination.The introduction frames the problem in settings where data protection rules keep images inside hospitals and local archives may offer few adaptation examples.Source: §1 · p. 1
  • A shared input-independent unitary cancels from fidelity, leaving squared inner products of frozen features and an identically zero contrastive gradient.The introduction describes this as an exact invariance, not a learned ranking change.Source: §1 · p. 2
  • QuPID makes retrieval input-dependent through data re-uploading and compares local-Pauli measurement readouts rather than quantum states.The paper uses “quantum” for a circuit-defined hypothesis class; every circuit is simulated classically, with no computational-advantage claim.Source: §1 · pp. 1–2
  • QuPID’s 60 shared parameters attain higher P@5 than adapters and LoRA with up to 5.25M parameters, with the lead over retuned adapters widest at 512 adaptation examples.The introduction also reports that an equally compact classical rotation-plane head narrows the full-budget margin, whose paired interval excludes zero.Source: §1 · p. 2
  • The paper characterizes QuPID as a structured feature map with 60 parameters jointly controlling 40 outputs, and analyzes its quadratic forms, re-uploading spectrum, and parameter-count generalization bound.Medical retrieval is the primary testbed; industrial inspection and fine-grained recognition provide additional tests.Source: §1 · p. 2

2 RELATED WORK

Related work motivates local adaptation for medical retrieval and places QuPID among parameter-efficient and measurement-based approaches. The paper distinguishes its retrieval-similarity use of a circuit from prior circuit-based weight or activation adaptation, while adopting classical simulation and matched controls as constraints on its claims.

2 RELATED WORK

  • Medical RAG uses retrieved context to reduce hallucination, but flat Euclidean embeddings can entangle clinically distinct, visually similar cases; centralized medical encoders do not address data-local adaptation.BiomedCLIP and MedCLIP serve as frozen references and as a QuPID backbone.Source: §2 · p. 2
  • Prior quantum parameter-efficient methods modify weights or activations, whereas QuPID places the circuit in a retriever’s similarity function and addresses its shared-unitary degeneracy.The paper also compares parameter-matched classical heads and random features as a compact nonlinear control.Source: §2 · p. 2
  • QuPID builds on measurement-based learning but targets label-free cosine retrieval, and the paper reports shared-backbone comparisons with parameter-, budget-, and wall-clock-matched controls rather than claiming hard simulation.The cited literature describes shallow local circuits as classically simulable and tuned classical baselines as strong competitors.Source: §2 · pp. 2–3

3 METHOD

The method first identifies why shared-unitary fidelity cannot adapt, then constructs an input-dependent measurement readout and trains it with label-free contrastive learning. Its analysis characterizes the readout and gives qualified spectral and generalization results; the paper also specifies important assumptions and deployment boundaries.

3.1 SETUP AND A DEGENERACY PITFALL IN QUANTUM RETRIEVAL

  • The setup seeks a lightweight transformation learned from unlabeled local data so pathologically consistent pairs score above pairs that merely share anatomy.The frozen ViT produces 1024-dimensional features for the hospital archive.Source: §3.1 · p. 3
  • Any input-independent shared unitary cancels from fidelity, leaving squared-cosine ranking on amplitude-encoded frozen features and a constant loss with zero gradient.Changing to another overlap-based similarity does not resolve this degeneracy; QuPID instead uses input dependence or a non-unitary readout.Source: §3.1 · p. 3

3.2 AMPLITUDE ENCODING WITH DATA RE-UPLOADING

  • Each circuit block combines trainable rotations, an entangling CNOT ring, and data re-uploading through fixed block-pooled feature projections; the default 10-qubit, three-block circuit has 60 trainable parameters.Measurement readout alone escapes the shared-unitary degeneracy, while re-uploading additionally enriches the function class.Source: §3.2 · p. 4

3.3 MEASUREMENT READOUT AND SIMILARITY

  • QuPID compares cosine similarity between 40 local-Pauli readouts, each an input-modulated quadratic form whose structured features share one circuit’s parameters.Without re-uploading, each component is a quadratic form in the normalized input; with re-uploading, trigonometric functions of linear input projections modulate it.Source: §3.3 · p. 4
  • For a clamped reference state and scalar probe, each re-uploading readout is a finite trigonometric polynomial with frequency support bounded by L(2nq − 1) when α = 1.This is a controlled-channel bound, not an end-to-end expressivity or classical-superiority result; frequency support does not mean every frequency is independently controllable.Source: §3.3 · p. 4

