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Hybrid Quantum-Classical Convolutional Neural Networks
Junhua Liu, Kwan Hui Lim, Kristin L. Wood, Wei Huang, Chu Guo, He-Liang Huang
TL;DR
Large classical inputs are difficult to encode into current quantum computers, motivating a quantum-classical architecture that preserves CNN locality while using quantum feature maps. The paper introduces QCCNN and an automatic-differentiation framework, then reports near-100% Tetris accuracy and higher accuracy than matched classical CNNs in the described settings.
Problem
Encoding large real-world inputs into one qubit per input element can be impractical on current quantum computers, limiting quantum machine-learning applications.
Method
QCCNN applies parameterized quantum circuits and correlational measurements to local windows, integrates the resulting classical arrays with CNN layers, and supports automatic hybrid-loss gradients.
Results
QCCNN reaches almost 100% testing accuracy in the reported two-label and four-label Tetris cases and achieves higher accuracy than CNN under the compared settings.
Takeaways & Limitations
QCCNN provides a CNN-like hybrid architecture designed for near-term quantum devices, retaining locality and nonlinearity while requiring only window-sized qubit registers.
Takeaways & Limitations
For the same window size N, the quantum feature map requires O(Nd) gate operations versus O(N) classical floating-point operations, so QCCNN is not computationally advantageous in that comparison.
Abstract
from arXiv · showhide
Deep learning has been shown to be able to recognize data patterns better than humans in specific circumstances or contexts. In parallel, quantum computing has demonstrated to be able to output complex wave functions with a few number of gate operations, which could generate distributions that are hard for a classical computer to produce. Here we propose a hybrid quantum-classical convolutional neural network (QCCNN), inspired by convolutional neural networks (CNNs) but adapted to quantum computing to enhance the feature mapping process. QCCNN is friendly to currently noisy intermediate-scale quantum computers, in terms of both number of qubits as well as circuit's depths, while retaining important features of classical CNN, such as nonlinearity and scalability. We also present a framework to automatically compute the gradients of hybrid quantum-classical loss functions which could be directly applied to other hybrid quantum-classical algorithms. We demonstrate the potential of this architecture by applying it to a Tetris dataset, and show that QCCNN can accomplish classification tasks with learning accuracy surpassing that of classical CNN.
I. INTRODUCTION
Quantum machine learning seeks to exploit quantum computing for machine-learning tasks, but encoding large classical inputs can exceed current hardware limits. The proposed QCCNN adapts CNN locality and scalability to quantum feature mapping while targeting near-term devices.
- Motivation: Quantum machine learning uses parameterized quantum circuits as a promising route for machine-learning algorithms suited to noisy intermediate-scale quantum devices.These circuits are described as naturally robust to noise and requiring shallow circuits.
- Challenge: Encoding an input array of size L into individual qubits produces an L-qubit state, making large real-world inputs impractical for current quantum computers.The stated hardware context includes systems with fewer than 100 qubits.
- Challenge: Classical fully connected layers also become inefficient for large inputs because their dense matrices require many parameters.CNNs address this by connecting outputs only to small input windows, reducing parameter counts.
- Contribution: QCCNN replaces the convolutional feature map with a parametric quantum circuit and uses correlational measurements as its outputs.The resulting quantum convolutional layer requires qubits only according to the feature-map window size rather than the full input size.
- Contribution: The proposed framework retains classical CNN features while supporting multilayer structures and automatic gradients for hybrid quantum-classical loss functions.The paper applies the architecture to Tetris classification and reports higher accuracy than classical CNNs.
II. HYBRID QUANTUM-CLASSICAL CONVOLUTIONAL NEURAL NETWORK ARCHITECTURE
QCCNN applies quantum filters locally to small input windows, measures scalar feature values, and then continues with classical CNN operations. Its design uses shallow, reusable circuits and can also process quantum inputs directly.
- Classical CNN structure: A CNN alternates convolutional and pooling layers before flattening and fully connected classification, with convolutional filters mapping local windows to output neurons.Pooling reduces dimensionality and can help prevent overfitting.
- Quantum convolutional layer: QCCNN maps each m×n input window to an N = mn-qubit state, evolves it with a parameterized circuit, and uses an observable expectation value as the feature-map output.The quantum filter replaces the classical convolutional filter while preserving local processing.
