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Evolving Hybrid Quantum-Classical Architectures for Image Classification
Devroop Kar, Daniel Krutz, Travis Desell
TL;DR
Manual circuit-architecture choices complicate hybrid quantum-classical image classification, where PQCs must process compressed image features. This work extends EXAQC to evolve PQCs within classical feature-extraction and prediction layers, reporting competitive accuracy across three benchmarks with compact circuits and fewer model parameters than classical counterparts.
Problem
PQC effectiveness depends on architectural choices that are usually specified manually, while image inputs far exceed the handful of qubits available on near-term hardware.
Source: §1 · pp. 1–2Method
EXAQC evolves a PQC between a classical image encoder and decoder, jointly learning the representation supplied to the circuit.
Source: §1 · p. 2, §2.1 · p. 3, §7 · p. 9Results
EXAQC achieves 98.42%, 90.62%, and 85.47% accuracy on full 10-class MNIST, Fashion-MNIST, and CIFAR-10, respectively, with evolved circuits containing 20–30 gates in the resource comparison.
Source: §7 · p. 9Takeaways & Limitations
On CIFAR-10, EXAQC reaches 85.68% with 100,173 parameters, matching the 10-layer CNN at 85.50% with 96.1% fewer parameters.
Source: §5 · p. 9Comparisons with prior work are not strictly controlled because preprocessing, classification settings, quantum representations, resource-counting conventions, and dataset formulations differ.
Source: §6 · p. 9
Abstract
from arXiv · showhide
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 ans\"atze, 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 ans\"atze 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.
1 INTRODUCTION
Choosing a PQC architecture remains difficult because gate composition, depth, connectivity, and encoding affect effectiveness and trainability, while image inputs far exceed the handful of qubits available on near-term hardware. This work extends EXAQC to image classification and reports competitive results across three datasets, with performance also varying by representation, encoding, and parameter budget.
1 INTRODUCTION
- Image inputs contain 784 values for MNIST and Fashion-MNIST and 3,072 for CIFAR-10, far exceeding the handful of qubits available on near-term hardware.Classical feature extractors compress images so the quantum circuit can retain a small input as source-image complexity grows.Source: §1 · pp. 1–2
- The work extends EXAQC to image classification by evolving PQCs between classical feature extraction and prediction, and investigates whether these modules can be compact and task-suited.It also introduces U3 gates as a quantum encoding mechanism, unlike previous works.Source: §1 · p. 2
RQ1: Scalability and Hybrid Effectiveness
- EXAQC reaches 98.42%, 90.62%, and 85.47% on the full 10-class MNIST, Fashion-MNIST, and CIFAR-10 tasks, exceeding compared architecture-search methods on CIFAR-10 while using fewer gates than EQNAS and AQEA-QAS.Source: §1 · p. 2
RQ2: Representation Dimensionality
- CIFAR-10 requires 8–10 qubits, 42–60-gate circuits, and a larger search budget, indicating that quantum representation affects performance and circuit size.The section frames this as a study of representation dimensionality and its effects on performance, complexity, convergence, and computational requirements.Source: §1 · p. 2
RQ3: Quantum Encoding Effectiveness
- On CIFAR-10, rotation-based encodings score 83.75–86.68% versus 61.38% for amplitude encoding; U3 performs best but produces the largest circuits.Encoding differences are under one point on MNIST.Source: §1 · p. 2
RQ4: Parameter Efficiency
- 85.68% vs. 85.50% on CIFAR-10 matches the 10-layer CNN with 96.1% fewer parameters, while 91.11% vs. 89.47% on Fashion-MNIST exceeds the one-layer CNN with 54.8% fewer parameters.These comparisons address whether evolved quantum components retain competitive performance with fewer trainable parameters.Source: §1 · p. 2
2 METHODOLOGY
EXAQC places an evolved parameterized quantum circuit between classical image-feature extraction and prediction. It jointly trains the hybrid model while evolving circuit structure, allowing input representation and circuit architecture to be varied rather than fixed in advance.