3.4 LABEL-FREE CONTRASTIVE ADAPTATION

  • Label-free adaptation uses SimCLR-style contrastive learning, pairing two pathology-preserving augmentations of an image as positives and using in-batch samples as negatives.In-batch negatives can include false negatives when patients share a pathology.Source: §3.4 · p. 5
  • A parameter-count bound gives a generalization-gap rate under bounded, smooth losses and a norm floor, motivating a small capacity budget rather than guaranteeing retrieval accuracy.The bound assumes a compact parameter domain and is generic to classes with the same conditions; reported training does not impose that box constraint.Source: §3.4 · p. 5
  • After classical simulation training, fixed parameters support GPU query-readout computation against cached archive readouts, without a quantum processor.On-site execution reduces data movement but is not formal privacy protection; the method operates on pooled backbone features and cannot restore information lost through frozen CLS aggregation.Source: §3.4 · p. 5

4 EXPERIMENTS

Under a shared label-free protocol, QuPID's 60-parameter readout outperforms larger adapters and LoRA on medical retrieval. The experiments also compare matched-budget designs and assess adaptation-size trends, broader benchmarks, generation, and modeled perturbations.

4.1 MAIN RETRIEVAL RESULTS

  • With 60 parameters, QuPID exceeds every adapter and LoRA configuration on ChestX-ray14 and MURA; versus the frozen encoder, P@5 rises +0.116 and +0.120.Its measured margins over a five-million-parameter adapter are +0.014 and +0.017. Evaluation used the same ViT-L/16 backbone and a label-free objective, with labels reserved for post-hoc evaluation.Source: §4 · p. 5, §4.1 · p. 6, Table 1 · p. 6
  • At 512 examples, QuPID reaches 0.401 P@5 versus 0.386 for the default 60-parameter rotation-plane head (+0.015); retuning reduces the Figure 2(c) margin to +0.040.At full budget, the same-control margin is +0.023; QuPID's full-to-512 drop is 0.027 versus 0.019 for the control.Source: Figure 2 · p. 6, §4.1 · p. 7
  • With backbone, readout, and hyperparameters unchanged, QuPID shows the same retrieval pattern on MVTec AD and CUB-200, with low-data margins roughly twice the full-budget margins.MVTec AD measures object-category retrieval, not defect localization.Source: §4.1 · p. 7
  • QuPID improves lexical-overlap metrics across both generation datasets and generators, while Adapter retains a small CIDEr advantage.CheXbert-F1 gains over Adapter are 0.018/0.017 and RadGraph-F1 gains are 0.011/0.012 for LLaVA-Med/CheXagent, respectively.Source: §4.1 · p. 7

4.2 ISOLATING THE MECHANISM

  • The 60-parameter circuit couples 40 measurement features through a norm-preserving transformation, making their shared quadratic forms input-dependent through re-uploading.The ten-qubit circuit is simulated exactly using 1024-dimensional linear algebra, so the controls test representational choices under classical simulation.Source: §4.2 · p. 8
  • Depth saturates beyond L = 3, and both single-qubit and pairwise readouts contribute; at full budget, the rotation-plane head narrows QuPID's margin to 0.023.The rotation-plane comparison evaluates the combined design, without separating input modulation, readout rank, and entanglement; restricted RFF and Quadratic controls are not exhaustive dequantizations.Source: §4.2 · p. 8
  • The default operating point lies on a plateau across tested qubit count, topology, readout width, temperature, and feature noise; modeled gate noise degrades retrieval gradually.At S = 10^4, finite-shot readout is within 0.002 P@5 of exact expectations; the simulations omit crosstalk, coherent errors, and readout error.Source: §4.2 · pp. 8–9, Figure 5 · p. 9
  • QuPID uses 1.60 times a lightweight adapter's per-epoch training time, while inference time and peak adaptation memory are comparable.Per-query inference is 7.6 versus 7.1 ms, and peak adaptation memory is 3,582 versus 3,728 MB; parameter efficiency is not computational efficiency.Source: §4.2 · pp. 8–9

5 LIMITATIONS AND CONCLUSION

QuPID's compact readout exceeds adapters and LoRA on P@5, but its conclusions are bounded by classical execution, pooled-feature information loss, and limits in the evaluation and comparison evidence.