- Quantum convolutional layer: The quantum convolutional layer is nonlinear, so it does not require an additional explicit activation such as ReLU.Its output is a classical array that can feed pooling, flattening, and fully connected layers.
- NISQ compatibility: Only the window-sized register is needed, and those qubits can be reused for subsequent windows, making the layer suitable for NISQ scenarios without qRAM.The measurement may capture cross-correlation within each window.
- Circuit design: The circuit interlaces single-qubit Ry layers with two-qubit CNOT layers, with a polynomial gate count L ∼ poly(N) and parameters determined by window size and circuit depth.Gradient-based optimization methods can train the resulting hybrid network.
- Quantum-input extension: For quantum inputs on an n×n lattice, the quantum filter can operate directly on each 2×2 sub-lattice while leaving the rest of the architecture unchanged.The paper identifies variational ground-state ansätze and quantum-state classification as example applications.
III. HYBRID AUTO-DIFFERENTIATION FRAMEWORK
The paper embeds quantum feature maps into automatic differentiation so hybrid loss gradients can be computed correctly through classical and quantum components. Training then uses standard gradient-based neural-network optimization.
- Gradient framework: The framework computes gradients of hybrid quantum-classical loss functions whose quantum subfunctions have the paper’s expectation-value form.When inputs require derivatives, their values are represented through an added single-qubit Ry layer.
- Correct differentiation: A naive finite-difference-style composition of shifted loss evaluations is generally incorrect when the outer classical function is nontrivial.The paper contrasts this with defining an adjoint function for the quantum feature map.
- Correct differentiation: The adjoint function combines the outer-function gradient with the current quantum-function gradient and passes the result backward through the loss computation.This makes the quantum operation compatible with standard automatic-differentiation backpropagation.
- Implementation: Once adjoint functions are defined for the elementary loss components, the hybrid loss gradient can be derived automatically.In this work, the full process is simulated on a classical computer.
- Optimization: The trained hybrid networks can use stochastic, batch, or minibatch gradient descent to optimize their parameters and then predict outputs.These procedures mirror regular neural-network training.
IV. NUMERICAL RESULTS AND DISCUSSIONS
The QCCNN is evaluated against one- and two-layer CNNs on two- and four-class Tetris image tasks. It achieves near-perfect accuracy, lower loss, faster convergence in the deeper structure, resilience to simulated noise, and higher accuracy than CNNs, although its feature-map gate complexity is higher.
- Dataset and benchmarks: 800 3 × 3 grayscale images were split into 80% training and 20% testing sets across four Tetris-brick classes, with a separate two-class S,T dataset.The four classes were S, L, O, and T; CNNs with one or two convolutional layers served as baselines.
- Classification results: QCCNN reached almost 100% accuracy and much lower loss than its classical counterpart in both two- and four-label tasks.The four-label task required more iterations to converge than the two-label task.
- Classification results: Two-layer QCCNN converged faster than the single-layer structure, especially for four labels.This pattern indicates better performance for the more complex classification setting with the deeper QCCNN structure.
- Circuit-depth study: A depth-1 quantum feature map already exceeded CNN accuracy with the same parameter count, while depths 2 and 4 remained slightly better than a modified CNN.The modified CNN enlarged its first-layer window to 3 × 3 to increase its parameter space.
- Noise resilience: Training accuracy 1 was reached even with simulated decoherence and measurement errors in the noisy one-layer QCCNN.The noisy-circuit study included T1, T2, and measurement errors.
- Computational considerations: For window size N and circuit depth d, the quantum feature map requires O(Nd) gate operations versus O(N) classical floating-point arithmetic.The paper therefore states that QCCNN is not advantageous from computational efficiency alone under this comparison.
V. CONCLUSION
The paper presents QCCNN as a hybrid architecture for real-world problems on current quantum computers, retaining key CNN properties while supporting broader hybrid applications. It also notes independently developed related approaches using qRAM and non-parametric random quantum circuits.
- QCCNN is designed for real-world problems on current quantum computers while addressing major quantum machine-learning input and output challenges.
- The architecture retains CNN nonlinearity, convolutional locality, and extensibility to deep structures for near-term quantum devices.
- QCCNN provides a framework for hybrid quantum-classical applications including discriminative and generative models.
- Its parametric quantum feature map can explore neighboring-data correlations in an exponentially large linear space.
- The authors identify independently developed related work using qRAM and non-parametric random quantum circuits for feature mapping.