2 METHODOLOGY
- A classical encoder compresses each image for an evolved PQC, whose measurements a classical decoder maps to class predictions.The design separates raw image dimensionality from the quantum representation dimensionality.Source: §2 · p. 2, Figure 1 · p. 3
2.1 HYBRID QUANTUM CLASSICAL ARCHITECTURE
- The hybrid model maps image x through encoder Eψ, quantum circuit Qθ,A with trainable parameters θ and evolved architecture A, then decoder Dϕ to produce predictions.The encoder maps image dimensions C × H × W to a quantum-facing representation of dimension dq.Source: §2.1 · p. 3
2.2 CLASSICAL FEATURE AND QUANTUM ENCODING
- RX and RY encodings use one feature per input qubit, U3 uses three features per qubit, and amplitude encoding maps dq features to ⌈log2(dq)⌉ qubits.The encoder may be an identity block, linear block, MLP, or configurable convolutional feature extractor followed by a projection.Source: §2.2 · p. 3
2.3 EVOLUTIONARY QUANTUM CIRCUIT SEARCH
- Each PQC is a variable-length genome of ordered gates, with evolution determining gate count and arrangement instead of fixing a circuit ansatz.Structural mutation can add, enable, disable, or reorder gates; crossover combines parent circuits, and compatible parameters can transfer to offspring.Source: §2.3 · pp. 3–4
- Candidate circuits are evaluated in parallel under asynchronous steady-state evolution, where offspring compete for population insertion after evaluation rather than waiting for generational replacement.Island-based evolution also allows multiple subpopulations to explore different architecture regions while exchanging information.Source: §2.3 · p. 4
2.4 TRAINING AND QUANTUM READOUT
- Encoder, quantum, and decoder parameters are trained by minimizing cross-entropy, validation performance guides evolutionary selection, and measured output qubits feed the classical decoder.Readout can provide computational-basis probabilities or Pauli-Z expectation values.Source: §2.4 · p. 4
3 EXPERIMENTAL DESIGN
The experimental design evaluates EXAQC across datasets, representation choices, quantum encodings, and classical baselines. It reports accuracy alongside circuit and model resources, with parameter reductions interpreted jointly with predictive performance.
3 EXPERIMENTAL DESIGN
- Test performance and variability are reported across 10 independent runs, circuit complexity by gate count, and quantum parameters as a resource measure; asynchronous search progress is counted by evaluated circuits.All evolutionary experiments use the same implementation and quantum simulation backend.Source: §3 · p. 4
Scalability and Representation Studies
- EXAQC is evaluated on MNIST, Fashion-MNIST, and CIFAR-10 for accuracy, circuit resources, and convergence; representation dimensionality and qubit count are reported separately when encoding maps multiple features per qubit.The representation study varies identity, MLP, or CNN encoders while holding the evolutionary configuration fixed.Source: §3 · p. 5
Encoding and Parameter Efficiency
- Amplitude, RX, RY, and U3 encodings are compared on each dataset with encoder and evolutionary configuration held fixed, reporting test accuracy and evolved gate and parameter counts.The evaluation asks whether encoding effects depend on the dataset.Source: §3 · p. 5
- Hybrid models are compared with classical MLP, CNN, and ResNet baselines; classical models replace the evolved PQC with fully connected transformations, with encoder and decoder configurations held constant where possible.Parameter reduction is assessed jointly with predictive performance because fewer parameters alone do not establish comparable accuracy.Source: §3 · pp. 4–5
4 RESULTS
The experiments evaluate predictive performance and circuit resources against prior quantum approaches, encoding sensitivity, and the accuracy–parameter trade-off against classical models. Results also show how an evolved CIFAR-10 hybrid processes compressed image features.