5 LIMITATIONS AND CONCLUSION

  • Classical circuit simulation and GPU inference are the deployment setting; pooled frozen [CLS] features cannot recover information already averaged away.Patch-token variants are left for future work; amplitude encoding also requires strict L2 normalization and power-of-two dimensions, so a 768-dimensional backbone requires zero-padding to 1024.Source: §5 · p. 9
  • The retriever is trained separately from the generator, generation metrics lack clinician assessment, and data-local adaptation is not formal privacy protection.The full-budget margin over the rotation-plane head has paired intervals excluding zero, but intervals do not exclude zero at 512 examples, including after validation-selected tuning.Source: §5 · p. 9
  • QuPID uses 60 parameters shared across 40 input-dependent measurement features and exceeds adapters and LoRA with up to 5.25M trainable parameters in P@5.The work presents circuit-defined measurement features as a practical route to parameter-efficient retrieval adaptation under classical GPU execution.Source: §5 · p. 9

ETHICS STATEMENT

The work uses publicly distributed datasets, including de-identified medical datasets, and frames the system as supervised clinical assistance rather than a replacement for decisionmaking.

ETHICS STATEMENT

  • The datasets are publicly distributed; medical datasets are de-identified, with ChestX-ray14 and MIMIC-CXR collected under curator IRB approval.MIMIC-CXR access follows a credentialed data use agreement, while MURA and CheXpert are distributed under research use agreements.Source: ETHICS STATEMENT · p. 10
  • Any deployment is intended to assist rather than replace clinical decisionmaking and requires physician supervision and applicable regulatory review.The system should include mechanisms for flagging low-confidence retrievals.Source: ETHICS STATEMENT · p. 10
  • Data-local adaptation reduces data movement but is not privacy-preserving learning and does not defend against parameter-level attacks such as membership inference.Source: ETHICS STATEMENT · p. 10

AI USE STATEMENT

The appendix introduces QuPID’s circuit ingredients and simulated implementation, then situates its GPU inference protocol among recent variational quantum learning practices. The authors also describe how generative AI assisted with manuscript preparation.

AI USE STATEMENT

  • Generative AI assisted with text editing, reference and figure-code work, proof revision, and drafting interpretive sentences; the authors checked the assisted content and report no AI-generated data or experimental values.The authors reviewed the content and take responsibility for the paper.Source: AI USE STATEMENT · p. 10

A BACKGROUND ON QUANTUM MACHINE LEARNING

  • The appendix gives a QuPID-focused introduction to qubits, amplitude encoding, parameterized circuits with data re-uploading, and measurement readout.It is not a general quantum-computing introduction, and readers familiar with those ingredients can skip to Appendix B.Source: A BACKGROUND ON QUANTUM MACHINE LEARNING · p. 15

A.1 QUBITS AND HILBERT-SPACE REPRESENTATIONS

  • With nq = log2 d, the state dimension equals the input dimension, while each measurement yields only one scalar expectation per observable.The paper therefore emphasizes encoding, circuit, and readout design rather than raw state dimension.Source: §A.1 · p. 15

A.2 AMPLITUDE ENCODING

  • Amplitude encoding places a normalized feature vector in the state amplitudes using nq = log2 d qubits, but discards feature scale and requires power-of-two d.Exact hardware preparation of an arbitrary d-dimensional amplitude state takes O(d) elementary gates; the reported results use simulation, where encoding is normalization.Source: §A.2 · p. 15

A.3 PARAMETERIZED QUANTUM CIRCUITS AND DATA RE-UPLOADING

  • Data re-uploading reinjects the input between trainable layers, making the overall map input-dependent and setting the Fourier spectrum available to the readout.A plain parameterized circuit instead applies a fixed unitary to the encoded state.Source: §A.3 · pp. 15–16

A.4 MEASUREMENT READOUT

  • QuPID compares separate measurement-readout vectors of local one- and two-body Pauli expectations, rather than comparing state overlaps.The paper links this readout choice to avoiding the inert shared-circuit fidelity construction and notes its locality keeps gradients well behaved.Source: §A.4 · p. 16

