Hybrid Classical-Quantum Transfer Learning with Noisy Quantum Circuits

Hybrid quantum classical neural networks integrate parameterized quantum circuits (PQCs) with established deep learning architectures, but their performance depends strongly on the choice of quantum circuit architecture, a choice that remains largely manual. Most existing approaches rely on hand-designed or fixed circuit ansätze, requiring circuit structure, gate composition, and qubit connectivity to be specified in advance with no guarantee that they suit the task. This limitation is especially acute in image classification, where quantum circuits must transform features extracted by classical networks while remaining compact enough for practical training, requirements that generic, task-agnostic ansätze are unlikely to satisfy simultaneously. We extend EXAQC, an evolutionary framework for automated quantum circuit discovery, to image classification. EXAQC evolves PQCs as intermediate processing modules while retaining classical feature-extraction and prediction layers. On MNIST, Fashion-MNIST, and CIFAR-10, EXAQC achieves 98.42%, 90.62%, and 85.47% accuracy, respectively, while using comparable gate counts to other quantum architecture-search methods. Against classical networks, evolved hybrid models maintain comparable accuracy with substantially fewer trainable parameters, reaching 85.68% on CIFAR-10 with over 25$\times$ fewer parameters than a 10-layer CNN. Encoding choice also matters: rotation-based encodings (RX, RY, U3) outperform amplitude encoding by 22-25 points on CIFAR-10. These results demonstrate that automated circuit discovery yields compact quantum modules that can replace larger classical components in vision architectures while retaining competitive accuracy.

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.

In the noisy intermediate-scale quantum (NISQ) regime, quantum devices contain hardware-specific noise sources which restrict device-invariant error mitigation strategies. We explore transfer learning approaches to apply noise models learned on one quantum device to a different device with the help of a small amount of data. We create a real-hardware dataset from two IBM quantum devices, ibm_fez (source) and ibm_marrakesh (target), comprising 170 noisy and ideal circuit output distributions, with device calibration features added. We train a residual neural network on the source device to map noisy to ideal outcomes. The zero-shot transfer test shows a KL divergence of 1.6706 (up from 0.3014), establishing device specificity. With K = 20 fine-tuning samples, KL drops to 1.1924 (28.6% improvement over zero-shot), recovering 34.9% of the gap between zero-shot and in-domain KL. Ablation studies reveal that the major cause of mismatches across devices is CX gate error, followed by readout error. The results show quantum noise can be learned and fine-tuned with minimal samples, and provide a plausible approach to cross-device quantum error mitigation.