4 RESULTS
- The evaluation covers predictive performance and circuit resources, quantum encoding sensitivity, and accuracy–parameter trade-offs against classical architectures.Experiments use 10 independent runs, 5–6 qubits for MNIST and Fashion-MNIST, and 8–10 qubits for CIFAR-10.Source: §4 · p. 5
4.1 COMPARISON WITH PRIOR IMAGE-CLASSIFICATION APPROACHES
- 98.42 ± 1.03%, 90.62 ± 0.8%, and 85.47 ± 1.37% accuracy on full 10-class MNIST, Fashion-MNIST, and CIFAR-10 exceed compared search methods on CIFAR-10.EXAQC uses 20 gates and 14 parameters on MNIST, and 30 gates and 21 parameters on Fashion-MNIST and CIFAR-10; its circuits use fewer gates than EQNAS and AQEA-QAS across all three datasets.Source: §4.1 · p. 5, Table 1 · p. 6
4.2 EFFECT OF QUANTUM ENCODING STRATEGY
- On CIFAR-10, amplitude encoding achieves 61.38±0.80%, versus 83.75±1.40%, 84.37±1.30%, and 86.68±1.50% for RX, RY, and U3.With qubit count held fixed, U3 receives three times as many input features as RX or RY; matching input dimensions instead would require tripling RX/RY qubits and increase computational expense.Source: §4.2 · p. 6, Table 2 · p. 7
4.3 PARAMETER REDUCTION
- 85.68% accuracy with 100,173 parameters on CIFAR-10 compares with 85.50% and 2,569,962 parameters for the 10-layer CNN.On Fashion-MNIST, the CNN-based EXAQC model achieves 91.11% with 33,844 parameters, compared with 89.47% and 74,922 parameters for the one-layer CNN.Source: Table 3 · p. 7, §4.3 · p. 7
4.4 CIRCUIT VISUALIZATION
- The CIFAR-10 encoder compresses 3,072 input values to 8 features, which are RY-encoded onto 8 qubits before quantum processing.The evolved circuit uses an irregular arrangement of rotations, controlled gates, and distant-qubit Ising interactions; probability readout yields 256 values that a linear decoder maps to 10 class logits.Source: §4.4 · pp. 7–8, Figure 3 · p. 8
5 DISCUSSION
EXAQC remains effective across MNIST, Fashion-MNIST, and CIFAR-10, while results vary with the classical representation and quantum encoding. The hybrid models also retain comparable classification performance to classical counterparts with fewer trainable parameters.
RQ1
- 98.42%, 90.62%, and 85.47% test accuracy on full 10-class MNIST, Fashion-MNIST, and CIFAR-10 accompany fewer gates than EQNAS and AQEA-QAS across all three datasets.On CIFAR-10, EXAQC exceeds the reported accuracies of the architecture-search methods included in Table 1.Source: §5 · p. 8
RQ2
- On Fashion-MNIST, a CNN encoder achieves 91.11% accuracy with 33,844 parameters, compared with 86.95% and 109,421 parameters using an MLP encoder.On CIFAR-10, simple encoders did not provide sufficiently informative features, and a CNN encoder was required to reach competitive accuracy.Source: §5 · p. 8
RQ3
- On CIFAR-10, RX, RY, and U3 achieve 83.75–86.68% accuracy versus 61.38% for amplitude encoding, while U3 uses 60 gates and 40 parameters.Encoding differences are smaller on MNIST, where all encodings fall within one percentage point (95.65–96.42%).Source: §5 · p. 8
RQ4
- On CIFAR-10, EXAQC achieves 85.68% with 100,173 parameters versus 85.50% for the 10-layer CNN, using 96.1% fewer parameters.On Fashion-MNIST, EXAQC achieves 91.11% versus 89.47% for the one-layer CNN with 54.8% fewer parameters; the evolved PQCs use 20–30 gates.Source: §5 · p. 9
6 LIMITATIONS AND FUTURE WORK
The evaluation has limits in cross-paper comparability, feature quality, hardware realism, and search cost. Future work targets more standardized comparisons, joint component optimization, hardware tests, and more efficient search.
6 LIMITATIONS AND FUTURE WORK
- Prior-work comparisons are not strictly controlled because preprocessing, classification settings, quantum representations, and resource-counting conventions differ.Prior works also use simplified dataset formulations; the authors call for standardized evaluations.Source: §6 · p. 9
- Evolved PQC effectiveness depends on classical encoder feature quality, motivating joint optimization of the encoder, quantum encoding, and circuit architecture.High-dimensional classification requires compact quantum-facing representations that preserve task-relevant information.Source: §6 · p. 9
- Because evaluation primarily relies on simulation, robustness under realistic noise and on quantum hardware remains to be assessed.Noise-aware evolutionary objectives are proposed as a natural extension.Source: §6 · p. 9
- Evolutionary search grows increasingly expensive as circuit and representation spaces expand, prompting work on distributed search and multi-objective optimization.The authors also propose evolving additional hybrid components, including quantum convolutional blocks.Source: §6 · p. 9
7 CONCLUSION
The paper extends EXAQC to hybrid image classification, evolving compact quantum components while learning the classical representation supplied to them. Across three benchmarks, the models achieve competitive accuracy with fewer trainable parameters than a 10-layer CNN on CIFAR-10.