A.5 REFERENCE IMPLEMENTATION

  • The reference implementation uses 2nqL = 60 trainable parameters; after training, GPU inference runs the input-dependent readout and reuses cached archive readouts.At nq = 10, the statevector has 1024 amplitudes, so hardware transfer is unnecessary for this deployment; the authors do not extend that argument to arbitrary larger circuits.Source: §A.5 · p. 16

A.6 POSITIONING AMONG RECENT VARIATIONAL QUANTUM LEARNING STUDIES

  • Recent variational quantum-learning studies predominantly use hybrid architectures, task-specific encodings, and simulation-based evaluation, conventions QuPID follows.QuPID trains its compact measured feature map by classical simulation and runs fixed-parameter inference on a GPU; simulated noise does not validate physical-device robustness.Source: §A.6 · p. 17, Table 2 · p. 17

B.1 PROOF OF PROPOSITION 1

A shared input-independent unitary cancels from fidelity, leaving rankings fixed to the frozen features and the contrastive gradient zero. The appendix bounds the re-uploading frequency range and generalization gap, then numerically verifies the degeneracy of the naive design.

B.1 PROOF OF PROPOSITION 1

  • The shared-unitary fidelity loss is constant in its parameters because the unitary cancels, so rankings equal squared-cosine rankings of frozen features.The result also extends to overlap-based distances and monotone transforms of fidelity.Source: §B.1 · pp. 17–18

B.2 PROOF SKETCH OF PROPOSITION 2

  • For one- and two-body observables, the local-readout frequency bound is 2814 at nq = 10 and L = 3, below the conservative bound of 3069.Neither bound guarantees that its boundary or every lower frequency is attained; the proposition gives no lower bound against classical surrogates.Source: §B.2 · p. 18, Figure 6 · p. 18

B.3 PROOF SKETCH OF PROPOSITION 3

  • The covering argument gives a uniform generalization gap with leading dependence p/n for the restricted class ΘR,c.The bound relies on a norm floor ∥z∥ ≥ c, which is not guaranteed by the architecture and is empirically checked only on observed data.Source: §B.3 · p. 19

B.4 NUMERICAL VERIFICATION OF PROPOSITION 1

  • 500 random draws reproduce the frozen ranking exactly, and the naive design’s parameter-shift gradient vanishes to floating-point precision.The corrected design satisfies none of the three degeneracy criteria.Source: §B.4 · pp. 19–20, Table 3 · p. 19

C EXPERIMENTAL SETUP

The experiments evaluate retrieval on patient-separated medical datasets, alongside report generation and non-medical benchmarks. Methods share a label-free training protocol and frozen ViT-L/16 features, with labels reserved for evaluation.

Datasets and splits

  • Medical retrieval uses ChestX-ray14 and MURA, with gallery, validation, and query patients kept pairwise disjoint.Relevance is label-set overlap on ChestX-ray14 and shared region-pathology category on MURA.Source: C EXPERIMENTAL SETUP · pp. 20–21

Baselines

  • Baselines include frozen ViT-L/16 features, adapters, LoRA, compact classical controls, and centrally pretrained medical encoders.All adaptation baselines start from 1024-dimensional ViT-L/16 features; post-encoder heads keep features frozen, while LoRA updates attention projections.Source: C EXPERIMENTAL SETUP · p. 20

Protocol and metrics

  • All methods train with the label-free objective, while labels are used only for post-hoc evaluation and not for tuning or model selection.The full adaptation budgets are 32,768 images on ChestX-ray14 and 16,384 on MURA; results report means and standard deviations over five seeds.Source: C EXPERIMENTAL SETUP · p. 20
  • Retrieval is assessed with P@5, MAP@10, and NDCG@10, while generation uses lexical metrics and clinical-efficacy proxies with frozen medical generators.Generation metrics include BLEU-4, ROUGE-L, METEOR, CIDEr-D, CheXbert micro-F1, and RadGraph-F1.Source: C EXPERIMENTAL SETUP · p. 20

D IMPLEMENTATION DETAILS

Implementation uses shared hyperparameters and a simulated circuit-training pipeline, with compact classical controls designed to probe the role of QuPID’s parameterization. The parameter-matched rotation-plane control shares the budget, isometry, and output width but not the input-dependent Pauli form.