7 CONCLUSION
- 98.42%, 90.62%, and 85.47% accuracy are achieved on full 10-class MNIST, Fashion-MNIST, and CIFAR-10, respectively.The evolved circuits contain 20–30 gates in the resource comparison.Source: §7 · p. 9
- 85.68% accuracy with 100,173 trainable parameters is achieved by the CIFAR-10 hybrid model, versus 85.50% with 2,569,962 parameters for the 10-layer CNN.The paper presents this comparison as evidence that evolved quantum components can replace larger classical components while retaining competitive performance.Source: §7 · p. 9
- On CIFAR-10, rotation-based encodings reach 83.75–86.68% accuracy, compared with 61.38% for amplitude encoding.U3 achieves the highest evaluated encoding accuracy, 86.68%.Source: §7 · p. 9
- EXAQC trains the classical encoder jointly with each evolved circuit, learning the representation supplied to the PQC.The conclusion identifies joint consideration of feature extraction, quantum encoding, and circuit architecture as important for parameter-efficient hybrid models.Source: §7 · p. 9
REPRODUCIBILITY STATEMENT
The reproducibility statement describes the experimental methods and setup and reports use of public datasets, multiple independent runs, and repository scripts.
REPRODUCIBILITY STATEMENT
- The methodology describes EXAQC search, the hybrid architecture, quantum encoding and readout strategies, and evaluation metrics.The experimental setup reports datasets, model configurations, hyperparameters, and independent-run counts.Source: REPRODUCIBILITY STATEMENT · p. 10
- Experiments use publicly available MNIST, Fashion-MNIST, and CIFAR-10 datasets with appropriate citations.Source: REPRODUCIBILITY STATEMENT · p. 10
- Results are reported across multiple independent runs with variation measures where applicable, and experiment scripts are available in the repository.Source: REPRODUCIBILITY STATEMENT · p. 10
AI USAGE
The appendix reviews hybrid image-classification and quantum architecture-search work, positioning EXAQC as evolving circuit structure within pipelines that use learned classical image features.
AI USAGE
- Generative AI assisted with unit tests, code review, and polishing the paper's writing.Source: AI USAGE · p. 10
A APPENDIX - RELATED WORK
- Prior hybrid image-classification approaches reduce image dimensionality before quantum processing, while EXAQC evolves circuit structure and tailors it to a learned classical encoder's features.Wang et al. (2022) use PCA or amplitude and angle encodings, while Liu et al. (2021) replace classical convolutional filters with PQCs; both use a single hand-designed circuit.Source: A APPENDIX - RELATED WORK · p. 14
- Quantum architecture search spans differentiable, predictor-based, hierarchical, and adaptive approaches, while evolutionary computation can modify discrete architecture and optimize continuous parameters.Source: A APPENDIX - RELATED WORK · p. 14
- Image-classification architecture-search methods differ in search strategy, preprocessing, class count, input representation, and circuit-resource constraints, limiting direct accuracy comparisons.The review also includes fixed or algorithm-specific quantum classifiers as performance comparisons, but notes that experimental-setting differences prevent direct accuracy comparisons.Source: A APPENDIX - RELATED WORK · p. 14
- The study distinguishes task-level scalability across image-classification problems from representation-level scalability in the features presented to the quantum circuit.It also evaluates circuit resources and whether evolved quantum components can replace larger classical components while retaining competitive performance.Source: A APPENDIX - RELATED WORK · p. 15
B.1 PARAMETER-EFFICIENCY ANALYSIS
The analysis gives a necessary-and-sufficient parameter budget for a hybrid replacement to use fewer trainable parameters than the affine transformation it replaces. It accounts for classical projection and readout layers as well as the evolved PQC.