Optimization

  • Gradients use a two-term parameter-shift rule per gate with the classical chain rule through cosine similarity and contrastive loss.Statevector backpropagation is used for simulation timings; the shift rule supplies the hardware cost model.Source: D IMPLEMENTATION DETAILS · p. 22

Parameter-matched controls

  • The Quadratic control uses 164 parameters across 40 outputs, but all outputs depend on four squared projections sharing the same span.Its quadratic forms have rank at most four, so its nominal parameter count does not match QuPID’s input access or expressivity.Source: D IMPLEMENTATION DETAILS · p. 22
  • The 60-parameter rotation-plane control matches QuPID’s budget, isometry, and 40-output width, but uses fixed rank-one quadratic forms.QuPID’s Pauli forms are full-rank and input-dependent; this comparison tests the combined parameterization rather than isolating those structural differences.Source: D IMPLEMENTATION DETAILS · p. 22

Rotation-plane configuration

  • The rotation-plane sweep fixes a 1024-dimensional input, 60 angles, 40 outputs, and a shared training configuration.Training uses AdamW, learning rate 10^-3, batch size 32, temperature 0.07, and 50 epochs.Source: D IMPLEMENTATION DETAILS · p. 22

E FULL RETRIEVAL METRICS

QuPID leads the reported retrieval metrics across both medical datasets, while its report-generation comparisons vary by metric. Representative reports illustrate how retrieved cases inform generated text, but cannot establish how often findings are supported.

E FULL RETRIEVAL METRICS

  • QuPID adds 0.116 P@5 on ChestX-ray14 and 0.120 on MURA over the frozen backbone; its gains over the strongest adapter are smaller.The gap over a five-million-parameter adapter is 0.014 to 0.017.Source: E FULL RETRIEVAL METRICS · pp. 22–23, Table 11 · p. 25
  • Across three non-medical benchmarks, the adapted readout exceeds the listed frozen and classical comparators at both budgets.These results test recurrence of the retrieval pattern, not transfer of one trained head between datasets.Source: E FULL RETRIEVAL METRICS · p. 24
  • The readout-only variant reaches 0.412 P@5, while re-uploading supplies the remaining 0.016 at full budget.The full-budget rotation-plane comparison has a 0.023 gap, motivating the equal-budget analysis.Source: E FULL RETRIEVAL METRICS · p. 24, Table 6 · p. 24
  • QuPID improves BLEU-4, ROUGE-L, and METEOR over Adapter, while Adapter retains a small CIDEr lead.The finding-based proxies favor QuPID for both generators, but measure agreement between extracted findings and references rather than clinical outcomes.Source: E FULL RETRIEVAL METRICS · pp. 24–25, Table 7 · p. 24, Table 8 · p. 25

F QUALITATIVE EXAMPLES

  • The selected retrieval-grounded examples show pathologically consistent cases narrowing a differential to pneumonia versus pulmonary edema and supporting a displaced radius fracture.Two selected examples cannot estimate how often findings are supported.Source: Figure 10 · p. 26

G ROBUSTNESS AND TRAINABILITY DIAGNOSTICS

The diagnostics find that feature perturbations do not disproportionately destabilize QuPID at the tested scale, while gradient and parameter-update checks support a trainable readout. Circuit and hyperparameter sweeps show where performance saturates, and a single cross-site test is encouraging but not conclusive.

G ROBUSTNESS AND TRAINABILITY DIAGNOSTICS

H.1 CIRCUIT DESIGN: QUBITS, ENTANGLING GATES, AND OBSERVABLES

  • Depth performance saturates by L = 3, while using ring connectivity recovers all but 0.001 P@5 of all-to-all connectivity with 10 rather than 45 CNOTs per layer.Removing CNOTs entirely costs 0.019 P@5; increasing readout width beyond two-body terms gains only 0.002 P@5.Source: §H.1 · pp. 27–28, Figure 12 · p. 28, Table 15 · p. 28

H.2 HYPERPARAMETER SENSITIVITY

  • P@5 varies by at most 0.011 across a sevenfold temperature range and 0.008 across an eightfold batch-size range, with defaults inside both plateaus.The defaults were fixed a priori on a disjoint pilot subset; the authors do not claim insensitivity to every hyperparameter.Source: §H.2 · p. 28, Figure 13 · p. 29

H.3 CROSS-SITE TRANSFER

  • On CheXpert without further training, QuPID gains 0.029 P@5 over frozen features versus 0.012 for the adapter, but the evidence is limited to one site pair.The adapted-module margin falls from 0.027 in-domain to 0.017 cross-site.Source: §H.3 · p. 29, Table 17 · p. 29

I NOISE-AWARE SIMULATION

  • These noise analyses are simulator-level diagnostics, not hardware benchmarks, and support no claim of robustness on physical devices.The evaluated channels act on Pauli components in observable-dependent ways; amplitude damping can shift readouts rather than merely scale them.Source: I NOISE-AWARE SIMULATION · p. 29, §I.1 · pp. 29–30

I.2 POST-TRAINING NOISE SENSITIVITY

The appendix tests evaluation-time noise, training through noise, finite-shot readout, and classical alternatives. Results show gradual degradation under modeled channels and advantages over the tested classical controls, alongside explicit limits on hardware and generalization claims.

I.2 POST-TRAINING NOISE SENSITIVITY

  • At p = 0.01, the largest post-training noise drop is 0.011 P@5, and at p = 0.05 QuPID remains above the frozen baseline of 0.312.Phase flip causes the smallest degradation in this experiment; amplitude damping and bit flip cause the largest.Source: §I.2 · p. 30, Table 18 · p. 30

I.3 NOISE-AWARE TRAINING

  • Noise-aware training recovers part of the post-training loss in every tested case, but no configuration returns to the noiseless 0.428 P@5.The authors describe this as mitigation, not evidence that noise is harmless or a useful regularizer.Source: Figure 14 · p. 30, §I.3 · p. 31, Table 19 · p. 31

I.4 SHOT BUDGET FOR HARDWARE READOUT

  • The sufficient shot bound preserves comparisons only when exact score gaps exceed γ, conditional on a norm floor, and does not address gate noise or hardware latency.For an archive-wide guarantee, the sufficient shot count depends logarithmically on archive size; it is not a prediction of average P@5.Source: §I.4 · p. 31

I.5 FINITE-SHOT READOUT

  • At S = 10^4 shots, retrieval is within 0.002 P@5 of the exact-expectation reference, while S = 10^2 gives a larger loss.This finite-sampling experiment leaves the circuit noiseless and does not establish the simultaneous ranking guarantee or device feasibility.Source: §I.5 · p. 32, Table 20 · p. 32

J.1 TRAIN–TEST RETRIEVAL GAPS

  • Observed train–test P@5 gaps range from 0.031 to 0.229 at n = 128 and from 0.002 to 0.045 at the full budget, increasing with parameter budget among four families.The 60-parameter and 164-parameter readouts have measured gap ratios of 0.61, 0.59, 0.57, 0.57, and 0.50 across the sweep; this does not test whether a contrastive-risk bound is tight.Source: §J.1 · pp. 32–33, Table 21 · p. 32, Figure 15 · p. 33

J.2 CAPACITY- AND REGULARIZATION-MATCHED BASELINES

  • At n = 512, retuning narrows the adapter margin from +0.054 to +0.040 P@5, while QuPID remains ahead at every tested adaptation size in this sweep.The selected adapter settings become wider and less regularized as adaptation data grows; this comparison covers a finite search space.Source: §J.2 · pp. 33–34, Table 22 · p. 33

J.3 OTHER CLASSICAL MODULES AT THE SAME BUDGET

  • At full budget and 512 examples, QuPID scores 0.428 and 0.401 P@5 versus 0.405 and 0.386 for the rotation-plane control, margins of +0.023 and +0.015.The default isometric control is the closest among the tested near-60-parameter classical modules.Source: §J.3 · p. 34, Table 23 · p. 34
  • QuPID leads the rotation-plane P@5 means by 0.015, 0.015, 0.019, 0.021, and 0.023 as adaptation size grows, while its train–test gap is a separate measure.The rotation-plane gap falls from 0.039 to 0.004.Source: §J.3 · pp. 34–35

J.4 STRONGER CLASSICAL SURROGATES

Stronger classical surrogates, report-generation comparisons, and deployment stress tests probe the scope of QuPID's advantage. The results favor QuPID among tested surrogates and settings, while the authors delimit what those comparisons establish.