B.1 PARAMETER-EFFICIENCY ANALYSIS
- The hybrid parameter count includes the input projection, evolved PQC, and output mapping, rather than counting only quantum-circuit parameters.The projection maps di dimensions to dq; the readout maps dr dimensions to do.Source: §B.1 · p. 15
- A hybrid replacement is parameter-efficient exactly when the evolved PQC’s trainable parameters are below BQ, the budget remaining after interface-layer costs.BQ = (di + 1)do - (di + 1)dq - (dr + 1)do.Source: §B.1 · pp. 15–16
- BQ must be positive for any parameter-efficient replacement to exist; if BQ ≤ 0, no nonnegative PQC parameter count can satisfy the condition.The condition follows because the PQC’s trainable-parameter count cannot be negative.Source: §B.1 · p. 16
- For fixed di, do, and dq, increasing the quantum readout dimension dr linearly reduces BQ, leaving less budget for the evolved PQC.A smaller readout representation therefore provides a larger quantum parameter budget.Source: §B.1 · p. 16
- Expectation-value readout provides at least as large a quantum parameter budget as full probability readout, with a strict advantage when no ≥ 2.The comparison is stated for the same number of measured output qubits.Source: §B.1 · p. 17
- When only single-parameter rotation gates and U3 gates are trainable, the circuit contributes m1 + 3m3 parameters and qualifies when this is below BQ.Each rotation gate contributes one trainable parameter and each U3 gate contributes three.Source: §B.1 · p. 18
- The counts cover trainable model parameters only: data-dependent encoding values and fixed gates are excluded, even though fixed gates affect circuit depth and execution cost.Encoding values count only if they are optimized model parameters.Source: §B.1 · p. 18
B.2 DATASETS
The section describes image benchmarks and the classical encoders and decoders that let EXAQC use compact quantum representations within a hybrid model.
B.2 DATASETS
- Each benchmark panel shows one example from each of ten classes; MNIST and Fashion-MNIST are 28 × 28 grayscale, while CIFAR-10 is 32 × 32 RGB.Source: Figure 4 · p. 18
B.3 ENCODER STRATEGIES
- A classical encoder maps images or feature vectors to the dimensionality needed by the quantum circuit, separating feature extraction from quantum-state preparation.Source: §B.3 · p. 19
- The identity encoder passes input features directly to the circuit and adds no trainable parameters, so input and output dimensions must match.Source: §B.3 · p. 19
- For larger inputs, the linear encoder learns a compact projection Wx + b, with image inputs flattened before the transformation.Source: §B.3 · p. 19
- The CNN encoder extracts spatial features through configurable convolutional blocks and adaptive pooling, then projects them to a compact circuit input.Source: §B.3 · p. 19
B.4 DECODER STRATEGIES
- The decoder maps quantum outputs to task outputs: clipped decoding selects outputs without added parameters, while linear decoding learns their mapping.Source: §B.4 · p. 20
B.5 OPERATOR ANALYSIS
EXAQC’s operators play complementary roles in evolving circuit complexity and structure, with their performance varying across datasets. The visualized MNIST and Fashion-MNIST architectures illustrate distinct compact hybrid designs.
B.5 OPERATOR ANALYSIS
- Circuit complexity rose rapidly early in evolution, then stabilized across all three datasets, with gate and parameter counts fluctuating rather than increasing monotonically.This pattern is consistent with EXAQC’s gate-adding and gate-removing operators.Source: §B.5 · p. 20, Figure 6 · p. 22
- On MNIST, disable-gate led global-best rate; reorder-gate led insertion on MNIST and global-best on Fashion-MNIST, while clone led all CIFAR-10 categories.Crossover operators were generally more disruptive, with n-ary crossover having the highest discard rate on all three datasets.Source: §B.5 · p. 21, Table 4 · p. 21
- Heterogeneous operators support solution preservation, complexity adjustment, structural refinement, and broader exploration; reorder-gate and qubit-swap effectively modify existing architectures.On CIFAR-10, clone’s lead across all three performance categories suggests preserving and propagating strong circuits is particularly valuable on the more complex task.Source: §B.5 · p. 21
B.6 CIRCUIT VISUALIZATION
- The MNIST example uses a two-layer MLP to reduce 784 pixels to six RY-encoded features, with a seven-gate circuit and 64 readout values mapped to 10 classes.Under computational-basis readout, only the controlled-RX and the IsingZZ gate acting on its target affect the output distribution.Source: §B.6 · p. 22, Figure 7 · p. 22
- The Fashion-MNIST example compresses 784 input pixels to five features for five-qubit RY encoding, then maps 32 readout values to 10 classes.Its evolved circuit combines parameterized two-qubit interactions with fixed gates.Source: §B.6 · p. 22, Figure 8 · p. 23