J.4 STRONGER CLASSICAL SURROGATES

  • At full budget, all reported paired intervals exclude zero; at 512 examples, intervals for the 600-parameter Givens and tuned rotation-plane heads include zero.Against the strongest surrogate, QuPID's win rates are 0.58 at full budget and 0.63 at 512 examples.Source: §J.4 · p. 35, Table 24 · p. 35
  • At full budget, QuPID reaches 0.428 P@5, above the tested classical surrogates, including a 328,000-parameter spectrum-sampled head at 0.407.Without input modulation, tested heads remain at or below 0.417; this family of constructions does not bound all classical methods.Source: §J.4 · pp. 35–36, Table 24 · p. 35

K DOES RETRIEVAL QUALITY DRIVE GENERATION

L.1 ARCHIVE SIZE

  • At the full-cache endpoint, QuPID falls from 0.502 to 0.428 P@5 and the adapter from 0.478 to 0.401, with QuPID's margin staying +0.024–+0.027 across cache sizes.The endpoint stores 112,120 images, with 81,664 eligible gallery images after patient exclusion; the sweep reports accuracy, not constant latency.Source: §L.1 · p. 37, Figure 17 · p. 37

L.2 FEATURE NORMALIZATION AND NORM SHIFT

  • Across tested preprocessing choices, P@5 varies by at most 0.012; whitening scores 0.431 versus 0.428 for default L2 normalization.The authors retain L2 normalization because the difference is within seed variation and whitening requires an additional archive pass.Source: §L.2 · p. 37, Table 26 · p. 38

L.3 SEQUENTIAL SITE ADAPTATION

  • After three sequential sites without replay, QuPID loses 0.026 P@5 on site 1 versus 0.058 and 0.060 for the two adapters, and its final module has the best mean across sites.No continual-learning method or prior-solution regularization is used, and joint training remains better for every method.Source: §L.3 · p. 38, Table 28 · p. 38

M.1 EQUAL WALL-CLOCK INSTEAD OF EQUAL PARAMETERS

The equal-wall-clock comparison gives classical baselines more adaptation time, while the rotation-plane tuning study uses its own validation-trial budget. The analysis also reports variability and effect sizes for paired comparisons and limits the scope of its empirical claims.

M.1 EQUAL WALL-CLOCK INSTEAD OF EQUAL PARAMETERS

  • At n = 512, QuPID’s margin over the three listed classical modules is +0.047, and at full budget it is +0.011; the ordering does not change with equal wall-clock time.The modules gain 0.003 to 0.011 P@5 from extra epochs and random restarts selected by contrastive validation loss.Source: §M.1 · p. 39, Table 29 · p. 39
  • At full budget, tuned rotation-plane scores 0.414 versus fixed QuPID at 0.428, a +0.014 margin whose paired 95% interval excludes zero; at 512, the +0.007 margin interval includes zero.The tuning study allowed 30 validation trials, with per-trial adaptation caps of 60 seconds at n = 512 and 3,600 seconds at full budget.Source: §M.1 · p. 39

M.2 VARIANCE DECOMPOSITION AND EFFECT SIZES

  • At n = 512, subset draws account for 72% of variance; at full budget, subset draws and initialization contribute comparably.The crossed design uses five initializations and five adaptation-subset draws.Source: Table 30 · p. 39, §M.2 · p. 40
  • Cliff’s δ is 0.44 at n = 512 and 0.21 at full budget, while QuPID’s per-query win rates are 0.67 and 0.58, respectively.The full-budget difference remains small; these statistics are conditional summaries for the included comparators, not a per-query guarantee.Source: Table 31 · p. 39, §M.2 · p. 40

N DESIGN CHOICES AND EMPIRICAL SCOPE

  • The reported evidence uses classical simulation and does not establish computational quantum advantage; the default paired interval includes zero at 512 but is positive at full budget.The intervals concern default paired comparisons under the stated approximation and fixed evaluation split.Source: §M.2 · p. 40, N DESIGN CHOICES AND EMPIRICAL SCOPE · p. 41

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